Research ArticleWavelet Transform-Based Damage Identification inBladed Disks and Rotating Blades

P Rajendran12 N Jamia3 S El-Borgi 1 and M I Friswell3

1Mechanical Engineering Program Texas AampM University at Qatar Engineering Building PO Box 23874 Education CityDoha Qatar2School of Mechanical Engineering SASTRA Deemed University anjavur 613401 Tamil Nadu India3Swansea University Bay Campus Fabian Way Swansea SA18EN UK

Correspondence should be addressed to S El-Borgi samiel_borgiqatartamuedu

Received 8 June 2018 Revised 31 August 2018 Accepted 19 September 2018 Published 17 October 2018

Academic Editor Marcello Vanali

Copyright copy 2018 P Rajendran et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Blade vibration and blade clearance are effective diagnostic features for the identification of blade damage in rotating machinesBlade tip-timing (BTT) is a noncontact method that is often used to monitor the vibration and clearance of blades in a rotatingmachinery Standard signal processing of BTTmeasurements give one blade response sample per revolution of the machine whichis often insufficient for the diagnosis of damage -is paper uses the raw data signals from the sensors directly and employsa wavelet energy-based mistuning index (WEBMI) to predict the presence and locations of damage in rotating blades -eLipschitz exponent is derived from the wavelet packet coefficients and used to estimate the severity of the damage In this studyexperiments were conducted to obtain BTTmeasurements on rotating blades at 100 rpm using three different sensors an activeeddy current sensor a passive eddy current sensor and an optical sensor In addition hammer excitation experiments wereconducted for various added mass (damage) cases to compute the damage severity for a bladed disk To simulate the damageexperimentally in the bladed disk and rotating blades masses were added to the blades to alter their dynamics and mimic thedamage -e results indicate that the WEBMI can detect the presence and location of damage in rotating blades using mea-surements from common BTT sensors To check the robustness of the proposed damage severity index the experimental resultswere compared with numerical simulation for the bladed disk and showed good agreement

1 Introduction

High cycle fatigue (HCF) causes damage to the blades duringthe operation of a turbomachine and if unnoticed may leadto catastrophic failures of the whole machine As a resultthere is an increase in maintenance cost and reduction inlead time -erefore an early assessment of the damage inrotating blades for condition-based maintenance improvesthe efficiency and increases the life of the turbomachineOver the past few decades many researchers have proposednoncontact measurement and data processing techniques tomonitor the vibration and clearance of blades in rotatingmachines due to the nonintrusive and easy installation ofsensors which allows prompt identification of potentialdamage-e blade tip-timing (BTT)method is a well-knownnoncontact method which measures the blade vibration and

blade tip-clearance during the engine operation and detectsthe different types of blade failures [1]-is concept relies ona number of probes fixed to the casing of the machine todetect the blade tip as it passes in front of the probes -eeffect of mistuned blades on the synchronous vibration ofrotating blades has been identified by BTT data analysis [2]-e blade vibration was monitored and blade cracks weredetected during machine operation [3] -e abnormalitiesfound in the vibration characteristics of the BTT datameasured during engine tests were used to identify bladedamage [4] BTT measurements were employed for iden-tifying the dynamic behavior and detecting a small mis-tuning pattern of rotating bladed disks [5] Along with bladevibration data the blade tip-clearance (BTC) measurementwhich is the gap between the blade tip and the casing ofa rotating machine is an additional diagnostic parameter

HindawiShock and VibrationVolume 2018 Article ID 3027980 16 pageshttpsdoiorg10115520183027980

that has been used to identify damage -ese measurementscan also be obtained by the blade tip sensors

Several blade vibration monitoring technologies havebeen summarized which distinguish between the effect ofthe cracks and any other source of damage based on theblade length measurements [1] -e tip timing data ofa rotor blade were measured in various engine trials toevaluate the ability of these sensors to detect dynamicforeign object damage events [6] A contactless diagnosticmethod was described to identify damage in steam turbineblades based on the axial blade lengthening parameter [7]However it is challenging to predict the anomalies in therotating blades using only blade lengthening and ampli-tude parameters Hence data-driven detection techniqueswere employed to analyze BTC data acquired from therotor disk to test the feasibility of the damage detectionmethodology [8]

In addition to the BTC data the modal parameters ofblades were utilized to detect damage in the rotatingblades -e experimental studies were performed on theassembled test rig of three spinning test blades and thelocation and length of a crack were estimated based on themodal parameters [9] -e blade natural frequencies andthe blade tip position were obtained from the BTTmethodto detect the blade crack in an aero engine [10] Chatterjeeand Kotambkar [11] investigated the mistuning induced bylacing wire damage in blade packets using modal char-acteristics Xu et al [12] studied the effect of cracks on thevibration characteristics of mistuned rotating blades basedon natural frequency vibration amplitude and vibrationlocalization parameters Nevertheless the modal param-eters are less sensitive to the low damage levels and thenatural frequencies and mode shapes are difficult tomeasure due to the subsampling frequency of the BTTsignals which depends on the rotating speed -us thesignal processing of BTT measurements is necessary toreconstruct the signal to solve the aliasing effect beforeapplying into damage detection algorithms Salhi et al [13]proposed a BTTsignal reconstruction method based on theShannon theorem However in practice BTT signals arenot really band limited and so aliasing effects still exist inthe reconstructed signals

-e low sample rate of BTT signals occurs because onlyone blade response sample per revolution is extracted fromthe processing of the raw sensor signal A sparse repre-sentation (SR) model was built for multimode blade vi-bration monitoring [14 15] However the sensor output isoften measured at a high sample rate and will containa combination of the blade vibration and the rotation of themachine Extracting suitable features from these signals todetect damage requires advanced signal processing toolssuch as the wavelet transform

-e wavelet packet transform (WPT) is a rich signal-processing tool which performs a complete decompositionincluding both low-frequency (approximate) and high-frequency (detailed) components -e WPT can also han-dle the subsampled signals and overcome the aliasing effectsin the reconstructed signals Zhongsheng [16] proposeda nonaliasing reconstruction algorithm of subsampled blade

tip-timing signals based on the Shannon theorem andWPT-eWPTwas applied to subsampled rotational mode shapesto detect the location and size of added mass in beam andplate structures by numerical simulation [17 18] Jamia et al[19] employed the WPT analysis to identify the presencelocation and severity of mistuning in a bladed disk byconducting a series of impact hammer tests -ey mainlyaddressed the presence and location of damage but they didnot justify the relationship between the damage severity andwavelet coefficients

For damage severity estimation Montanari et al [20]introduced continuous wavelet transform- (CWT-) basedcrack index to detect and estimate the crack location andsize of different beams using first three mode shapes Honget al [21] introduced the Lipschitz exponent which can beused as a damage extent indicator in a beam using theCWT Douka et al [22] and Loutridis et al [23] introducedan intensity factor that estimates the size of the crack fromthe coefficients of the CWT -e Lipschitz (Hoelder) ex-ponent (α) and intensity factor (K) were derived from theCWT coefficients to quantify the relationship between thedamage and the change in the wavelet coefficients derivedfrom modal and elemental strain energy data [24] Chenet al [25] employed a Lipschitz exponent to quantify thesignal singularity of the acceleration responses of a five-storey building model using the CWT analysis Forpractical applications a fast numerical algorithm is rec-ommended in order to obtain the discrete data points oneshould sample the continuous wavelet algorithm ona dyadic grid because it was proved that the wavelettransform on a dyadic grid is complete and stable [26]Błaszczuk and Pozorski [27] discussed the application ofthe discrete wavelet transform (DWT) and the Lipschitzexponent to estimate the function differentiability of thebeam structural response

In summary based on the above literature review thefollowing points can be concluded (a) blade vibration andblade tip-clearance are effective diagnostic features fordetecting blade damage in a rotating machine (b) directBTT signals have difficulty in interpreting damage in ro-tating blades (c) modal parameters are insensitive toidentify mistuning or damage in rotating blades (d) thesignal processing of BTTmeasurements is required beforeapplying the WPT analysis (e) the WPT analysis is a richsignal-processing tool which can even handle BTT-reconstructed signals to detect anomalous features and(f ) the Lipschitz exponent has been employed to quantifydamage In light of this the novelty of this study is to applythe raw signals from BTT sensors into a WPT analysis todetect the presence and location of damage in rotatingblades and estimate the Lipschitz exponents from thewavelet packet coefficients to quantify the severity ofdamage in the bladed disk and rotating blades An initialstudy is also reported that demonstrates the effectivenessof the Lipschitz exponent to quantify damage in stationarybladed disks using impact tests with the response mea-sured by accelerometers

-e paper is organized as follows Section 2 describes theformulation of the proposed WEBMI and the damage

2 Shock and Vibration

severity index -e performance of impact hammer tests toestimate the damage severity of bladed disks is brieflyexplained in Section 3 Details of the BTT experiments andmeasurement results are presented and discussed in Section4 Finally a summary and concluding remarks of this studyare provided in Section 5

2 Wavelet Energy-Based Mistuning Index

In this study the wavelet energy-based mistuning index(WEBMI) is employed to detect the presence and location ofdamage in the rotating blades using measurements from theBTT sensors For the sake of understanding the WEBMI isbriefly discussed along with the threshold based on thestatistical confidence -e description of the Lipschitz ex-ponent is then given followed by the definition of theproposed severity index

21 Introduction of the WPT -e wavelet packet ψijk is

a function where i j and k are the frequency modulationscale (decomposition level) and translation parametersrespectively -us

ψijk 2j2ψi 2j

tminus k1113872 1113873 (1)

where ψi indicates the frequency modulation of the waveletfunction After the jth level of decomposition the originalsignal f(t) can be expressed as

f(t) 2j1113944i1

fij(t) (2)

-e wavelet packet component signal fij(t) can be

represented by a linear combination of the wavelet packetfunctions ψi

jk(t) as

fij(t) Ns 1113944

k0C

ijk(t)ψi

jk(t) (3)

where Ns denotes the number of samples for four revolu-tions and the wavelet packet coefficient Ci

jk can be obtainedfrom

Cijk 1113946

T

0f(t)ψi

jk(t)dt

Cijk A

ijk if i 1 3 5

Cijk D

ijk if i 2 4 6

(4)

where Aijk and Di

jk are the approximate and detail co-efficients respectively -e wavelet packet functions areassumed to be orthogonal that is

1113946 T

0ψr

jk(t)ψq

jk(t)dt 0 if rne q (5)

-us the wavelet component energy at the jth level forthe ith modal component is defined as the energy stored inthe component signal fi

j(t) and is given by

Eij 1113946

T

0f

ij(t)

2dt (6)

-e component signal fij(t) is extracted from the jth

level but is translated in the time domain such that 0lt tltT-e estimated component energy Ei

j is the energy stored indifferent frequency bands at the jth scale -e rate of changeof the signal wavelet component energy ΔE at the jth leveland the ith component can be expressed as

ΔEij

Eij1113872 1113873

dminus Ei

j1113872 1113873u

11138681113868111386811138681113868

11138681113868111386811138681113868

Eij1113872 1113873

u

(7)

where the subscripts d and u denote the damaged andundamaged cases respectively -e rate of change in energyΔE defines the WEBMI

22 reshold To increase the robustness of prediction ofthe damage location a threshold is established using thestatistical properties and the one-sided confidence limit ofthe damage indices from successive measurements -emean and standard deviation of the estimated WEBMIvalues are given by μW and σW respectively -us the one-sided upper confidence limit for the WEBMI is given by thefollowing equation [28]

ULW μW + ZβσW

Nradic1113888 1113889 (8)

where N is the total number of WEBMI values that can beobtained after completing the wavelet packet de-composition at a given level Zβ is the value of the standardnormal distribution with zero mean and unit variance thatgives a cumulative probability of 100 (1minus β) -is upperlimit can be defined as a threshold value and any indexthat exceeds the threshold can indicate the exact locationof damage -e brief damage detection methodology usingthe WPT analysis is provided by the flowchart shown inFigure 1

23e Lipschitz Exponent A function f(t) has a Lipschitzexponent αge 0 at the point t v if there exists a constant D

and a polynomial pv(t) of degree M (where M is the largestinteger satisfying Mle α) such that [21]

f(t) pv(t) + εv(t) (9)

where

εv(t)1113868111386811138681113868

1113868111386811138681113868leD|tminus v|α (10)

-e Lipschitz exponent α measures the differentiabilityof the functionf(t) the function is not differentiable at t v

if 0lt αlt 1 All of the discontinuities in the function f(t) atthe point t v are contained in the function εv(t)

When the Lipschitz exponent is applied to the wavelettransform then determining the moments of the motherwavelet that vanish is important A function ψ(t) is said tohave n vanishing moments if it satisfies the followingcondition

1113946+infin

minusinfintkψ(t)dt 0 for 0le kle n (11)

Shock and Vibration 3

Suppose that the number of vanishing moments of thewavelet function is greater than the Lipschitz exponentie ngt α -en the wavelet transform retains only thesingular part of the function f(t) because

Wpv(t) 0 (12)

and hence

Wf(t) Wεv(t) (13)

where W defines the wavelet transform-e maximum wavelet packet coefficients reduce as the

level of decomposition j decreases For isolated singularitiesthe wavelet maximum is bounded by an exponential decay lawwith an exponent equal to the Lipschitz exponent α Błaszczukand Pozorski [27] proposed an inequality in the form

|Wf(t)|leD times 2minusj(α+(12)) (14)

or equivalently

log2|Wf(t)|leminusj α +12

1113874 1113875 + log2 D (15)

-us a plot of |Wf(t)| against j gives a straight line withslope minus(α + 12) and this slope can be estimated from twovalues of j

24 e Damage Index -e key difference in the currentanalysis is to replace the wavelet packet coefficient Wf(t)by the absolute difference between the WEBMI and theupper control limit |WEBMI minusUL| -e energy at any levelof decomposition depends directly on the wavelet co-efficients and thus if damage causes a discontinuity in thewavelet transform then it will also provide a discontinuity intheWEBMI-e estimate of the Lipschitz exponent in termsof the WEBMI is given by

α minuslog2 (WEBMI minusUL)jj2

11138681113868111386811138681113868

11138681113868111386811138681113868 + log2 (WEBMI minusUL)jj1

11138681113868111386811138681113868

11138681113868111386811138681113868

j2 minus j1

minus12

(16)

where j1 and j2 are the decomposition levels chosen for theestimation

3 A Bladed Disk Example

-is study is an extension of our previous work thatidentified mistuning in a bladed disk using the WPTmethodology [19] To quantify the damage the proposeddamage severity index is now demonstrated on a bladed diskexample-e simulation consists of a disk with 20 blades andtwo degrees of freedom per blade as shown in Figure 2where the damage is simulated by a stiffness reduction of oneblade -e experimental example consists of a disk with 12blades where the ldquodamagerdquo is implemented by adding massto one of the blades as shown in Figure 3 -e equivalence ofthe damage in the simulation and experiment is then de-termined by considering the change in the first naturalfrequency of the blade

31 Numerical Simulation -e numerical simulation wasperformed on a reduced-order two degrees of freedom perblade model of the bladed disk developed by Salhi et al [29]and used by Jamia et al [19] to demonstrate theWEBMI-ebladed disk was composed of 20 blades Figure 2 showsa schematic of the two DOFmodels where only three sectorsof the bladed disk are shown as a mass-spring system Animpulse was applied to one blade and the correspondingtime response was obtained from each blade tip -e outputonly response signal was used in the WPTanalysis to obtainthe WEBMI -e Lipschitz exponent was derived from theWPT analysis to estimate the damage severity in the bladeddisk

Raw BTTimpulse time responses from undamaged anddamaged cases

Signal processing of raw BTT signals

Reconstructed BTTimpulse time signal of each bladesignal decomposed into different frequency bandwidth

