Rotor Health

8/8/2019 Rotor Health

1/13

Helicopter Rotor Health Monitoring

Using Adaptive Estimation

Jonathan Alkahe

Omri Rand

Yaakov Oshman

Technion Israel Institute of Technology

Department of Aerospace Engineering

Haifa 32000, Israel

Abstract

A new health and usage monitoring methodology for detection and identification of damage ina helicopter rotor is presented. A fullscale rotor analysis in forward flight has been carried outusing a detailed model of the coupled bladefuselage behavior. Several rotor component faults,as well as local blade stiffness defects are considered. A set of Kalman filters is constructed,where the calculated blade tip response, in addition to elastic modes, comprise a state vector.In the proposed approach, each filter is based on the assumption that a particular fault hasoccurred. The best fitting model, according to measurements taken from the truth model, isdetermined in a probabilistic manner. In the numerical study used to demonstrate the perfor-mance of the method, two sets of noisy measurements are generated. The first set is based onblade tip sensors, and the second set consists of nonrotating hub loads. A MonteCarlo anal-ysis followed by a statistical experiment enable a comprehensive view of the statistical natureof the results. A parametric study is presented and conclusions concerning the detectability of

damage in a helicopter rotor and the efficiency of the proposed method are drawn.

Introduction

The detection of damage as a part of self healthand usage monitoring system (HUMS) in struc-tural systems is an important contributor to theirsafety, reliability and structural integrity. Earlydamage detection has the potential of reducinglife cycle costs and possibly increasing replace-ment time intervals. If damage is located and

monitored, then components of the structure maybe replaced before some critical point is reachedand a dangerous failure occurs. Particularly, thecomponents of a helicopter rotor are subjected tohigh periodic loads and expected to perform un-der harsh environmental conditions. These fac-tors, combined with the absence of redundantload paths, frequently resides in early replace-ment of structural components, therefore causing

Graduate Student.Associate Professor.Associate Professor.

Presented at the American Helicopter Society 57thAnnual Forum, Washington, DC, May 9-11, 2001.

Copyright c by the American Helicopter SocietyInternational, Inc. All rights reserved.

an increase in maintenance costs.One class of damage detection methods in

which damage is seen as a change in the param-eters of a structural model is based on modalinformation.17 Typically, modalbased damagedetection methods use a finite element model ofthe system combined with experimental modaldata to determine damage location and extent.The effect of cracks on the natural frequenciesof a cantilever beam is demonstrated in Refs. 34. These cracks were modeled using rotationalsprings with equivalent stiffness. Since naturalfrequencies change very slightly as crack size andlocation varies, the addition of noise, not treatedin these studies, would significantly decrease theidentification capability.

In Ref. 5 the changes in mode shape due to thepresence of structural damage was determined. Afinite element model with reductions of the mod-ulus of elasticity in prescribed segments was im-plemented. It was shown that the elastic rotation

undergoes a step jump in value when crossing thedamage location, while the displacement param-eter takes a change in its slope.


2/13


3/13

The MultipleModel Adaptive Esti-

mation approach

In various estimation problems, specifically indamage detection cases, uncertain parameters ex-ist within the system model used for algorithm

design. Typically, these parameters can undergolarge jump changes. Such problems give rise tothe need for the estimation of parameter valuessimultaneously with estimation of state variables.One means of accomplishing this is the multi-ple model adaptive estimation (MMAE) tech-nique.20,21 The system is assumed to be ade-quately represented by a linear stochastic statemodel, with uncertain parameters affecting thematrices defining the structure of the model orthe noise distribution model. It is further as-sumed that the parameters can take only dis-

crete values. In cases where continuous param-eter values are presented, representative discretevalues have to be chosen throughout the contin-uous range of possible values. A Kalman filter isthen designed for each choice of parameter value,resulting in a bank of K separate filters. Basedon the residuals of each one of these K filters, theconditional probabilities of each discrete parame-ter value being correct (given the measurementhistory up to that time) are evaluated iteratively.This procedure is summarized in Fig. 1.

Filter of

Fault 1

Fault 2

Filter ofUndamaged

Case

ProbabilitieProbabilities

Computation

Filter of2

J

x

r

1

1

x2

r

xJ

r

Measurements

Noisy Model

Figure 1: The MMAE procedure

Following the development presented inRefs. 21,22, consider the system model describedby the firstorder, linear, stochastic differentialstate equation of the form:

x(t) =F(a)x(t)+G(a)w(t) (1)

with noisy measurements described by

z(ti) =C(a)x(ti)+v(ti) (2)

where x(t) is the system state vector and z(t)is the measurement vector. It is assumed thatw(t) and v(t) are independent, zeromean, white

Gaussian noise processes with covariances Q(t)and R(t), respectively. a is a vector containingall the uncertain dynamic parameters given in thesystem model. F(a) is the system plant matrix,G(a) is the noise distribution matrix and C(a)is the measurement matrix. Since a may assume

a continuous range of values over the space of al-lowable parameters, it is necessary to discretize ainto a set ofJvector values: a1, a2,..., aJ. A mul-tiple model adaptive estimator consists of J in-dependent Kalman filters, in which the jth filteris constructed according to a specific parameterset aj. These J filters form a bank of elemen-tal filters which are processed in parallel. Eachelemental filter produces its own estimate of thetrue state, denoted as xj(ti), for the jth hypothe-sized value ofa. The residuals of all J elementalfilters are then used to calculate the probabil-

ity that a assumes the value aj at time ti, forj = 1, 2,...,J. This probability is called the hy-pothesis conditional probability and is denotedas pj(ti). This conditional probability representsthe validity of the jth filters system model attime ti. The hypothesis conditional probabilitiespj(ti), j= 1, 2,...,J, are calculated at each sampletime ti, by the recursive equation:

pj(ti) =fz(ti|a,Z(ti1)) (zi|aj ,Zi1)pj(ti1)Jk=1 fz(ti|a,Z(ti1)) (zi|aj ,Zi1)pk(ti1)

(3)where Z(ti1) is the measurement history fromthe first sample time until sample time ti1,and the innovation probability density functionis given by

fz(ti|a,Z(ti1)) (zi|aj, Zi1) =1

(2)S/2 |Ak (ti)|1/2

exp

1

2rTk (ti)A

1k (ti) rk (ti)

(4)

where S is the number of sensors. The kth filterresidual vector is:

rk(ti) =z(ti)