Compute the wavelet packet coefficients (WPC) atdesired level

Entropy methodif

Aj1 lt Dj

2No

Optimal lsquojthrsquo level of decomposition by entropy method

Estimate the component energy at lsquojthrsquo level using WPC

Choose the first component energy for damage detection

Estimate the threshold value for WEBMI usingone-sided upper confidence limit UL

ULW = μW + ZβσW

N

Compute the WEBMI for all blades

∆Ej1 =

Ej1

d Ej1

u

Ej1

u

ndash

Detect the presence and location of damage that exceedsthreshold value WEBMI ndashULα

WEBMI

Estimate the damage severity by Lipschitz exponent lsquoαrsquoindex

Figure 1 Damage detection methodology

4 Shock and Vibration

-e model used has two DOFs per sector representingthe blade and the disk sector Each disk sector is coupledwith the neighboring sectors by the stiffness kc -e stiffnessof an individual blade is represented by ka It is assumed thateach blade in the assembly has one significant mode which istypically the first bending mode No centrifugal stiffening orrotational dynamics effects are considered explicitly in thismodel although centrifugal stiffening could be included byincreasing the blade stiffness ka A proportional dampingmodel is assumed A free vibration response of each bladeand disk sector is generated

-e equation of motion of the bladed disk model in freevibration is defined as

Meuroq(t) + C _q(t) + Kq(t) 0 (17)

where q(t) is the vector of displacements correspondingto (2 times 20) DOF -e displacement of the n-th sector isgiven by

qn(t)

qn1(t)

qn2(t)

1113890 1113891 (18)

where the subscripts 1 and 2 represent the blade and the disksector respectively

M C andK represent the structural mass damping andstiffness matrices of the dimension N times N withN 2nb 40 where nb is the number of blades -e massmatrix is given by

M

Ms 0 0 0

0 Ms 0 0

0 0 Ms 0

0 0 Ms

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with Ms ma 0

0 md

1113890 1113891

(19)

where ma and md are the modal masses of the blade and thecorresponding disk sector respectively -e stiffness matrixK is given by

K

Ka Kb 0 Kb

Kb Ka Kb 00 Kb Ka

Kb

Kb 0 Ka

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with Ka

ka minuska

minuska ka + kd + 2kc

1113890 1113891

and Kb

0 00 minuskc

1113890 1113891

(20)

-e proportional damping matrix is given by

C αM + βK (21)

where the proportionality factors α and β are 10823 and76536 times 10minus5 respectively -e damping ratios for all

Blade

Sector n ndash 1 Sector n Sector n + 1

Disk

ma

md

kcka

kd

ξ

Figure 2 Two degrees of freedom per sector model

Impacthammer

DAQ

(a)

Acclerometers

Magnet

(b)

Figure 3 (a) Impact hammer test setup (b) blade with added magnet mass

Shock and Vibration 5

modes are approximately equal to 001 A bladed disk issimulated with the parameters given in Table 1

To examine the relationship between the Lipschitz ex-ponent α and the damage severity in the bladed diska numerical analysis was performed for different stiffnessreductions that varied from 1 to 9 In this study thewavelet function db6 was chosen which has three vanishingmoments and the first wavelet packet energy was consideredin the damage identification methodology as indicated in[19] -en the Lipschitz exponent α was computed with theinput of two different levels (j 2 and j 6) of coefficientsusing Equation (16) -e minimum level of j 2 was re-quired to detect the damage and j 6 was chosen to satisfythe vanishing moments condition for the db6 waveletHigher-order wavelet functions were investigated but in thiscase the db6 wavelet is optimal to estimate the singularity ofthe function

Figure 4 shows that the Lipschitz exponent α de-creases exponentially as the stiffness reduction increaseswhich means the differentiability of the function de-creases as the damage severity increases -e Lipschitzexponent α has an ability to predict the differentiabil-ity of the function for a stiffness change as small as 1-e Lipschitz exponent obeys the vanishing momentscondition which means the chosen ldquodb6rdquo wavelet func-tion was suitable for this study -e minimum stiffnesschanges due to damage were 1 in this case smallerstiffness changes will generally require higher orderwavelet functions

32 ExperimentalValidation To check the robustness of theproposed damage severity index an impact hammer test wasconducted at Swansea University To perform this experi-ment a 4-channel data acquisition (DAQ) system threeaccelerometers an impact hammer and data acquisitionsoftware were used (see Figure 3(a)) and the experimentalprocedure was briefly explained in [19] In this study theadded mass was varied from 11 g to 99 g with an incrementof 11 g on the middle blade to estimate the added mass(damage) severity as shown in Figure 3(b) -e mass wasadded using rectangular magnets of mass 33 g shown inFigure 3(b) and circular magnets of mass 11 g mounted onthe beam at centre position approximately 15mm from theblade root Table 2 shows the combination and location ofthe magnets to realise the different mass values -e ex-perimental Lipschitz exponent α was estimated and isshown in Figure 4 as a function of the mass added -eresults clearly show that the Lipschitz exponent reduces withthe mass added but there are definite steps in the exponentIn fact the reduction in the Lipschitz exponent appears to beless than expected when a rectangular magnet is added to thebeam -e magnets add some stiffness to the beam in ad-dition to the mass and the mass and stiffness have oppositeeffects on the natural frequencies However the change innatural frequency due to added mass shown in Figure 5obtained from the experimental response data shows thatthe natural frequency changes smoothly with the massadded

1 2 3 4 5 6 7 8 9Stiffness reduction ()

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

Numerical

10 20 30 40 50 60 70 80 90 100Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Exp data

Figure 4 -e change in the Lipschitz exponent due to damageseverity

Table 1 -e properties of the bladed diskma 1 kgmd 1 kgka 10 kNmkd 20 kNmkc 02 ka kNmnb 20

Table 2 -e position of the masses added to the blade for thedifferent damage cases in the bladed disk experiment

Mass added Rectangular magnets (33 g) Round magnets (11 g)11 g mdash Top22 g mdash Top + bottom33 g Top mdash44 g Top Top55 g Top Top times 266 g Top + bottom mdash77 g Top + bottom Top88 g Top + bottom Top + bottom99 g Top times 3 mdash

0 20 40 60 80 100Added mass (g)

ndash08

ndash06

ndash04

ndash02

0

Nat

ural

freq

uenc

y ch

ange

()

Figure 5 -e change in the experimental natural frequency due tomass added

6 Shock and Vibration

33 Comparing Simulated and Experimental Results Tocompare the simulated and experimental results a re-lationship must be found between the stiffness reduction inthe simulation and the added mass in the experiment -isrelationship was determined by equating the change in thenatural frequency due to ldquodamagerdquo In the simulation thecomputed change in the first natural frequency for stiffnessreduction of 5 was 03267 whereas the change in the firstexperimental natural frequency due to an added mass of 55 gwas about 036-us the numerical first natural frequencychange due to a 5 stiffness reduction was close to theexperimental first natural frequency change due to the addedmass of 55 g A finite element (FE) analysis of the blade wasalso performed to give an alternative comparison Each bladein the disk is considered as a cantilever beam with di-mensions 100 times 31 times 4mm Youngrsquos modulus was de-termined as 166GPa by model updating to match with theexperimental first natural frequency for the undamaged casefor a mass density of 7870 kgm3 -e beam was divided into20 elements to achieve an accurate estimate of the firstnatural frequency and the damage (mass) was introducedfrom the second to fourth element of the beam to corre-spond with the location of the addedmass in the experiment-e added mass of 55 g was simulated in the FE model andthe change in the first natural frequency was about 03818which is approximately equal to the experimental change inthe first natural frequency -us in Figure 4 a linear re-lationship between added mass and stiffness reduction isbased on the equivalence of a 5 stiffness reduction and anadded mass of 55 g Figure 4 then shows a reasonableagreement between the experimental results and the nu-merical results

4 Experimental Validation for a RotatingBladed Disk

41 e Bladed Disk Test Rig A test rig was designed andmanufactured at Swansea University in order to generateBTT measurements using different types of sensors andvalidate the proposed technique -e sensors were selectedto be typical of those used to obtain BTT measurementsie an active eddy current sensor (AECS) a passive eddycurrent sensor (PECS) and an optical sensor -e test rig iscomposed of a bladed disk with 12 blades surrounded bya cylindrical casing at the distance δ (the gap between theblade tip and the sensor) -e bladed disk is clamped to theend of a rotating shaft supported by two ball bearings fittedin two split plummer block housings -e shaft is driven bya servo motor at 100 rpm -e manufactured test rig detailsare shown in Figure 6

-e ldquodamagerdquo is induced by adding mass to one of theblades -e sensors were mounted to the casing to detectthe blade tip displacement as it passes in front of theprobes as shown in Figure 7(a) -e sensor outputs weremeasured by a 4-channel Data Physics DAQ system fora period of 32 s with a sampling rate of 10240Hz -edamage was simulated by the added mass realised asmagnets are placed 15mm from the root of the blade asshown in Figure 7(b) In this study the blades were run at

100 rpm -ere was no explicit excitation of the blades inthe experiments although the resolution of the encoderused for the speed control means that the bending vi-bration of the blades will be excited via the torsional vi-bration of the shaft -is may be demonstrated byestimating the speed of the machine based on the time ofarrival of a particular blade a nonconstant speed will arisefrom a combination of the shaft speed variation and theblade vibration Figure 8 shows a typical example of es-timated speed and shows a small variation of 003 whichprovides sufficient excitation for the WEBMI methodDifferent test cases were performed where the mass addedwas changed ie (i) a single added mass to blade 8 (ii)multiple masses added to blades 4 and 8 and (iii) a singlemass added to blade 8 that varied from 11 g to 99 g thedescription of the added masses and their position for thedifferent damage cases is given in Table 2

42 Signal Processing of Measurements from the BTT Sensors-e raw signal was obtained from the AECS for a speed of100 rpm as shown in Figure 9 for illustration purposes -eraw signal cannot be directly used in the WPTmethodologysince the response from individual blades needs to beextracted -e WPT methodology may then be applied toeach blade response One of the major advantages of theproposed approach is that a single noncontact sensormounted on the stator is sufficient to predict the damagelocation and severity for all of the blades-e steps to extractindividual blade response are as follows

(i) Initially the measurements are obtained for 32 s asshown in Figure 9

(ii) To identify the reference blade a trial was conductedby removing a blade from the bladed disk assembly-en the signal was obtained with 11 peaks and inthis case it is clear which signals correspond to thereference blade and the damaged (added mass)blade from the removed blade signal

(iii) -e reference blade (blade 1) is defined as the bladewith the highest amplitude peak and subsequentpeaks were ordered sequentially as the responsefrom the other blades (up to blade 12) for a com-plete revolution For illustration four completerevolutions are considered here and the remaining

Figure 6 -e manufactured test rig

Shock and Vibration 7

samples were discarded More revolutions can beused if required

(iv) Individual blade responses can be extracted bychoosing a fixed sample time that fully containsa single blade response (both before and after thepeak) but is less that TN where T represents oneperiod of rotation and N is the number of blades

(v) Given knowledge of the number of blades the re-sponses from all of the blades can be allocated toindividual blades and merged over multiple revo-lutions as shown in Figure 10 for blade 1

After processing the signal each blade BTTsignal may beapplied into the WPTmethodology to detect the damage inthe rotating blades Brief details about the WPT method-ology and the formulation of the wavelet energy basedmistuning index (WEBMI) were discussed in Section 2

43 SingleAddedMass Locations -e sampling frequency ofblade response measures from the standard processing of

BTTsignals completely depends on the rotating speed of themachine since there is only one measurement for each bladepassing However this study has considered the sensoroutput directly at a constant sample rate of 10240Hz -edamage identification study was conducted for a speed of100 rpm and the addedmass of 99 g was located at a positionof 15mm from the root of blade 8 -e signals from the BTTsensors of all blades for the undamaged and damaged casesfrom the AECS are shown in Figure 11 -e sample time foreach blade was based on 500 samples (250 each side of thepeak) and the reconstructed signals for blade 8 for theundamaged and the damaged cases are shown in Figure 12Comparing the damaged signal with the undamaged signalthere are small shifts observed in the responses of blade 8 dueto the added mass at blade 8 However the interpretation ofthe shift in the signal alone cannot provide a robust damagefeature for the rotating blades -erefore the signal for eachblade was subjected to the WPTmethod which decomposedthe signal into different frequency bandwidth signals todetect the damage effectively In this study the wavelet

AECSPECS

Optical sensor

(a)

Magnet added mass

(b)

Figure 7 (a) BTT experimental test rig (b) blade with magnet added mass

0 2 4 6 8 10 12 14 16 18 20Number of cycles

100015

10002

100025

10003

100035

10004

100045

10005

100055

10006

Spee

d of

revo

lutio

n (R

PM)

Figure 8 Speed variation

0 05 1 15 2 25 3Time (secs)

0

05

1

15

2

25

3

35Bl

ade r

espo

nse (

V)

Figure 9 A raw BTT signal from the AECS at a speed of 100 rpm

8 Shock and Vibration

function ldquodb6rdquo with three vanishing moments was chosenwhich satisfied the vanishing moments condition for esti-mating the damage location and severity in the rotatingblades

In order to select the optimal decomposition level theShannon entropy method was employed as briefly dis-cussed in [19] Based on this method the entropy of bothapproximate and detailed coefficients was estimated ateach level At level 2 the entropy was 000933 which wasless than the entropy of the detailed coefficients which was003069 hence the decomposition level 2 was selected asan optimal level to detect the changes of 99 g added mass inthe rotating blade For the case of BTT signals the vicinityof minute changes can be observed from the approximatecomponent energy as shown in Figure 13(a) However itis difficult to predict the damage at the exact location-us the threshold limit with a high confidence intervalwas applied to the WEBMI and the resulting WEBMI-UL

indicates a substantial peak at the exact location of blade 8as shown in Figure 13(b)

In order to check the effectiveness of the other sensorsthe PECS and optical sensor were employed simulta-neously in addition to the AECS to monitor the blade tipdisplacement as shown in Figure 7(a) -e reconstructedBTT signals of the undamaged and the damaged blade 8from the PECS and the optical sensors are shown in Fig-ures 14 and 15 -ere is hardly any change found in theundamaged BTT signal of blade 8 (see Figure 14(a)) fromthe PECS whereas for the damaged signal of blade 8Figure 14(b) shows subtle changes in the time response dueto the added mass placed on blade 8 In fact the amplitudesof the blade response measured from the PECS are very lowcompared to the AECS and the optical sensor Howeverthis will not affect the damage identification process Onthe other hand the optical sensor BTT response of un-damaged blade 8 (see Figure 15(a)) shows no changes but

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(a)

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(b)

Figure 11 AECS reconstructed BTT signals of all blades for a speed of 100 rpm (a) Undamaged and (b) damaged cases

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

35

Blad

e res

pons

e (V

)

Figure 10 Reconstructed blade 1 BTT signal up to four completed revolutions

Shock and Vibration 9

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

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severity index -e performance of impact hammer tests toestimate the damage severity of bladed disks is brieflyexplained in Section 3 Details of the BTT experiments andmeasurement results are presented and discussed in Section4 Finally a summary and concluding remarks of this studyare provided in Section 5

2 Wavelet Energy-Based Mistuning Index

In this study the wavelet energy-based mistuning index(WEBMI) is employed to detect the presence and location ofdamage in the rotating blades using measurements from theBTT sensors For the sake of understanding the WEBMI isbriefly discussed along with the threshold based on thestatistical confidence -e description of the Lipschitz ex-ponent is then given followed by the definition of theproposed severity index

21 Introduction of the WPT -e wavelet packet ψijk is

a function where i j and k are the frequency modulationscale (decomposition level) and translation parametersrespectively -us

ψijk 2j2ψi 2j

tminus k1113872 1113873 (1)

where ψi indicates the frequency modulation of the waveletfunction After the jth level of decomposition the originalsignal f(t) can be expressed as

f(t) 2j1113944i1

fij(t) (2)

-e wavelet packet component signal fij(t) can be

represented by a linear combination of the wavelet packetfunctions ψi

jk(t) as

fij(t) Ns 1113944

k0C

ijk(t)ψi

jk(t) (3)

where Ns denotes the number of samples for four revolu-tions and the wavelet packet coefficient Ci

jk can be obtainedfrom

Cijk 1113946

T

0f(t)ψi

jk(t)dt

Cijk A

ijk if i 1 3 5

Cijk D

ijk if i 2 4 6

(4)

where Aijk and Di

jk are the approximate and detail co-efficients respectively -e wavelet packet functions areassumed to be orthogonal that is

1113946 T

0ψr

jk(t)ψq

jk(t)dt 0 if rne q (5)

-us the wavelet component energy at the jth level forthe ith modal component is defined as the energy stored inthe component signal fi

j(t) and is given by

Eij 1113946

T

0f

ij(t)

2dt (6)

-e component signal fij(t) is extracted from the jth

level but is translated in the time domain such that 0lt tltT-e estimated component energy Ei

j is the energy stored indifferent frequency bands at the jth scale -e rate of changeof the signal wavelet component energy ΔE at the jth leveland the ith component can be expressed as

ΔEij

Eij1113872 1113873

dminus Ei

j1113872 1113873u

11138681113868111386811138681113868

11138681113868111386811138681113868

Eij1113872 1113873

u

(7)

where the subscripts d and u denote the damaged andundamaged cases respectively -e rate of change in energyΔE defines the WEBMI

22 reshold To increase the robustness of prediction ofthe damage location a threshold is established using thestatistical properties and the one-sided confidence limit ofthe damage indices from successive measurements -emean and standard deviation of the estimated WEBMIvalues are given by μW and σW respectively -us the one-sided upper confidence limit for the WEBMI is given by thefollowing equation [28]

ULW μW + ZβσW

Nradic1113888 1113889 (8)

where N is the total number of WEBMI values that can beobtained after completing the wavelet packet de-composition at a given level Zβ is the value of the standardnormal distribution with zero mean and unit variance thatgives a cumulative probability of 100 (1minus β) -is upperlimit can be defined as a threshold value and any indexthat exceeds the threshold can indicate the exact locationof damage -e brief damage detection methodology usingthe WPT analysis is provided by the flowchart shown inFigure 1

23e Lipschitz Exponent A function f(t) has a Lipschitzexponent αge 0 at the point t v if there exists a constant D

and a polynomial pv(t) of degree M (where M is the largestinteger satisfying Mle α) such that [21]

f(t) pv(t) + εv(t) (9)

where

εv(t)1113868111386811138681113868

1113868111386811138681113868leD|tminus v|α (10)

-e Lipschitz exponent α measures the differentiabilityof the functionf(t) the function is not differentiable at t v

if 0lt αlt 1 All of the discontinuities in the function f(t) atthe point t v are contained in the function εv(t)

When the Lipschitz exponent is applied to the wavelettransform then determining the moments of the motherwavelet that vanish is important A function ψ(t) is said tohave n vanishing moments if it satisfies the followingcondition

1113946+infin

minusinfintkψ(t)dt 0 for 0le kle n (11)

Shock and Vibration 3

Suppose that the number of vanishing moments of thewavelet function is greater than the Lipschitz exponentie ngt α -en the wavelet transform retains only thesingular part of the function f(t) because

Wpv(t) 0 (12)

and hence

Wf(t) Wεv(t) (13)

where W defines the wavelet transform-e maximum wavelet packet coefficients reduce as the

level of decomposition j decreases For isolated singularitiesthe wavelet maximum is bounded by an exponential decay lawwith an exponent equal to the Lipschitz exponent α Błaszczukand Pozorski [27] proposed an inequality in the form

|Wf(t)|leD times 2minusj(α+(12)) (14)

or equivalently

log2|Wf(t)|leminusj α +12

1113874 1113875 + log2 D (15)

-us a plot of |Wf(t)| against j gives a straight line withslope minus(α + 12) and this slope can be estimated from twovalues of j

24 e Damage Index -e key difference in the currentanalysis is to replace the wavelet packet coefficient Wf(t)by the absolute difference between the WEBMI and theupper control limit |WEBMI minusUL| -e energy at any levelof decomposition depends directly on the wavelet co-efficients and thus if damage causes a discontinuity in thewavelet transform then it will also provide a discontinuity intheWEBMI-e estimate of the Lipschitz exponent in termsof the WEBMI is given by

α minuslog2 (WEBMI minusUL)jj2

11138681113868111386811138681113868

11138681113868111386811138681113868 + log2 (WEBMI minusUL)jj1

11138681113868111386811138681113868

11138681113868111386811138681113868

j2 minus j1

minus12

(16)

where j1 and j2 are the decomposition levels chosen for theestimation

3 A Bladed Disk Example

-is study is an extension of our previous work thatidentified mistuning in a bladed disk using the WPTmethodology [19] To quantify the damage the proposeddamage severity index is now demonstrated on a bladed diskexample-e simulation consists of a disk with 20 blades andtwo degrees of freedom per blade as shown in Figure 2where the damage is simulated by a stiffness reduction of oneblade -e experimental example consists of a disk with 12blades where the ldquodamagerdquo is implemented by adding massto one of the blades as shown in Figure 3 -e equivalence ofthe damage in the simulation and experiment is then de-termined by considering the change in the first naturalfrequency of the blade

31 Numerical Simulation -e numerical simulation wasperformed on a reduced-order two degrees of freedom perblade model of the bladed disk developed by Salhi et al [29]and used by Jamia et al [19] to demonstrate theWEBMI-ebladed disk was composed of 20 blades Figure 2 showsa schematic of the two DOFmodels where only three sectorsof the bladed disk are shown as a mass-spring system Animpulse was applied to one blade and the correspondingtime response was obtained from each blade tip -e outputonly response signal was used in the WPTanalysis to obtainthe WEBMI -e Lipschitz exponent was derived from theWPT analysis to estimate the damage severity in the bladeddisk

Raw BTTimpulse time responses from undamaged anddamaged cases

Signal processing of raw BTT signals

Reconstructed BTTimpulse time signal of each bladesignal decomposed into different frequency bandwidth

Compute the wavelet packet coefficients (WPC) atdesired level

Entropy methodif

Aj1 lt Dj

2No

Optimal lsquojthrsquo level of decomposition by entropy method

Estimate the component energy at lsquojthrsquo level using WPC

Choose the first component energy for damage detection

Estimate the threshold value for WEBMI usingone-sided upper confidence limit UL

ULW = μW + ZβσW

N

Compute the WEBMI for all blades

∆Ej1 =

Ej1

d Ej1

u

Ej1

u

ndash

Detect the presence and location of damage that exceedsthreshold value WEBMI ndashULα

WEBMI

Estimate the damage severity by Lipschitz exponent lsquoαrsquoindex

Figure 1 Damage detection methodology

4 Shock and Vibration

-e model used has two DOFs per sector representingthe blade and the disk sector Each disk sector is coupledwith the neighboring sectors by the stiffness kc -e stiffnessof an individual blade is represented by ka It is assumed thateach blade in the assembly has one significant mode which istypically the first bending mode No centrifugal stiffening orrotational dynamics effects are considered explicitly in thismodel although centrifugal stiffening could be included byincreasing the blade stiffness ka A proportional dampingmodel is assumed A free vibration response of each bladeand disk sector is generated

-e equation of motion of the bladed disk model in freevibration is defined as

Meuroq(t) + C _q(t) + Kq(t) 0 (17)

where q(t) is the vector of displacements correspondingto (2 times 20) DOF -e displacement of the n-th sector isgiven by

qn(t)

qn1(t)

qn2(t)

1113890 1113891 (18)

where the subscripts 1 and 2 represent the blade and the disksector respectively

M C andK represent the structural mass damping andstiffness matrices of the dimension N times N withN 2nb 40 where nb is the number of blades -e massmatrix is given by

M

Ms 0 0 0

0 Ms 0 0

0 0 Ms 0

0 0 Ms

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with Ms ma 0

0 md

1113890 1113891

(19)

where ma and md are the modal masses of the blade and thecorresponding disk sector respectively -e stiffness matrixK is given by

K

Ka Kb 0 Kb

Kb Ka Kb 00 Kb Ka

Kb

Kb 0 Ka

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with Ka

ka minuska

minuska ka + kd + 2kc

1113890 1113891

and Kb

0 00 minuskc

1113890 1113891

(20)

-e proportional damping matrix is given by

C αM + βK (21)

where the proportionality factors α and β are 10823 and76536 times 10minus5 respectively -e damping ratios for all

Blade

Sector n ndash 1 Sector n Sector n + 1

Disk

ma

md

kcka

kd

ξ

Figure 2 Two degrees of freedom per sector model

Impacthammer

DAQ

(a)

Acclerometers

Magnet

(b)

Figure 3 (a) Impact hammer test setup (b) blade with added magnet mass

Shock and Vibration 5

modes are approximately equal to 001 A bladed disk issimulated with the parameters given in Table 1

To examine the relationship between the Lipschitz ex-ponent α and the damage severity in the bladed diska numerical analysis was performed for different stiffnessreductions that varied from 1 to 9 In this study thewavelet function db6 was chosen which has three vanishingmoments and the first wavelet packet energy was consideredin the damage identification methodology as indicated in[19] -en the Lipschitz exponent α was computed with theinput of two different levels (j 2 and j 6) of coefficientsusing Equation (16) -e minimum level of j 2 was re-quired to detect the damage and j 6 was chosen to satisfythe vanishing moments condition for the db6 waveletHigher-order wavelet functions were investigated but in thiscase the db6 wavelet is optimal to estimate the singularity ofthe function

Figure 4 shows that the Lipschitz exponent α de-creases exponentially as the stiffness reduction increaseswhich means the differentiability of the function de-creases as the damage severity increases -e Lipschitzexponent α has an ability to predict the differentiabil-ity of the function for a stiffness change as small as 1-e Lipschitz exponent obeys the vanishing momentscondition which means the chosen ldquodb6rdquo wavelet func-tion was suitable for this study -e minimum stiffnesschanges due to damage were 1 in this case smallerstiffness changes will generally require higher orderwavelet functions

32 ExperimentalValidation To check the robustness of theproposed damage severity index an impact hammer test wasconducted at Swansea University To perform this experi-ment a 4-channel data acquisition (DAQ) system threeaccelerometers an impact hammer and data acquisitionsoftware were used (see Figure 3(a)) and the experimentalprocedure was briefly explained in [19] In this study theadded mass was varied from 11 g to 99 g with an incrementof 11 g on the middle blade to estimate the added mass(damage) severity as shown in Figure 3(b) -e mass wasadded using rectangular magnets of mass 33 g shown inFigure 3(b) and circular magnets of mass 11 g mounted onthe beam at centre position approximately 15mm from theblade root Table 2 shows the combination and location ofthe magnets to realise the different mass values -e ex-perimental Lipschitz exponent α was estimated and isshown in Figure 4 as a function of the mass added -eresults clearly show that the Lipschitz exponent reduces withthe mass added but there are definite steps in the exponentIn fact the reduction in the Lipschitz exponent appears to beless than expected when a rectangular magnet is added to thebeam -e magnets add some stiffness to the beam in ad-dition to the mass and the mass and stiffness have oppositeeffects on the natural frequencies However the change innatural frequency due to added mass shown in Figure 5obtained from the experimental response data shows thatthe natural frequency changes smoothly with the massadded

1 2 3 4 5 6 7 8 9Stiffness reduction ()

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

Numerical

10 20 30 40 50 60 70 80 90 100Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Exp data

Figure 4 -e change in the Lipschitz exponent due to damageseverity

Table 1 -e properties of the bladed diskma 1 kgmd 1 kgka 10 kNmkd 20 kNmkc 02 ka kNmnb 20

Table 2 -e position of the masses added to the blade for thedifferent damage cases in the bladed disk experiment

Mass added Rectangular magnets (33 g) Round magnets (11 g)11 g mdash Top22 g mdash Top + bottom33 g Top mdash44 g Top Top55 g Top Top times 266 g Top + bottom mdash77 g Top + bottom Top88 g Top + bottom Top + bottom99 g Top times 3 mdash

0 20 40 60 80 100Added mass (g)

ndash08

ndash06

ndash04

ndash02

0

Nat

ural

freq

uenc

y ch

ange

()

Figure 5 -e change in the experimental natural frequency due tomass added

6 Shock and Vibration

33 Comparing Simulated and Experimental Results Tocompare the simulated and experimental results a re-lationship must be found between the stiffness reduction inthe simulation and the added mass in the experiment -isrelationship was determined by equating the change in thenatural frequency due to ldquodamagerdquo In the simulation thecomputed change in the first natural frequency for stiffnessreduction of 5 was 03267 whereas the change in the firstexperimental natural frequency due to an added mass of 55 gwas about 036-us the numerical first natural frequencychange due to a 5 stiffness reduction was close to theexperimental first natural frequency change due to the addedmass of 55 g A finite element (FE) analysis of the blade wasalso performed to give an alternative comparison Each bladein the disk is considered as a cantilever beam with di-mensions 100 times 31 times 4mm Youngrsquos modulus was de-termined as 166GPa by model updating to match with theexperimental first natural frequency for the undamaged casefor a mass density of 7870 kgm3 -e beam was divided into20 elements to achieve an accurate estimate of the firstnatural frequency and the damage (mass) was introducedfrom the second to fourth element of the beam to corre-spond with the location of the addedmass in the experiment-e added mass of 55 g was simulated in the FE model andthe change in the first natural frequency was about 03818which is approximately equal to the experimental change inthe first natural frequency -us in Figure 4 a linear re-lationship between added mass and stiffness reduction isbased on the equivalence of a 5 stiffness reduction and anadded mass of 55 g Figure 4 then shows a reasonableagreement between the experimental results and the nu-merical results

4 Experimental Validation for a RotatingBladed Disk

41 e Bladed Disk Test Rig A test rig was designed andmanufactured at Swansea University in order to generateBTT measurements using different types of sensors andvalidate the proposed technique -e sensors were selectedto be typical of those used to obtain BTT measurementsie an active eddy current sensor (AECS) a passive eddycurrent sensor (PECS) and an optical sensor -e test rig iscomposed of a bladed disk with 12 blades surrounded bya cylindrical casing at the distance δ (the gap between theblade tip and the sensor) -e bladed disk is clamped to theend of a rotating shaft supported by two ball bearings fittedin two split plummer block housings -e shaft is driven bya servo motor at 100 rpm -e manufactured test rig detailsare shown in Figure 6

-e ldquodamagerdquo is induced by adding mass to one of theblades -e sensors were mounted to the casing to detectthe blade tip displacement as it passes in front of theprobes as shown in Figure 7(a) -e sensor outputs weremeasured by a 4-channel Data Physics DAQ system fora period of 32 s with a sampling rate of 10240Hz -edamage was simulated by the added mass realised asmagnets are placed 15mm from the root of the blade asshown in Figure 7(b) In this study the blades were run at

100 rpm -ere was no explicit excitation of the blades inthe experiments although the resolution of the encoderused for the speed control means that the bending vi-bration of the blades will be excited via the torsional vi-bration of the shaft -is may be demonstrated byestimating the speed of the machine based on the time ofarrival of a particular blade a nonconstant speed will arisefrom a combination of the shaft speed variation and theblade vibration Figure 8 shows a typical example of es-timated speed and shows a small variation of 003 whichprovides sufficient excitation for the WEBMI methodDifferent test cases were performed where the mass addedwas changed ie (i) a single added mass to blade 8 (ii)multiple masses added to blades 4 and 8 and (iii) a singlemass added to blade 8 that varied from 11 g to 99 g thedescription of the added masses and their position for thedifferent damage cases is given in Table 2

42 Signal Processing of Measurements from the BTT Sensors-e raw signal was obtained from the AECS for a speed of100 rpm as shown in Figure 9 for illustration purposes -eraw signal cannot be directly used in the WPTmethodologysince the response from individual blades needs to beextracted -e WPT methodology may then be applied toeach blade response One of the major advantages of theproposed approach is that a single noncontact sensormounted on the stator is sufficient to predict the damagelocation and severity for all of the blades-e steps to extractindividual blade response are as follows

(i) Initially the measurements are obtained for 32 s asshown in Figure 9

(ii) To identify the reference blade a trial was conductedby removing a blade from the bladed disk assembly-en the signal was obtained with 11 peaks and inthis case it is clear which signals correspond to thereference blade and the damaged (added mass)blade from the removed blade signal

(iii) -e reference blade (blade 1) is defined as the bladewith the highest amplitude peak and subsequentpeaks were ordered sequentially as the responsefrom the other blades (up to blade 12) for a com-plete revolution For illustration four completerevolutions are considered here and the remaining

Figure 6 -e manufactured test rig

Shock and Vibration 7

samples were discarded More revolutions can beused if required

(iv) Individual blade responses can be extracted bychoosing a fixed sample time that fully containsa single blade response (both before and after thepeak) but is less that TN where T represents oneperiod of rotation and N is the number of blades

(v) Given knowledge of the number of blades the re-sponses from all of the blades can be allocated toindividual blades and merged over multiple revo-lutions as shown in Figure 10 for blade 1

After processing the signal each blade BTTsignal may beapplied into the WPTmethodology to detect the damage inthe rotating blades Brief details about the WPT method-ology and the formulation of the wavelet energy basedmistuning index (WEBMI) were discussed in Section 2

43 SingleAddedMass Locations -e sampling frequency ofblade response measures from the standard processing of

BTTsignals completely depends on the rotating speed of themachine since there is only one measurement for each bladepassing However this study has considered the sensoroutput directly at a constant sample rate of 10240Hz -edamage identification study was conducted for a speed of100 rpm and the addedmass of 99 g was located at a positionof 15mm from the root of blade 8 -e signals from the BTTsensors of all blades for the undamaged and damaged casesfrom the AECS are shown in Figure 11 -e sample time foreach blade was based on 500 samples (250 each side of thepeak) and the reconstructed signals for blade 8 for theundamaged and the damaged cases are shown in Figure 12Comparing the damaged signal with the undamaged signalthere are small shifts observed in the responses of blade 8 dueto the added mass at blade 8 However the interpretation ofthe shift in the signal alone cannot provide a robust damagefeature for the rotating blades -erefore the signal for eachblade was subjected to the WPTmethod which decomposedthe signal into different frequency bandwidth signals todetect the damage effectively In this study the wavelet

AECSPECS

Optical sensor

(a)

Magnet added mass

(b)

Figure 7 (a) BTT experimental test rig (b) blade with magnet added mass

0 2 4 6 8 10 12 14 16 18 20Number of cycles

100015

10002

100025

10003

100035

10004

100045

10005

100055

10006

Spee

d of

revo

lutio

n (R

PM)

Figure 8 Speed variation

0 05 1 15 2 25 3Time (secs)

0

05

1

15

2

25

3

35Bl

ade r

espo

nse (

V)

Figure 9 A raw BTT signal from the AECS at a speed of 100 rpm

8 Shock and Vibration

function ldquodb6rdquo with three vanishing moments was chosenwhich satisfied the vanishing moments condition for esti-mating the damage location and severity in the rotatingblades

In order to select the optimal decomposition level theShannon entropy method was employed as briefly dis-cussed in [19] Based on this method the entropy of bothapproximate and detailed coefficients was estimated ateach level At level 2 the entropy was 000933 which wasless than the entropy of the detailed coefficients which was003069 hence the decomposition level 2 was selected asan optimal level to detect the changes of 99 g added mass inthe rotating blade For the case of BTT signals the vicinityof minute changes can be observed from the approximatecomponent energy as shown in Figure 13(a) However itis difficult to predict the damage at the exact location-us the threshold limit with a high confidence intervalwas applied to the WEBMI and the resulting WEBMI-UL

indicates a substantial peak at the exact location of blade 8as shown in Figure 13(b)

In order to check the effectiveness of the other sensorsthe PECS and optical sensor were employed simulta-neously in addition to the AECS to monitor the blade tipdisplacement as shown in Figure 7(a) -e reconstructedBTT signals of the undamaged and the damaged blade 8from the PECS and the optical sensors are shown in Fig-ures 14 and 15 -ere is hardly any change found in theundamaged BTT signal of blade 8 (see Figure 14(a)) fromthe PECS whereas for the damaged signal of blade 8Figure 14(b) shows subtle changes in the time response dueto the added mass placed on blade 8 In fact the amplitudesof the blade response measured from the PECS are very lowcompared to the AECS and the optical sensor Howeverthis will not affect the damage identification process Onthe other hand the optical sensor BTT response of un-damaged blade 8 (see Figure 15(a)) shows no changes but

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(a)

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(b)

Figure 11 AECS reconstructed BTT signals of all blades for a speed of 100 rpm (a) Undamaged and (b) damaged cases

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

35

Blad

e res

pons

e (V

)

Figure 10 Reconstructed blade 1 BTT signal up to four completed revolutions

Shock and Vibration 9

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

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Submit your manuscripts atwwwhindawicom

Suppose that the number of vanishing moments of thewavelet function is greater than the Lipschitz exponentie ngt α -en the wavelet transform retains only thesingular part of the function f(t) because

Wpv(t) 0 (12)

and hence

Wf(t) Wεv(t) (13)

where W defines the wavelet transform-e maximum wavelet packet coefficients reduce as the

level of decomposition j decreases For isolated singularitiesthe wavelet maximum is bounded by an exponential decay lawwith an exponent equal to the Lipschitz exponent α Błaszczukand Pozorski [27] proposed an inequality in the form

|Wf(t)|leD times 2minusj(α+(12)) (14)

or equivalently

log2|Wf(t)|leminusj α +12

1113874 1113875 + log2 D (15)

-us a plot of |Wf(t)| against j gives a straight line withslope minus(α + 12) and this slope can be estimated from twovalues of j

24 e Damage Index -e key difference in the currentanalysis is to replace the wavelet packet coefficient Wf(t)by the absolute difference between the WEBMI and theupper control limit |WEBMI minusUL| -e energy at any levelof decomposition depends directly on the wavelet co-efficients and thus if damage causes a discontinuity in thewavelet transform then it will also provide a discontinuity intheWEBMI-e estimate of the Lipschitz exponent in termsof the WEBMI is given by

α minuslog2 (WEBMI minusUL)jj2

11138681113868111386811138681113868

11138681113868111386811138681113868 + log2 (WEBMI minusUL)jj1

11138681113868111386811138681113868

11138681113868111386811138681113868

j2 minus j1

minus12

(16)

where j1 and j2 are the decomposition levels chosen for theestimation

3 A Bladed Disk Example

-is study is an extension of our previous work thatidentified mistuning in a bladed disk using the WPTmethodology [19] To quantify the damage the proposeddamage severity index is now demonstrated on a bladed diskexample-e simulation consists of a disk with 20 blades andtwo degrees of freedom per blade as shown in Figure 2where the damage is simulated by a stiffness reduction of oneblade -e experimental example consists of a disk with 12blades where the ldquodamagerdquo is implemented by adding massto one of the blades as shown in Figure 3 -e equivalence ofthe damage in the simulation and experiment is then de-termined by considering the change in the first naturalfrequency of the blade

31 Numerical Simulation -e numerical simulation wasperformed on a reduced-order two degrees of freedom perblade model of the bladed disk developed by Salhi et al [29]and used by Jamia et al [19] to demonstrate theWEBMI-ebladed disk was composed of 20 blades Figure 2 showsa schematic of the two DOFmodels where only three sectorsof the bladed disk are shown as a mass-spring system Animpulse was applied to one blade and the correspondingtime response was obtained from each blade tip -e outputonly response signal was used in the WPTanalysis to obtainthe WEBMI -e Lipschitz exponent was derived from theWPT analysis to estimate the damage severity in the bladeddisk

Raw BTTimpulse time responses from undamaged anddamaged cases

Signal processing of raw BTT signals

Reconstructed BTTimpulse time signal of each bladesignal decomposed into different frequency bandwidth

Compute the wavelet packet coefficients (WPC) atdesired level

Entropy methodif

Aj1 lt Dj

2No

Optimal lsquojthrsquo level of decomposition by entropy method

Estimate the component energy at lsquojthrsquo level using WPC

Choose the first component energy for damage detection

Estimate the threshold value for WEBMI usingone-sided upper confidence limit UL

ULW = μW + ZβσW

N

Compute the WEBMI for all blades

∆Ej1 =

Ej1

d Ej1

u

Ej1

u

ndash

Detect the presence and location of damage that exceedsthreshold value WEBMI ndashULα

WEBMI

Estimate the damage severity by Lipschitz exponent lsquoαrsquoindex

Figure 1 Damage detection methodology

4 Shock and Vibration

-e model used has two DOFs per sector representingthe blade and the disk sector Each disk sector is coupledwith the neighboring sectors by the stiffness kc -e stiffnessof an individual blade is represented by ka It is assumed thateach blade in the assembly has one significant mode which istypically the first bending mode No centrifugal stiffening orrotational dynamics effects are considered explicitly in thismodel although centrifugal stiffening could be included byincreasing the blade stiffness ka A proportional dampingmodel is assumed A free vibration response of each bladeand disk sector is generated

-e equation of motion of the bladed disk model in freevibration is defined as

Meuroq(t) + C _q(t) + Kq(t) 0 (17)

where q(t) is the vector of displacements correspondingto (2 times 20) DOF -e displacement of the n-th sector isgiven by

qn(t)

qn1(t)

qn2(t)

1113890 1113891 (18)

where the subscripts 1 and 2 represent the blade and the disksector respectively

M C andK represent the structural mass damping andstiffness matrices of the dimension N times N withN 2nb 40 where nb is the number of blades -e massmatrix is given by

M

Ms 0 0 0

0 Ms 0 0

0 0 Ms 0

0 0 Ms

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with Ms ma 0

0 md

1113890 1113891

(19)

where ma and md are the modal masses of the blade and thecorresponding disk sector respectively -e stiffness matrixK is given by

K

Ka Kb 0 Kb

Kb Ka Kb 00 Kb Ka

Kb

Kb 0 Ka

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with Ka

ka minuska

minuska ka + kd + 2kc

1113890 1113891

and Kb

0 00 minuskc

1113890 1113891

(20)

-e proportional damping matrix is given by

C αM + βK (21)

where the proportionality factors α and β are 10823 and76536 times 10minus5 respectively -e damping ratios for all

Blade

Sector n ndash 1 Sector n Sector n + 1

Disk

ma

md

kcka

kd

ξ

Figure 2 Two degrees of freedom per sector model

Impacthammer

DAQ

(a)

Acclerometers

Magnet

(b)

Figure 3 (a) Impact hammer test setup (b) blade with added magnet mass

Shock and Vibration 5

modes are approximately equal to 001 A bladed disk issimulated with the parameters given in Table 1

To examine the relationship between the Lipschitz ex-ponent α and the damage severity in the bladed diska numerical analysis was performed for different stiffnessreductions that varied from 1 to 9 In this study thewavelet function db6 was chosen which has three vanishingmoments and the first wavelet packet energy was consideredin the damage identification methodology as indicated in[19] -en the Lipschitz exponent α was computed with theinput of two different levels (j 2 and j 6) of coefficientsusing Equation (16) -e minimum level of j 2 was re-quired to detect the damage and j 6 was chosen to satisfythe vanishing moments condition for the db6 waveletHigher-order wavelet functions were investigated but in thiscase the db6 wavelet is optimal to estimate the singularity ofthe function

Figure 4 shows that the Lipschitz exponent α de-creases exponentially as the stiffness reduction increaseswhich means the differentiability of the function de-creases as the damage severity increases -e Lipschitzexponent α has an ability to predict the differentiabil-ity of the function for a stiffness change as small as 1-e Lipschitz exponent obeys the vanishing momentscondition which means the chosen ldquodb6rdquo wavelet func-tion was suitable for this study -e minimum stiffnesschanges due to damage were 1 in this case smallerstiffness changes will generally require higher orderwavelet functions

32 ExperimentalValidation To check the robustness of theproposed damage severity index an impact hammer test wasconducted at Swansea University To perform this experi-ment a 4-channel data acquisition (DAQ) system threeaccelerometers an impact hammer and data acquisitionsoftware were used (see Figure 3(a)) and the experimentalprocedure was briefly explained in [19] In this study theadded mass was varied from 11 g to 99 g with an incrementof 11 g on the middle blade to estimate the added mass(damage) severity as shown in Figure 3(b) -e mass wasadded using rectangular magnets of mass 33 g shown inFigure 3(b) and circular magnets of mass 11 g mounted onthe beam at centre position approximately 15mm from theblade root Table 2 shows the combination and location ofthe magnets to realise the different mass values -e ex-perimental Lipschitz exponent α was estimated and isshown in Figure 4 as a function of the mass added -eresults clearly show that the Lipschitz exponent reduces withthe mass added but there are definite steps in the exponentIn fact the reduction in the Lipschitz exponent appears to beless than expected when a rectangular magnet is added to thebeam -e magnets add some stiffness to the beam in ad-dition to the mass and the mass and stiffness have oppositeeffects on the natural frequencies However the change innatural frequency due to added mass shown in Figure 5obtained from the experimental response data shows thatthe natural frequency changes smoothly with the massadded

1 2 3 4 5 6 7 8 9Stiffness reduction ()

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

Numerical

10 20 30 40 50 60 70 80 90 100Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Exp data

Figure 4 -e change in the Lipschitz exponent due to damageseverity

Table 1 -e properties of the bladed diskma 1 kgmd 1 kgka 10 kNmkd 20 kNmkc 02 ka kNmnb 20

Table 2 -e position of the masses added to the blade for thedifferent damage cases in the bladed disk experiment

Mass added Rectangular magnets (33 g) Round magnets (11 g)11 g mdash Top22 g mdash Top + bottom33 g Top mdash44 g Top Top55 g Top Top times 266 g Top + bottom mdash77 g Top + bottom Top88 g Top + bottom Top + bottom99 g Top times 3 mdash

0 20 40 60 80 100Added mass (g)

ndash08

ndash06

ndash04

ndash02

0

Nat

ural

freq

uenc

y ch

ange

()

Figure 5 -e change in the experimental natural frequency due tomass added

6 Shock and Vibration

33 Comparing Simulated and Experimental Results Tocompare the simulated and experimental results a re-lationship must be found between the stiffness reduction inthe simulation and the added mass in the experiment -isrelationship was determined by equating the change in thenatural frequency due to ldquodamagerdquo In the simulation thecomputed change in the first natural frequency for stiffnessreduction of 5 was 03267 whereas the change in the firstexperimental natural frequency due to an added mass of 55 gwas about 036-us the numerical first natural frequencychange due to a 5 stiffness reduction was close to theexperimental first natural frequency change due to the addedmass of 55 g A finite element (FE) analysis of the blade wasalso performed to give an alternative comparison Each bladein the disk is considered as a cantilever beam with di-mensions 100 times 31 times 4mm Youngrsquos modulus was de-termined as 166GPa by model updating to match with theexperimental first natural frequency for the undamaged casefor a mass density of 7870 kgm3 -e beam was divided into20 elements to achieve an accurate estimate of the firstnatural frequency and the damage (mass) was introducedfrom the second to fourth element of the beam to corre-spond with the location of the addedmass in the experiment-e added mass of 55 g was simulated in the FE model andthe change in the first natural frequency was about 03818which is approximately equal to the experimental change inthe first natural frequency -us in Figure 4 a linear re-lationship between added mass and stiffness reduction isbased on the equivalence of a 5 stiffness reduction and anadded mass of 55 g Figure 4 then shows a reasonableagreement between the experimental results and the nu-merical results

4 Experimental Validation for a RotatingBladed Disk

41 e Bladed Disk Test Rig A test rig was designed andmanufactured at Swansea University in order to generateBTT measurements using different types of sensors andvalidate the proposed technique -e sensors were selectedto be typical of those used to obtain BTT measurementsie an active eddy current sensor (AECS) a passive eddycurrent sensor (PECS) and an optical sensor -e test rig iscomposed of a bladed disk with 12 blades surrounded bya cylindrical casing at the distance δ (the gap between theblade tip and the sensor) -e bladed disk is clamped to theend of a rotating shaft supported by two ball bearings fittedin two split plummer block housings -e shaft is driven bya servo motor at 100 rpm -e manufactured test rig detailsare shown in Figure 6

-e ldquodamagerdquo is induced by adding mass to one of theblades -e sensors were mounted to the casing to detectthe blade tip displacement as it passes in front of theprobes as shown in Figure 7(a) -e sensor outputs weremeasured by a 4-channel Data Physics DAQ system fora period of 32 s with a sampling rate of 10240Hz -edamage was simulated by the added mass realised asmagnets are placed 15mm from the root of the blade asshown in Figure 7(b) In this study the blades were run at

100 rpm -ere was no explicit excitation of the blades inthe experiments although the resolution of the encoderused for the speed control means that the bending vi-bration of the blades will be excited via the torsional vi-bration of the shaft -is may be demonstrated byestimating the speed of the machine based on the time ofarrival of a particular blade a nonconstant speed will arisefrom a combination of the shaft speed variation and theblade vibration Figure 8 shows a typical example of es-timated speed and shows a small variation of 003 whichprovides sufficient excitation for the WEBMI methodDifferent test cases were performed where the mass addedwas changed ie (i) a single added mass to blade 8 (ii)multiple masses added to blades 4 and 8 and (iii) a singlemass added to blade 8 that varied from 11 g to 99 g thedescription of the added masses and their position for thedifferent damage cases is given in Table 2

42 Signal Processing of Measurements from the BTT Sensors-e raw signal was obtained from the AECS for a speed of100 rpm as shown in Figure 9 for illustration purposes -eraw signal cannot be directly used in the WPTmethodologysince the response from individual blades needs to beextracted -e WPT methodology may then be applied toeach blade response One of the major advantages of theproposed approach is that a single noncontact sensormounted on the stator is sufficient to predict the damagelocation and severity for all of the blades-e steps to extractindividual blade response are as follows

(i) Initially the measurements are obtained for 32 s asshown in Figure 9

(ii) To identify the reference blade a trial was conductedby removing a blade from the bladed disk assembly-en the signal was obtained with 11 peaks and inthis case it is clear which signals correspond to thereference blade and the damaged (added mass)blade from the removed blade signal

(iii) -e reference blade (blade 1) is defined as the bladewith the highest amplitude peak and subsequentpeaks were ordered sequentially as the responsefrom the other blades (up to blade 12) for a com-plete revolution For illustration four completerevolutions are considered here and the remaining

Figure 6 -e manufactured test rig

Shock and Vibration 7

samples were discarded More revolutions can beused if required

(iv) Individual blade responses can be extracted bychoosing a fixed sample time that fully containsa single blade response (both before and after thepeak) but is less that TN where T represents oneperiod of rotation and N is the number of blades

(v) Given knowledge of the number of blades the re-sponses from all of the blades can be allocated toindividual blades and merged over multiple revo-lutions as shown in Figure 10 for blade 1

After processing the signal each blade BTTsignal may beapplied into the WPTmethodology to detect the damage inthe rotating blades Brief details about the WPT method-ology and the formulation of the wavelet energy basedmistuning index (WEBMI) were discussed in Section 2

43 SingleAddedMass Locations -e sampling frequency ofblade response measures from the standard processing of

BTTsignals completely depends on the rotating speed of themachine since there is only one measurement for each bladepassing However this study has considered the sensoroutput directly at a constant sample rate of 10240Hz -edamage identification study was conducted for a speed of100 rpm and the addedmass of 99 g was located at a positionof 15mm from the root of blade 8 -e signals from the BTTsensors of all blades for the undamaged and damaged casesfrom the AECS are shown in Figure 11 -e sample time foreach blade was based on 500 samples (250 each side of thepeak) and the reconstructed signals for blade 8 for theundamaged and the damaged cases are shown in Figure 12Comparing the damaged signal with the undamaged signalthere are small shifts observed in the responses of blade 8 dueto the added mass at blade 8 However the interpretation ofthe shift in the signal alone cannot provide a robust damagefeature for the rotating blades -erefore the signal for eachblade was subjected to the WPTmethod which decomposedthe signal into different frequency bandwidth signals todetect the damage effectively In this study the wavelet

AECSPECS

Optical sensor

(a)

Magnet added mass

(b)

Figure 7 (a) BTT experimental test rig (b) blade with magnet added mass

0 2 4 6 8 10 12 14 16 18 20Number of cycles

100015

10002

100025

10003

100035

10004

100045

10005

100055

10006

Spee

d of

revo

lutio

n (R

PM)

Figure 8 Speed variation

0 05 1 15 2 25 3Time (secs)

0

05

1

15

2

25

3

35Bl

ade r

espo

nse (

V)

Figure 9 A raw BTT signal from the AECS at a speed of 100 rpm

8 Shock and Vibration

function ldquodb6rdquo with three vanishing moments was chosenwhich satisfied the vanishing moments condition for esti-mating the damage location and severity in the rotatingblades

In order to select the optimal decomposition level theShannon entropy method was employed as briefly dis-cussed in [19] Based on this method the entropy of bothapproximate and detailed coefficients was estimated ateach level At level 2 the entropy was 000933 which wasless than the entropy of the detailed coefficients which was003069 hence the decomposition level 2 was selected asan optimal level to detect the changes of 99 g added mass inthe rotating blade For the case of BTT signals the vicinityof minute changes can be observed from the approximatecomponent energy as shown in Figure 13(a) However itis difficult to predict the damage at the exact location-us the threshold limit with a high confidence intervalwas applied to the WEBMI and the resulting WEBMI-UL

indicates a substantial peak at the exact location of blade 8as shown in Figure 13(b)

In order to check the effectiveness of the other sensorsthe PECS and optical sensor were employed simulta-neously in addition to the AECS to monitor the blade tipdisplacement as shown in Figure 7(a) -e reconstructedBTT signals of the undamaged and the damaged blade 8from the PECS and the optical sensors are shown in Fig-ures 14 and 15 -ere is hardly any change found in theundamaged BTT signal of blade 8 (see Figure 14(a)) fromthe PECS whereas for the damaged signal of blade 8Figure 14(b) shows subtle changes in the time response dueto the added mass placed on blade 8 In fact the amplitudesof the blade response measured from the PECS are very lowcompared to the AECS and the optical sensor Howeverthis will not affect the damage identification process Onthe other hand the optical sensor BTT response of un-damaged blade 8 (see Figure 15(a)) shows no changes but

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(a)

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(b)

Figure 11 AECS reconstructed BTT signals of all blades for a speed of 100 rpm (a) Undamaged and (b) damaged cases

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

35

Blad

e res

pons

e (V

)

Figure 10 Reconstructed blade 1 BTT signal up to four completed revolutions

Shock and Vibration 9

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

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Submit your manuscripts atwwwhindawicom

-e model used has two DOFs per sector representingthe blade and the disk sector Each disk sector is coupledwith the neighboring sectors by the stiffness kc -e stiffnessof an individual blade is represented by ka It is assumed thateach blade in the assembly has one significant mode which istypically the first bending mode No centrifugal stiffening orrotational dynamics effects are considered explicitly in thismodel although centrifugal stiffening could be included byincreasing the blade stiffness ka A proportional dampingmodel is assumed A free vibration response of each bladeand disk sector is generated

-e equation of motion of the bladed disk model in freevibration is defined as

Meuroq(t) + C _q(t) + Kq(t) 0 (17)

where q(t) is the vector of displacements correspondingto (2 times 20) DOF -e displacement of the n-th sector isgiven by

qn(t)

qn1(t)

qn2(t)

1113890 1113891 (18)

where the subscripts 1 and 2 represent the blade and the disksector respectively

M C andK represent the structural mass damping andstiffness matrices of the dimension N times N withN 2nb 40 where nb is the number of blades -e massmatrix is given by

M

Ms 0 0 0

0 Ms 0 0

0 0 Ms 0

0 0 Ms

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with Ms ma 0

0 md

1113890 1113891

(19)

where ma and md are the modal masses of the blade and thecorresponding disk sector respectively -e stiffness matrixK is given by

K

Ka Kb 0 Kb

Kb Ka Kb 00 Kb Ka

Kb

Kb 0 Ka

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

with Ka

ka minuska

minuska ka + kd + 2kc

1113890 1113891

and Kb

0 00 minuskc

1113890 1113891

(20)

-e proportional damping matrix is given by

C αM + βK (21)

where the proportionality factors α and β are 10823 and76536 times 10minus5 respectively -e damping ratios for all

Blade

Sector n ndash 1 Sector n Sector n + 1

Disk

ma

md

kcka

kd

ξ

Figure 2 Two degrees of freedom per sector model

Impacthammer

DAQ

(a)

Acclerometers

Magnet

(b)

Figure 3 (a) Impact hammer test setup (b) blade with added magnet mass

Shock and Vibration 5

modes are approximately equal to 001 A bladed disk issimulated with the parameters given in Table 1

To examine the relationship between the Lipschitz ex-ponent α and the damage severity in the bladed diska numerical analysis was performed for different stiffnessreductions that varied from 1 to 9 In this study thewavelet function db6 was chosen which has three vanishingmoments and the first wavelet packet energy was consideredin the damage identification methodology as indicated in[19] -en the Lipschitz exponent α was computed with theinput of two different levels (j 2 and j 6) of coefficientsusing Equation (16) -e minimum level of j 2 was re-quired to detect the damage and j 6 was chosen to satisfythe vanishing moments condition for the db6 waveletHigher-order wavelet functions were investigated but in thiscase the db6 wavelet is optimal to estimate the singularity ofthe function

Figure 4 shows that the Lipschitz exponent α de-creases exponentially as the stiffness reduction increaseswhich means the differentiability of the function de-creases as the damage severity increases -e Lipschitzexponent α has an ability to predict the differentiabil-ity of the function for a stiffness change as small as 1-e Lipschitz exponent obeys the vanishing momentscondition which means the chosen ldquodb6rdquo wavelet func-tion was suitable for this study -e minimum stiffnesschanges due to damage were 1 in this case smallerstiffness changes will generally require higher orderwavelet functions

32 ExperimentalValidation To check the robustness of theproposed damage severity index an impact hammer test wasconducted at Swansea University To perform this experi-ment a 4-channel data acquisition (DAQ) system threeaccelerometers an impact hammer and data acquisitionsoftware were used (see Figure 3(a)) and the experimentalprocedure was briefly explained in [19] In this study theadded mass was varied from 11 g to 99 g with an incrementof 11 g on the middle blade to estimate the added mass(damage) severity as shown in Figure 3(b) -e mass wasadded using rectangular magnets of mass 33 g shown inFigure 3(b) and circular magnets of mass 11 g mounted onthe beam at centre position approximately 15mm from theblade root Table 2 shows the combination and location ofthe magnets to realise the different mass values -e ex-perimental Lipschitz exponent α was estimated and isshown in Figure 4 as a function of the mass added -eresults clearly show that the Lipschitz exponent reduces withthe mass added but there are definite steps in the exponentIn fact the reduction in the Lipschitz exponent appears to beless than expected when a rectangular magnet is added to thebeam -e magnets add some stiffness to the beam in ad-dition to the mass and the mass and stiffness have oppositeeffects on the natural frequencies However the change innatural frequency due to added mass shown in Figure 5obtained from the experimental response data shows thatthe natural frequency changes smoothly with the massadded

1 2 3 4 5 6 7 8 9Stiffness reduction ()

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

Numerical

10 20 30 40 50 60 70 80 90 100Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Exp data

Figure 4 -e change in the Lipschitz exponent due to damageseverity

Table 1 -e properties of the bladed diskma 1 kgmd 1 kgka 10 kNmkd 20 kNmkc 02 ka kNmnb 20

Table 2 -e position of the masses added to the blade for thedifferent damage cases in the bladed disk experiment

Mass added Rectangular magnets (33 g) Round magnets (11 g)11 g mdash Top22 g mdash Top + bottom33 g Top mdash44 g Top Top55 g Top Top times 266 g Top + bottom mdash77 g Top + bottom Top88 g Top + bottom Top + bottom99 g Top times 3 mdash

0 20 40 60 80 100Added mass (g)

ndash08

ndash06

ndash04

ndash02

0

Nat

ural

freq

uenc

y ch

ange

()

Figure 5 -e change in the experimental natural frequency due tomass added

6 Shock and Vibration

33 Comparing Simulated and Experimental Results Tocompare the simulated and experimental results a re-lationship must be found between the stiffness reduction inthe simulation and the added mass in the experiment -isrelationship was determined by equating the change in thenatural frequency due to ldquodamagerdquo In the simulation thecomputed change in the first natural frequency for stiffnessreduction of 5 was 03267 whereas the change in the firstexperimental natural frequency due to an added mass of 55 gwas about 036-us the numerical first natural frequencychange due to a 5 stiffness reduction was close to theexperimental first natural frequency change due to the addedmass of 55 g A finite element (FE) analysis of the blade wasalso performed to give an alternative comparison Each bladein the disk is considered as a cantilever beam with di-mensions 100 times 31 times 4mm Youngrsquos modulus was de-termined as 166GPa by model updating to match with theexperimental first natural frequency for the undamaged casefor a mass density of 7870 kgm3 -e beam was divided into20 elements to achieve an accurate estimate of the firstnatural frequency and the damage (mass) was introducedfrom the second to fourth element of the beam to corre-spond with the location of the addedmass in the experiment-e added mass of 55 g was simulated in the FE model andthe change in the first natural frequency was about 03818which is approximately equal to the experimental change inthe first natural frequency -us in Figure 4 a linear re-lationship between added mass and stiffness reduction isbased on the equivalence of a 5 stiffness reduction and anadded mass of 55 g Figure 4 then shows a reasonableagreement between the experimental results and the nu-merical results

4 Experimental Validation for a RotatingBladed Disk

41 e Bladed Disk Test Rig A test rig was designed andmanufactured at Swansea University in order to generateBTT measurements using different types of sensors andvalidate the proposed technique -e sensors were selectedto be typical of those used to obtain BTT measurementsie an active eddy current sensor (AECS) a passive eddycurrent sensor (PECS) and an optical sensor -e test rig iscomposed of a bladed disk with 12 blades surrounded bya cylindrical casing at the distance δ (the gap between theblade tip and the sensor) -e bladed disk is clamped to theend of a rotating shaft supported by two ball bearings fittedin two split plummer block housings -e shaft is driven bya servo motor at 100 rpm -e manufactured test rig detailsare shown in Figure 6

-e ldquodamagerdquo is induced by adding mass to one of theblades -e sensors were mounted to the casing to detectthe blade tip displacement as it passes in front of theprobes as shown in Figure 7(a) -e sensor outputs weremeasured by a 4-channel Data Physics DAQ system fora period of 32 s with a sampling rate of 10240Hz -edamage was simulated by the added mass realised asmagnets are placed 15mm from the root of the blade asshown in Figure 7(b) In this study the blades were run at

100 rpm -ere was no explicit excitation of the blades inthe experiments although the resolution of the encoderused for the speed control means that the bending vi-bration of the blades will be excited via the torsional vi-bration of the shaft -is may be demonstrated byestimating the speed of the machine based on the time ofarrival of a particular blade a nonconstant speed will arisefrom a combination of the shaft speed variation and theblade vibration Figure 8 shows a typical example of es-timated speed and shows a small variation of 003 whichprovides sufficient excitation for the WEBMI methodDifferent test cases were performed where the mass addedwas changed ie (i) a single added mass to blade 8 (ii)multiple masses added to blades 4 and 8 and (iii) a singlemass added to blade 8 that varied from 11 g to 99 g thedescription of the added masses and their position for thedifferent damage cases is given in Table 2

42 Signal Processing of Measurements from the BTT Sensors-e raw signal was obtained from the AECS for a speed of100 rpm as shown in Figure 9 for illustration purposes -eraw signal cannot be directly used in the WPTmethodologysince the response from individual blades needs to beextracted -e WPT methodology may then be applied toeach blade response One of the major advantages of theproposed approach is that a single noncontact sensormounted on the stator is sufficient to predict the damagelocation and severity for all of the blades-e steps to extractindividual blade response are as follows

(i) Initially the measurements are obtained for 32 s asshown in Figure 9

(ii) To identify the reference blade a trial was conductedby removing a blade from the bladed disk assembly-en the signal was obtained with 11 peaks and inthis case it is clear which signals correspond to thereference blade and the damaged (added mass)blade from the removed blade signal

(iii) -e reference blade (blade 1) is defined as the bladewith the highest amplitude peak and subsequentpeaks were ordered sequentially as the responsefrom the other blades (up to blade 12) for a com-plete revolution For illustration four completerevolutions are considered here and the remaining

Figure 6 -e manufactured test rig

Shock and Vibration 7

samples were discarded More revolutions can beused if required

(iv) Individual blade responses can be extracted bychoosing a fixed sample time that fully containsa single blade response (both before and after thepeak) but is less that TN where T represents oneperiod of rotation and N is the number of blades

(v) Given knowledge of the number of blades the re-sponses from all of the blades can be allocated toindividual blades and merged over multiple revo-lutions as shown in Figure 10 for blade 1

After processing the signal each blade BTTsignal may beapplied into the WPTmethodology to detect the damage inthe rotating blades Brief details about the WPT method-ology and the formulation of the wavelet energy basedmistuning index (WEBMI) were discussed in Section 2

43 SingleAddedMass Locations -e sampling frequency ofblade response measures from the standard processing of

BTTsignals completely depends on the rotating speed of themachine since there is only one measurement for each bladepassing However this study has considered the sensoroutput directly at a constant sample rate of 10240Hz -edamage identification study was conducted for a speed of100 rpm and the addedmass of 99 g was located at a positionof 15mm from the root of blade 8 -e signals from the BTTsensors of all blades for the undamaged and damaged casesfrom the AECS are shown in Figure 11 -e sample time foreach blade was based on 500 samples (250 each side of thepeak) and the reconstructed signals for blade 8 for theundamaged and the damaged cases are shown in Figure 12Comparing the damaged signal with the undamaged signalthere are small shifts observed in the responses of blade 8 dueto the added mass at blade 8 However the interpretation ofthe shift in the signal alone cannot provide a robust damagefeature for the rotating blades -erefore the signal for eachblade was subjected to the WPTmethod which decomposedthe signal into different frequency bandwidth signals todetect the damage effectively In this study the wavelet

AECSPECS

Optical sensor

(a)

Magnet added mass

(b)

Figure 7 (a) BTT experimental test rig (b) blade with magnet added mass

0 2 4 6 8 10 12 14 16 18 20Number of cycles

100015

10002

100025

10003

100035

10004

100045

10005

100055

10006

Spee

d of

revo

lutio

n (R

PM)

Figure 8 Speed variation

0 05 1 15 2 25 3Time (secs)

0

05

1

15

2

25

3

35Bl

ade r

espo

nse (

V)

Figure 9 A raw BTT signal from the AECS at a speed of 100 rpm

8 Shock and Vibration

function ldquodb6rdquo with three vanishing moments was chosenwhich satisfied the vanishing moments condition for esti-mating the damage location and severity in the rotatingblades

In order to select the optimal decomposition level theShannon entropy method was employed as briefly dis-cussed in [19] Based on this method the entropy of bothapproximate and detailed coefficients was estimated ateach level At level 2 the entropy was 000933 which wasless than the entropy of the detailed coefficients which was003069 hence the decomposition level 2 was selected asan optimal level to detect the changes of 99 g added mass inthe rotating blade For the case of BTT signals the vicinityof minute changes can be observed from the approximatecomponent energy as shown in Figure 13(a) However itis difficult to predict the damage at the exact location-us the threshold limit with a high confidence intervalwas applied to the WEBMI and the resulting WEBMI-UL

indicates a substantial peak at the exact location of blade 8as shown in Figure 13(b)

In order to check the effectiveness of the other sensorsthe PECS and optical sensor were employed simulta-neously in addition to the AECS to monitor the blade tipdisplacement as shown in Figure 7(a) -e reconstructedBTT signals of the undamaged and the damaged blade 8from the PECS and the optical sensors are shown in Fig-ures 14 and 15 -ere is hardly any change found in theundamaged BTT signal of blade 8 (see Figure 14(a)) fromthe PECS whereas for the damaged signal of blade 8Figure 14(b) shows subtle changes in the time response dueto the added mass placed on blade 8 In fact the amplitudesof the blade response measured from the PECS are very lowcompared to the AECS and the optical sensor Howeverthis will not affect the damage identification process Onthe other hand the optical sensor BTT response of un-damaged blade 8 (see Figure 15(a)) shows no changes but

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(a)

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(b)

Figure 11 AECS reconstructed BTT signals of all blades for a speed of 100 rpm (a) Undamaged and (b) damaged cases

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

35

Blad

e res

pons

e (V

)

Figure 10 Reconstructed blade 1 BTT signal up to four completed revolutions

Shock and Vibration 9

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

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modes are approximately equal to 001 A bladed disk issimulated with the parameters given in Table 1

To examine the relationship between the Lipschitz ex-ponent α and the damage severity in the bladed diska numerical analysis was performed for different stiffnessreductions that varied from 1 to 9 In this study thewavelet function db6 was chosen which has three vanishingmoments and the first wavelet packet energy was consideredin the damage identification methodology as indicated in[19] -en the Lipschitz exponent α was computed with theinput of two different levels (j 2 and j 6) of coefficientsusing Equation (16) -e minimum level of j 2 was re-quired to detect the damage and j 6 was chosen to satisfythe vanishing moments condition for the db6 waveletHigher-order wavelet functions were investigated but in thiscase the db6 wavelet is optimal to estimate the singularity ofthe function

Figure 4 shows that the Lipschitz exponent α de-creases exponentially as the stiffness reduction increaseswhich means the differentiability of the function de-creases as the damage severity increases -e Lipschitzexponent α has an ability to predict the differentiabil-ity of the function for a stiffness change as small as 1-e Lipschitz exponent obeys the vanishing momentscondition which means the chosen ldquodb6rdquo wavelet func-tion was suitable for this study -e minimum stiffnesschanges due to damage were 1 in this case smallerstiffness changes will generally require higher orderwavelet functions

32 ExperimentalValidation To check the robustness of theproposed damage severity index an impact hammer test wasconducted at Swansea University To perform this experi-ment a 4-channel data acquisition (DAQ) system threeaccelerometers an impact hammer and data acquisitionsoftware were used (see Figure 3(a)) and the experimentalprocedure was briefly explained in [19] In this study theadded mass was varied from 11 g to 99 g with an incrementof 11 g on the middle blade to estimate the added mass(damage) severity as shown in Figure 3(b) -e mass wasadded using rectangular magnets of mass 33 g shown inFigure 3(b) and circular magnets of mass 11 g mounted onthe beam at centre position approximately 15mm from theblade root Table 2 shows the combination and location ofthe magnets to realise the different mass values -e ex-perimental Lipschitz exponent α was estimated and isshown in Figure 4 as a function of the mass added -eresults clearly show that the Lipschitz exponent reduces withthe mass added but there are definite steps in the exponentIn fact the reduction in the Lipschitz exponent appears to beless than expected when a rectangular magnet is added to thebeam -e magnets add some stiffness to the beam in ad-dition to the mass and the mass and stiffness have oppositeeffects on the natural frequencies However the change innatural frequency due to added mass shown in Figure 5obtained from the experimental response data shows thatthe natural frequency changes smoothly with the massadded

1 2 3 4 5 6 7 8 9Stiffness reduction ()

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

Numerical

10 20 30 40 50 60 70 80 90 100Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Exp data

Figure 4 -e change in the Lipschitz exponent due to damageseverity

Table 1 -e properties of the bladed diskma 1 kgmd 1 kgka 10 kNmkd 20 kNmkc 02 ka kNmnb 20

Table 2 -e position of the masses added to the blade for thedifferent damage cases in the bladed disk experiment

Mass added Rectangular magnets (33 g) Round magnets (11 g)11 g mdash Top22 g mdash Top + bottom33 g Top mdash44 g Top Top55 g Top Top times 266 g Top + bottom mdash77 g Top + bottom Top88 g Top + bottom Top + bottom99 g Top times 3 mdash

0 20 40 60 80 100Added mass (g)

ndash08

ndash06

ndash04

ndash02

0

Nat

ural

freq

uenc

y ch

ange

()

Figure 5 -e change in the experimental natural frequency due tomass added

6 Shock and Vibration

33 Comparing Simulated and Experimental Results Tocompare the simulated and experimental results a re-lationship must be found between the stiffness reduction inthe simulation and the added mass in the experiment -isrelationship was determined by equating the change in thenatural frequency due to ldquodamagerdquo In the simulation thecomputed change in the first natural frequency for stiffnessreduction of 5 was 03267 whereas the change in the firstexperimental natural frequency due to an added mass of 55 gwas about 036-us the numerical first natural frequencychange due to a 5 stiffness reduction was close to theexperimental first natural frequency change due to the addedmass of 55 g A finite element (FE) analysis of the blade wasalso performed to give an alternative comparison Each bladein the disk is considered as a cantilever beam with di-mensions 100 times 31 times 4mm Youngrsquos modulus was de-termined as 166GPa by model updating to match with theexperimental first natural frequency for the undamaged casefor a mass density of 7870 kgm3 -e beam was divided into20 elements to achieve an accurate estimate of the firstnatural frequency and the damage (mass) was introducedfrom the second to fourth element of the beam to corre-spond with the location of the addedmass in the experiment-e added mass of 55 g was simulated in the FE model andthe change in the first natural frequency was about 03818which is approximately equal to the experimental change inthe first natural frequency -us in Figure 4 a linear re-lationship between added mass and stiffness reduction isbased on the equivalence of a 5 stiffness reduction and anadded mass of 55 g Figure 4 then shows a reasonableagreement between the experimental results and the nu-merical results

4 Experimental Validation for a RotatingBladed Disk

41 e Bladed Disk Test Rig A test rig was designed andmanufactured at Swansea University in order to generateBTT measurements using different types of sensors andvalidate the proposed technique -e sensors were selectedto be typical of those used to obtain BTT measurementsie an active eddy current sensor (AECS) a passive eddycurrent sensor (PECS) and an optical sensor -e test rig iscomposed of a bladed disk with 12 blades surrounded bya cylindrical casing at the distance δ (the gap between theblade tip and the sensor) -e bladed disk is clamped to theend of a rotating shaft supported by two ball bearings fittedin two split plummer block housings -e shaft is driven bya servo motor at 100 rpm -e manufactured test rig detailsare shown in Figure 6

-e ldquodamagerdquo is induced by adding mass to one of theblades -e sensors were mounted to the casing to detectthe blade tip displacement as it passes in front of theprobes as shown in Figure 7(a) -e sensor outputs weremeasured by a 4-channel Data Physics DAQ system fora period of 32 s with a sampling rate of 10240Hz -edamage was simulated by the added mass realised asmagnets are placed 15mm from the root of the blade asshown in Figure 7(b) In this study the blades were run at

100 rpm -ere was no explicit excitation of the blades inthe experiments although the resolution of the encoderused for the speed control means that the bending vi-bration of the blades will be excited via the torsional vi-bration of the shaft -is may be demonstrated byestimating the speed of the machine based on the time ofarrival of a particular blade a nonconstant speed will arisefrom a combination of the shaft speed variation and theblade vibration Figure 8 shows a typical example of es-timated speed and shows a small variation of 003 whichprovides sufficient excitation for the WEBMI methodDifferent test cases were performed where the mass addedwas changed ie (i) a single added mass to blade 8 (ii)multiple masses added to blades 4 and 8 and (iii) a singlemass added to blade 8 that varied from 11 g to 99 g thedescription of the added masses and their position for thedifferent damage cases is given in Table 2

42 Signal Processing of Measurements from the BTT Sensors-e raw signal was obtained from the AECS for a speed of100 rpm as shown in Figure 9 for illustration purposes -eraw signal cannot be directly used in the WPTmethodologysince the response from individual blades needs to beextracted -e WPT methodology may then be applied toeach blade response One of the major advantages of theproposed approach is that a single noncontact sensormounted on the stator is sufficient to predict the damagelocation and severity for all of the blades-e steps to extractindividual blade response are as follows

(i) Initially the measurements are obtained for 32 s asshown in Figure 9

(ii) To identify the reference blade a trial was conductedby removing a blade from the bladed disk assembly-en the signal was obtained with 11 peaks and inthis case it is clear which signals correspond to thereference blade and the damaged (added mass)blade from the removed blade signal

(iii) -e reference blade (blade 1) is defined as the bladewith the highest amplitude peak and subsequentpeaks were ordered sequentially as the responsefrom the other blades (up to blade 12) for a com-plete revolution For illustration four completerevolutions are considered here and the remaining

Figure 6 -e manufactured test rig

Shock and Vibration 7

samples were discarded More revolutions can beused if required

(iv) Individual blade responses can be extracted bychoosing a fixed sample time that fully containsa single blade response (both before and after thepeak) but is less that TN where T represents oneperiod of rotation and N is the number of blades

(v) Given knowledge of the number of blades the re-sponses from all of the blades can be allocated toindividual blades and merged over multiple revo-lutions as shown in Figure 10 for blade 1

After processing the signal each blade BTTsignal may beapplied into the WPTmethodology to detect the damage inthe rotating blades Brief details about the WPT method-ology and the formulation of the wavelet energy basedmistuning index (WEBMI) were discussed in Section 2

43 SingleAddedMass Locations -e sampling frequency ofblade response measures from the standard processing of

BTTsignals completely depends on the rotating speed of themachine since there is only one measurement for each bladepassing However this study has considered the sensoroutput directly at a constant sample rate of 10240Hz -edamage identification study was conducted for a speed of100 rpm and the addedmass of 99 g was located at a positionof 15mm from the root of blade 8 -e signals from the BTTsensors of all blades for the undamaged and damaged casesfrom the AECS are shown in Figure 11 -e sample time foreach blade was based on 500 samples (250 each side of thepeak) and the reconstructed signals for blade 8 for theundamaged and the damaged cases are shown in Figure 12Comparing the damaged signal with the undamaged signalthere are small shifts observed in the responses of blade 8 dueto the added mass at blade 8 However the interpretation ofthe shift in the signal alone cannot provide a robust damagefeature for the rotating blades -erefore the signal for eachblade was subjected to the WPTmethod which decomposedthe signal into different frequency bandwidth signals todetect the damage effectively In this study the wavelet

AECSPECS

Optical sensor

(a)

Magnet added mass

(b)

Figure 7 (a) BTT experimental test rig (b) blade with magnet added mass

0 2 4 6 8 10 12 14 16 18 20Number of cycles

100015

10002

100025

10003

100035

10004

100045

10005

100055

10006

Spee

d of

revo

lutio

n (R

PM)

Figure 8 Speed variation

0 05 1 15 2 25 3Time (secs)

0

05

1

15

2

25

3

35Bl

ade r

espo

nse (

V)

Figure 9 A raw BTT signal from the AECS at a speed of 100 rpm

8 Shock and Vibration

function ldquodb6rdquo with three vanishing moments was chosenwhich satisfied the vanishing moments condition for esti-mating the damage location and severity in the rotatingblades

In order to select the optimal decomposition level theShannon entropy method was employed as briefly dis-cussed in [19] Based on this method the entropy of bothapproximate and detailed coefficients was estimated ateach level At level 2 the entropy was 000933 which wasless than the entropy of the detailed coefficients which was003069 hence the decomposition level 2 was selected asan optimal level to detect the changes of 99 g added mass inthe rotating blade For the case of BTT signals the vicinityof minute changes can be observed from the approximatecomponent energy as shown in Figure 13(a) However itis difficult to predict the damage at the exact location-us the threshold limit with a high confidence intervalwas applied to the WEBMI and the resulting WEBMI-UL

indicates a substantial peak at the exact location of blade 8as shown in Figure 13(b)

In order to check the effectiveness of the other sensorsthe PECS and optical sensor were employed simulta-neously in addition to the AECS to monitor the blade tipdisplacement as shown in Figure 7(a) -e reconstructedBTT signals of the undamaged and the damaged blade 8from the PECS and the optical sensors are shown in Fig-ures 14 and 15 -ere is hardly any change found in theundamaged BTT signal of blade 8 (see Figure 14(a)) fromthe PECS whereas for the damaged signal of blade 8Figure 14(b) shows subtle changes in the time response dueto the added mass placed on blade 8 In fact the amplitudesof the blade response measured from the PECS are very lowcompared to the AECS and the optical sensor Howeverthis will not affect the damage identification process Onthe other hand the optical sensor BTT response of un-damaged blade 8 (see Figure 15(a)) shows no changes but

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(a)

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(b)

Figure 11 AECS reconstructed BTT signals of all blades for a speed of 100 rpm (a) Undamaged and (b) damaged cases

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

35

Blad

e res

pons

e (V

)

Figure 10 Reconstructed blade 1 BTT signal up to four completed revolutions

Shock and Vibration 9

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

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33 Comparing Simulated and Experimental Results Tocompare the simulated and experimental results a re-lationship must be found between the stiffness reduction inthe simulation and the added mass in the experiment -isrelationship was determined by equating the change in thenatural frequency due to ldquodamagerdquo In the simulation thecomputed change in the first natural frequency for stiffnessreduction of 5 was 03267 whereas the change in the firstexperimental natural frequency due to an added mass of 55 gwas about 036-us the numerical first natural frequencychange due to a 5 stiffness reduction was close to theexperimental first natural frequency change due to the addedmass of 55 g A finite element (FE) analysis of the blade wasalso performed to give an alternative comparison Each bladein the disk is considered as a cantilever beam with di-mensions 100 times 31 times 4mm Youngrsquos modulus was de-termined as 166GPa by model updating to match with theexperimental first natural frequency for the undamaged casefor a mass density of 7870 kgm3 -e beam was divided into20 elements to achieve an accurate estimate of the firstnatural frequency and the damage (mass) was introducedfrom the second to fourth element of the beam to corre-spond with the location of the addedmass in the experiment-e added mass of 55 g was simulated in the FE model andthe change in the first natural frequency was about 03818which is approximately equal to the experimental change inthe first natural frequency -us in Figure 4 a linear re-lationship between added mass and stiffness reduction isbased on the equivalence of a 5 stiffness reduction and anadded mass of 55 g Figure 4 then shows a reasonableagreement between the experimental results and the nu-merical results

4 Experimental Validation for a RotatingBladed Disk

41 e Bladed Disk Test Rig A test rig was designed andmanufactured at Swansea University in order to generateBTT measurements using different types of sensors andvalidate the proposed technique -e sensors were selectedto be typical of those used to obtain BTT measurementsie an active eddy current sensor (AECS) a passive eddycurrent sensor (PECS) and an optical sensor -e test rig iscomposed of a bladed disk with 12 blades surrounded bya cylindrical casing at the distance δ (the gap between theblade tip and the sensor) -e bladed disk is clamped to theend of a rotating shaft supported by two ball bearings fittedin two split plummer block housings -e shaft is driven bya servo motor at 100 rpm -e manufactured test rig detailsare shown in Figure 6

-e ldquodamagerdquo is induced by adding mass to one of theblades -e sensors were mounted to the casing to detectthe blade tip displacement as it passes in front of theprobes as shown in Figure 7(a) -e sensor outputs weremeasured by a 4-channel Data Physics DAQ system fora period of 32 s with a sampling rate of 10240Hz -edamage was simulated by the added mass realised asmagnets are placed 15mm from the root of the blade asshown in Figure 7(b) In this study the blades were run at

100 rpm -ere was no explicit excitation of the blades inthe experiments although the resolution of the encoderused for the speed control means that the bending vi-bration of the blades will be excited via the torsional vi-bration of the shaft -is may be demonstrated byestimating the speed of the machine based on the time ofarrival of a particular blade a nonconstant speed will arisefrom a combination of the shaft speed variation and theblade vibration Figure 8 shows a typical example of es-timated speed and shows a small variation of 003 whichprovides sufficient excitation for the WEBMI methodDifferent test cases were performed where the mass addedwas changed ie (i) a single added mass to blade 8 (ii)multiple masses added to blades 4 and 8 and (iii) a singlemass added to blade 8 that varied from 11 g to 99 g thedescription of the added masses and their position for thedifferent damage cases is given in Table 2

42 Signal Processing of Measurements from the BTT Sensors-e raw signal was obtained from the AECS for a speed of100 rpm as shown in Figure 9 for illustration purposes -eraw signal cannot be directly used in the WPTmethodologysince the response from individual blades needs to beextracted -e WPT methodology may then be applied toeach blade response One of the major advantages of theproposed approach is that a single noncontact sensormounted on the stator is sufficient to predict the damagelocation and severity for all of the blades-e steps to extractindividual blade response are as follows

(i) Initially the measurements are obtained for 32 s asshown in Figure 9

(ii) To identify the reference blade a trial was conductedby removing a blade from the bladed disk assembly-en the signal was obtained with 11 peaks and inthis case it is clear which signals correspond to thereference blade and the damaged (added mass)blade from the removed blade signal

(iii) -e reference blade (blade 1) is defined as the bladewith the highest amplitude peak and subsequentpeaks were ordered sequentially as the responsefrom the other blades (up to blade 12) for a com-plete revolution For illustration four completerevolutions are considered here and the remaining

Figure 6 -e manufactured test rig

Shock and Vibration 7

samples were discarded More revolutions can beused if required

(iv) Individual blade responses can be extracted bychoosing a fixed sample time that fully containsa single blade response (both before and after thepeak) but is less that TN where T represents oneperiod of rotation and N is the number of blades

(v) Given knowledge of the number of blades the re-sponses from all of the blades can be allocated toindividual blades and merged over multiple revo-lutions as shown in Figure 10 for blade 1

After processing the signal each blade BTTsignal may beapplied into the WPTmethodology to detect the damage inthe rotating blades Brief details about the WPT method-ology and the formulation of the wavelet energy basedmistuning index (WEBMI) were discussed in Section 2

43 SingleAddedMass Locations -e sampling frequency ofblade response measures from the standard processing of

BTTsignals completely depends on the rotating speed of themachine since there is only one measurement for each bladepassing However this study has considered the sensoroutput directly at a constant sample rate of 10240Hz -edamage identification study was conducted for a speed of100 rpm and the addedmass of 99 g was located at a positionof 15mm from the root of blade 8 -e signals from the BTTsensors of all blades for the undamaged and damaged casesfrom the AECS are shown in Figure 11 -e sample time foreach blade was based on 500 samples (250 each side of thepeak) and the reconstructed signals for blade 8 for theundamaged and the damaged cases are shown in Figure 12Comparing the damaged signal with the undamaged signalthere are small shifts observed in the responses of blade 8 dueto the added mass at blade 8 However the interpretation ofthe shift in the signal alone cannot provide a robust damagefeature for the rotating blades -erefore the signal for eachblade was subjected to the WPTmethod which decomposedthe signal into different frequency bandwidth signals todetect the damage effectively In this study the wavelet

AECSPECS

Optical sensor

(a)

Magnet added mass

(b)

Figure 7 (a) BTT experimental test rig (b) blade with magnet added mass

0 2 4 6 8 10 12 14 16 18 20Number of cycles

100015

10002

100025

10003

100035

10004

100045

10005

100055

10006

Spee

d of

revo

lutio

n (R

PM)

Figure 8 Speed variation

0 05 1 15 2 25 3Time (secs)

0

05

1

15

2

25

3

35Bl

ade r

espo

nse (

V)

Figure 9 A raw BTT signal from the AECS at a speed of 100 rpm

8 Shock and Vibration

function ldquodb6rdquo with three vanishing moments was chosenwhich satisfied the vanishing moments condition for esti-mating the damage location and severity in the rotatingblades

In order to select the optimal decomposition level theShannon entropy method was employed as briefly dis-cussed in [19] Based on this method the entropy of bothapproximate and detailed coefficients was estimated ateach level At level 2 the entropy was 000933 which wasless than the entropy of the detailed coefficients which was003069 hence the decomposition level 2 was selected asan optimal level to detect the changes of 99 g added mass inthe rotating blade For the case of BTT signals the vicinityof minute changes can be observed from the approximatecomponent energy as shown in Figure 13(a) However itis difficult to predict the damage at the exact location-us the threshold limit with a high confidence intervalwas applied to the WEBMI and the resulting WEBMI-UL

indicates a substantial peak at the exact location of blade 8as shown in Figure 13(b)

In order to check the effectiveness of the other sensorsthe PECS and optical sensor were employed simulta-neously in addition to the AECS to monitor the blade tipdisplacement as shown in Figure 7(a) -e reconstructedBTT signals of the undamaged and the damaged blade 8from the PECS and the optical sensors are shown in Fig-ures 14 and 15 -ere is hardly any change found in theundamaged BTT signal of blade 8 (see Figure 14(a)) fromthe PECS whereas for the damaged signal of blade 8Figure 14(b) shows subtle changes in the time response dueto the added mass placed on blade 8 In fact the amplitudesof the blade response measured from the PECS are very lowcompared to the AECS and the optical sensor Howeverthis will not affect the damage identification process Onthe other hand the optical sensor BTT response of un-damaged blade 8 (see Figure 15(a)) shows no changes but

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(a)

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(b)

Figure 11 AECS reconstructed BTT signals of all blades for a speed of 100 rpm (a) Undamaged and (b) damaged cases

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

35

Blad

e res

pons

e (V

)

Figure 10 Reconstructed blade 1 BTT signal up to four completed revolutions

Shock and Vibration 9

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

samples were discarded More revolutions can beused if required

(iv) Individual blade responses can be extracted bychoosing a fixed sample time that fully containsa single blade response (both before and after thepeak) but is less that TN where T represents oneperiod of rotation and N is the number of blades

(v) Given knowledge of the number of blades the re-sponses from all of the blades can be allocated toindividual blades and merged over multiple revo-lutions as shown in Figure 10 for blade 1

After processing the signal each blade BTTsignal may beapplied into the WPTmethodology to detect the damage inthe rotating blades Brief details about the WPT method-ology and the formulation of the wavelet energy basedmistuning index (WEBMI) were discussed in Section 2

43 SingleAddedMass Locations -e sampling frequency ofblade response measures from the standard processing of

BTTsignals completely depends on the rotating speed of themachine since there is only one measurement for each bladepassing However this study has considered the sensoroutput directly at a constant sample rate of 10240Hz -edamage identification study was conducted for a speed of100 rpm and the addedmass of 99 g was located at a positionof 15mm from the root of blade 8 -e signals from the BTTsensors of all blades for the undamaged and damaged casesfrom the AECS are shown in Figure 11 -e sample time foreach blade was based on 500 samples (250 each side of thepeak) and the reconstructed signals for blade 8 for theundamaged and the damaged cases are shown in Figure 12Comparing the damaged signal with the undamaged signalthere are small shifts observed in the responses of blade 8 dueto the added mass at blade 8 However the interpretation ofthe shift in the signal alone cannot provide a robust damagefeature for the rotating blades -erefore the signal for eachblade was subjected to the WPTmethod which decomposedthe signal into different frequency bandwidth signals todetect the damage effectively In this study the wavelet

AECSPECS

Optical sensor

(a)

Magnet added mass

(b)

Figure 7 (a) BTT experimental test rig (b) blade with magnet added mass

0 2 4 6 8 10 12 14 16 18 20Number of cycles

100015

10002

100025

10003

100035

10004

100045

10005

100055

10006

Spee

d of

revo

lutio

n (R

PM)

Figure 8 Speed variation

0 05 1 15 2 25 3Time (secs)

0

05

1

15

2

25

3

35Bl

ade r

espo

nse (

V)

Figure 9 A raw BTT signal from the AECS at a speed of 100 rpm

8 Shock and Vibration

function ldquodb6rdquo with three vanishing moments was chosenwhich satisfied the vanishing moments condition for esti-mating the damage location and severity in the rotatingblades

In order to select the optimal decomposition level theShannon entropy method was employed as briefly dis-cussed in [19] Based on this method the entropy of bothapproximate and detailed coefficients was estimated ateach level At level 2 the entropy was 000933 which wasless than the entropy of the detailed coefficients which was003069 hence the decomposition level 2 was selected asan optimal level to detect the changes of 99 g added mass inthe rotating blade For the case of BTT signals the vicinityof minute changes can be observed from the approximatecomponent energy as shown in Figure 13(a) However itis difficult to predict the damage at the exact location-us the threshold limit with a high confidence intervalwas applied to the WEBMI and the resulting WEBMI-UL

indicates a substantial peak at the exact location of blade 8as shown in Figure 13(b)

In order to check the effectiveness of the other sensorsthe PECS and optical sensor were employed simulta-neously in addition to the AECS to monitor the blade tipdisplacement as shown in Figure 7(a) -e reconstructedBTT signals of the undamaged and the damaged blade 8from the PECS and the optical sensors are shown in Fig-ures 14 and 15 -ere is hardly any change found in theundamaged BTT signal of blade 8 (see Figure 14(a)) fromthe PECS whereas for the damaged signal of blade 8Figure 14(b) shows subtle changes in the time response dueto the added mass placed on blade 8 In fact the amplitudesof the blade response measured from the PECS are very lowcompared to the AECS and the optical sensor Howeverthis will not affect the damage identification process Onthe other hand the optical sensor BTT response of un-damaged blade 8 (see Figure 15(a)) shows no changes but

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(a)

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(b)

Figure 11 AECS reconstructed BTT signals of all blades for a speed of 100 rpm (a) Undamaged and (b) damaged cases

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

35

Blad

e res

pons

e (V

)

Figure 10 Reconstructed blade 1 BTT signal up to four completed revolutions

Shock and Vibration 9

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

function ldquodb6rdquo with three vanishing moments was chosenwhich satisfied the vanishing moments condition for esti-mating the damage location and severity in the rotatingblades

In order to select the optimal decomposition level theShannon entropy method was employed as briefly dis-cussed in [19] Based on this method the entropy of bothapproximate and detailed coefficients was estimated ateach level At level 2 the entropy was 000933 which wasless than the entropy of the detailed coefficients which was003069 hence the decomposition level 2 was selected asan optimal level to detect the changes of 99 g added mass inthe rotating blade For the case of BTT signals the vicinityof minute changes can be observed from the approximatecomponent energy as shown in Figure 13(a) However itis difficult to predict the damage at the exact location-us the threshold limit with a high confidence intervalwas applied to the WEBMI and the resulting WEBMI-UL

indicates a substantial peak at the exact location of blade 8as shown in Figure 13(b)

In order to check the effectiveness of the other sensorsthe PECS and optical sensor were employed simulta-neously in addition to the AECS to monitor the blade tipdisplacement as shown in Figure 7(a) -e reconstructedBTT signals of the undamaged and the damaged blade 8from the PECS and the optical sensors are shown in Fig-ures 14 and 15 -ere is hardly any change found in theundamaged BTT signal of blade 8 (see Figure 14(a)) fromthe PECS whereas for the damaged signal of blade 8Figure 14(b) shows subtle changes in the time response dueto the added mass placed on blade 8 In fact the amplitudesof the blade response measured from the PECS are very lowcompared to the AECS and the optical sensor Howeverthis will not affect the damage identification process Onthe other hand the optical sensor BTT response of un-damaged blade 8 (see Figure 15(a)) shows no changes but

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(a)

Time (secs)0 05 1 15 2

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

(b)

Figure 11 AECS reconstructed BTT signals of all blades for a speed of 100 rpm (a) Undamaged and (b) damaged cases

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

35

Blad

e res

pons

e (V

)

Figure 10 Reconstructed blade 1 BTT signal up to four completed revolutions

Shock and Vibration 9

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

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Submit your manuscripts atwwwhindawicom

the blade 8 damaged response reveals bump characteristics atthe root of the BTT signal as shown in Figure 15(b) -isphenomenon occurs due to the optical sensor picking up thesignal directly from the presence of the magnet It is observedthat the damaged blade BTT signal from the optical sensorprovides the trend for the damage existence and location Stilla robust damage identification methodology is required topredict the exact damage location -us the BTTsignals wereapplied to the WPT methodology which required a level 3decomposition to detect the exact damage (added mass)location in the rotating blades It is found that the estimatedWEBMI is not distinct for the damaged blade corre-sponding to the PECS and the optical sensor cases asshown in Figures 16(a) and 17(a) -erefore the statisticalthreshold limit was applied to the WEBMI to pinpoint the

exact location of the damage as shown in Figures 16(b) and17(b)

44 Multiple Added Masses Locations -e WPT method-ology has identified the single added mass location in therotating blades at constant speed and different sensors casesIn practice damage may occur in more than one location inthe rotating bladed disk Hence this study extends the WPTidentification methodology for the case of multiple damagedblades -e BTT measurements were performed for twoadded masses (each 66 g) located near the roots of blade 4and blade 8 -is study was conducted at 100 rpm -ereconstructed BTT signals were obtained for blades 4 and 8from the three sensors and are shown in Figures 18(a)ndash18(f )

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

WEB

MI-

UL

times10ndash3

(b)

Figure 13 AECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

(b)

Figure 12 AECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

10 Shock and Vibration

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

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Shock and Vibration

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Submit your manuscripts atwwwhindawicom

-ere are some apparent shifts found in the BTT signals asshown in Figures 18(a) 18(d) and 18(f) whereas only subtleshifts are observed in Figures 18(b) 18(c) and 18(e)However it is challenging to detect damage from the shift inthe BTTresponses-erefore the BTTsignals were subjectedto the WPT analysis with the choice of the ldquodb6rdquo waveletfunction which required a level 6 decomposition It ischallenging to detect the damage (added masses) at multiplelocations using the AECS and PECS results even after tryingwith the different component energies For the last com-ponent energy the peaks are distinct only at single locationof the added mass as shown in Figures 19 and 20 Yet theoptical sensor can detect the damage (added masses) atmultiple locations at blades 4 and 8 as shown in Figure 21-erefore the optical sensor is more reliable than the AECSand the PECS sensors to reveal the subtle changes in themultiple locations from the BTT signals

45 Estimation of Damage Severity Damage severity is thethird level of the damage identification methodology after theidentification of damage existence and the location of damage-e Lipschitz exponent ldquoαrdquo was derived from the WPTanalysis to estimate the damage severity in the rotating blade-e formulation of the Lipschitz exponent ldquoαrdquo is brieflyexplained in Sections 23 and 24 -is section discusses thequantification of damage (addedmass) severity in the rotatingblade based on the BTT measurements -erefore the BTTexperiments were performedwith the addedmass varied from11 g to 99 g with an increment of 11 g at blade 8 for a constantspeed of 100 rpm As we observed from Section 44 the opticalsensor is robust to predict the minute changes in the BTTsignals Hence the following discussion regarding the damageseverity is based on the optical sensor results

In this study the wavelet function ldquodb6rdquo was chosenwhich has three vanishing moments and the first wavelet

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

0

05

1

15

2

25

3

35

4

45

5

55

(b)

Figure 15 Optical sensor reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(a)

Time (secs)0 002 004 006 008 01 012 014 016 018

Blad

e res

pons

e (V

)

ndash01

ndash008

ndash006

ndash004

ndash002

0

002

004

006

008

01

(b)

Figure 14 PECS reconstructed BTT signals of blade 8 for a speed of 100 rpm (a) Undamaged and (b) damaged cases

Shock and Vibration 11

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

packet energy was considered in the damage identificationmethodology as shown in Figure 1 -en the Lipschitz ex-ponent ldquoαrdquo was calculated with the input of two differentlevels (eg j 5 and j 9) of coefficients using the relationgiven in Section 24 It is observed that the Lipschitz exponentldquoαrdquo decreases monotonically as the added mass increaseswhich means the differentiability of the function decreases asthe damage severity increases as shown in Figure 22 Anapproximately uniform drop is found up to an added mass of55 g which indicates the sensitivity of the Lipschitz exponentdue to the change in mass up to 55 g However this behaviordecays slowly as added mass increases In addition Figure 22shows that the experimental Lipschitz exponent approxi-mately follows the behavior of a cubic polynomial with an R2

value of 09985 -e Lipschitz exponent ldquoαrdquo has an ability topredict the differentiability of the function for an added massas small as 11 g -e Lipschitz exponent αle n obeys thevanishing moments condition which means the chosen ldquodb6rdquowavelet function was appropriate for this study In order topredict less than 11 g of added mass even higher-orderwavelet functions are desirable -us the Lipschitz expo-nent is a promising index to quantify the damage severity inrotating blades based on the BTT measurements

5 Conclusions

-is study has consideredWPT-based damage identificationin rotating blades and bladed disk using BTTmeasurements

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

times10ndash3

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

WEB

MI-

UL

(b)

Figure 17 Optical sensor results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

4

45

5

WEB

MI-

UL

times10ndash3

(b)

Figure 16 PECS results for the added mass located at blade 8 (a) WEBMI and (b) WEBMI-UL

12 Shock and Vibration

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3Bl

ade r

espo

nse (

V)

UndamDam

(a)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

05

1

15

2

25

3

Blad

e res

pons

e (V

)

(b)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01

ndash005

0

005

01

Blad

e res

pons

e (V

)

(c)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

ndash01ndash008ndash006ndash004ndash002

0002004006008

01

Blad

e res

pons

e (V

)

(d)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

0

1

2

3

4

5

Blad

e res

pons

e (V

)

(e)

UndamDam

0 002 004 006 008 01 012 014 016 018Time (secs)

005

115

225

335

445

5

Blad

e res

pons

e (V

)

(f )

Figure 18 Reconstructed BTTsignals of undamaged and damaged cases of blades 4 and 8 from (a b) AECS (c d) PECS and (e f ) opticalsensor respectively

Shock and Vibration 13

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

5

10

15

20

25

30

35W

EBM

I

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

2

4

6

8

10

12

14

16

18

WEB

MI-

UL

(b)

Figure 19 AECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

05

1

15

2

25

3

35

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

01

02

03

04

05

06

07

08

09

1W

EBM

I-U

L

(b)

Figure 20 PECS results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

02

04

06

08

1

12

WEB

MI

(a)

1 2 3 4 5 6 7 8 9 10 11 12Blade number

0

0005

001

0015

002

0025

003

0035

004

WEB

MI-

UL

(b)

Figure 21 Optical sensor results for the added mass located at blades 4 and 8 (a) WEBMI and (b) WEBMI-UL

14 Shock and Vibration

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

and impact hammer tests To check the feasibility of theWEBMI for the rotating blades the BTT experiments wereconducted at 100 rpm using three sensors for different levelsof added mass and locations -e signal processing of the rawBTT signal was performed before applying the WPT analysis-e reconstructed BTTsignal of each blade was then applied tothe WPTmethodology to estimate the WEBMI It is observedthat the WEBMI can identify the damage (added mass)presence and location in the rotating blades-e optical sensoris robust to predict themultiple addedmasses locations and thesmall damage severity cases compared to the AECS and thePECS -e Lipschitz exponent ldquoαrdquo was employed to estimatethe damage severity in both static bladed disk and the rotatingblades Numerical simulations were performed on a non-rotating bladed disk for various stiffness reductions that rangedfrom 1 to 9 It was found that the experimental results havegood agreement with the numerical results A relationshipbetween the stiffness reduction in the simulations and theadded mass in the experiments was determined and it wasconcluded that the added mass used in this study is approx-imately equivalent to the corresponding stiffness reduction inthe bladed disk For the case of rotating blades the experi-mental Lipschitz exponent ldquoαrdquo decreases monotonically as thedamage severity (added mass) increases and shows goodagreement with a cubic polynomial curve fit Hence theproposed WEBMI is a promising diagnosis tool to detect thedamage presence location and the severity in the bladed diskand rotating blades

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e authors gratefully acknowledge the support of the QatarNational Research Fund through grant number NPRP 7-1153-2-432

References

[1] A Von F Mathieu and M P Tappert ldquoHealth monitoringand prognostics of blades and disks with blade tip sensorsrdquo inProceedings of IEEE Aerospace Conference pp 433ndash440 BigSky MT USA March 2000

[2] G Dimitriadis I B Carrington J RWright and J E CooperldquoBlade-tip timing measurement of synchronous vibrations ofrotating bladed assembliesrdquo Mechanical Systems and SignalProcessing vol 16 no 4 pp 599ndash622 2002

[3] V Georgiev M Holk V Kraus et al ldquo-e blade fluttermeasurement based on the blade tip timing methodrdquo inProceedings of the 15th WSEAS International Conference onSystem pp 270ndash275 Corfu Island Greece July 2011

[4] S Madhavan R Jain C Sujatha and A S Sekhar ldquoVibrationbased damage detection of rotor blades in a gas turbine en-ginerdquo Engineering Failure Analysis vol 46 pp 26ndash39 2014

[5] G Battiato C M Firrone and T M Berruti ldquoForced re-sponse of rotating bladed disks blade tip-timing measure-mentsrdquo Mechanical Systems and Signal Processing vol 85pp 912ndash926 2017

[6] K S Chana and D N Cardwell ldquo-e use of eddy currentsensor based blade tip timing for FOD detectionrdquo in Pro-ceedings of ASME Controls Diagnostics and Instrumentationpp 169ndash178 Berlin Germany June 2008

[7] P Prochzka and F Vank ldquoContactless diagnostics of turbineblade vibration and damagerdquo Journal of Physics ConferenceSeries vol 305 article 012116 2011

[8] M Woike A Abdul-Aziz N Oza and B Matthews ldquoNewsensors and techniques for the structural health monitoring ofpropulsion systemsrdquo Scientific World Journal vol 2013Article ID 596506 10 pages 2013

[9] M Lackner Vibration and Crack Detection in Gas TurbineEngine Compressor Blades using Eddy Current SensorsMassachusetts Institute of Technology Cambridge MA USA2002

[10] S S Guru S Shylaja S Kumar and R Murthy ldquoPre-emptiverotor blade damage identification by blade tip timingmethodrdquo Journal of Engineering for Gas Turbines and Powervol 136 no 7 article 72504 2014

[11] A Chatterjee and M S Kotambkar ldquoModal characteristics ofturbine blade packets under lacing wire damage inducedmistuningrdquo Journal of Sound and Vibration vol 343pp 49ndash70 2015

[12] H Xu Z Chen Y Yang L Tao and X Chen ldquoEffects of crackon vibration characteristics of mistuned rotated bladesrdquoShock and Vibration vol 2017 Article ID 1785759 18 pages2017

[13] B Salhi J Lardis M Berthillier P Voinis and C BodelldquoModal parameter identification of mistuned bladed disksusing tip timing datardquo Journal of Sound and Vibrationvol 314 no 35 pp 885ndash906 2008

[14] J Lin Z Hu Z S Chen Y M Yang and H L Xu ldquoSparsereconstruction of blade tip-timing signals for multi-modeblade vibration monitoringrdquo Mechanical Systems and Sig-nal Processing vol 81 pp 250ndash258 2016

[15] M Pan Y Yang F Guan H Hu and H Xu ldquoSparse rep-resentation based frequency detection and uncertainty

20 30 40 50 60 70 80 90Added mass (g)

02

04

06

08

1

12

14

16

18

2

22

Lips

chitz

expo

nent

(α)

ExperimentCubic polynomial fit

Figure 22 -e change in the experimental Lipschitz exponent dueto damage severity

Shock and Vibration 15

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

reduction in blade tip timing measurement for multi-modeblade vibration monitoringrdquo Sensors vol 17 no 8 pp 1ndash192017

[16] C Zhongsheng Y Yongmin G Bin and H Zheng ldquoBladedamage prognosis based on kernel principal componentanalysis and grey model using subsampled tip-timing signalsrdquoProceedings of the Institution of Mechanical Engineers Part CJournal of Mechanical Engineering Science vol 228 no 17pp 3178ndash3185 2014

[17] R Prakash and S M Srinivasan ldquoRotational mode shapebased added mass identification using wavelet packet trans-formrdquo International Journal for Computational Methods inEngineering Science andMechanics vol 16 no 3 pp 182ndash1872015

[18] P Rajendran and S M Srinivasan ldquoIdentification of addedmass in the composite plate structure based on wavelet packettransformrdquo Strain vol 52 no 1 pp 14ndash25 2016

[19] N Jamia P Rajendran S El-Borgi and M I FriswellldquoMistuning identification in a bladed disk using waveletpacket transformrdquo Acta Mechanica vol 229 no 3pp 1275ndash1295 2018

[20] L Montanari A Spagnoli B Basu and B Broderick ldquoOn theeffect of spatial sampling in damage detection of crackedbeams by continuous wavelet transformrdquo Journal of Soundand Vibration vol 345 pp 233ndash249 2015

[21] J C Hong Y Y Kim H C Lee and Y W Lee ldquoDamagedetection using the Lipschitz exponent estimated by thewavelet transform applications to vibration modes ofa beamrdquo International Journal of Solids and Structures vol 39no 7 pp 1803ndash1816 2002

[22] E Douka S Loutridis and A Trochidis ldquoCrack identificationin beams using wavelet analysisrdquo International Journal ofSolids and Structures vol 40 no 13-14 pp 3557ndash3569 2003

[23] S Loutridis E Douka and A Trochidis ldquoCrack identificationin double-cracked beams using wavelet analysisrdquo Journal ofSound and Vibration vol 277 no 13-14 pp 1025ndash1039 2004

[24] D M Reddy and S Swarnamani ldquoDamage detection andidentification in structures by spatial wavelet based ap-proachrdquo International Journal of Applied Science and Engi-neering vol 10 no 1 pp 69ndash87 2012

[25] B Chen Y Kang P Li and W Xie ldquoDetection on structuralsudden damage using continuous wavelet transform andLipschitz exponentrdquo Shock and Vibration vol 2015 ArticleID 832738 17 pages 2015

[26] S Mallat and S Zhong ldquoCharacterization of signals frommultiscale edgesrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 14 no 7 pp 710ndash732 1992

[27] J Błaszczuk and Z Pozorski ldquoApplication of the Lipschitzexponent and the wavelet transform to function discontinuityestimationrdquo Scientific Research of the Institute of Mathematicsand Computer Science vol 6 no 1 pp 23ndash29 2007

[28] A H S Ang and W H Tang Probability Concepts inEngineeringPlanning and Design Vol I John Wiley amp SonsNew York NY USA 1975

[29] B Salhi J Lardies andM Berthillier ldquoIdentification of modalparameters and aeroelastic coefficients in bladed disk as-sembliesrdquo Mechanical Systems and Signal Processing vol 23no 6 pp 1894ndash1908 2009

16 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom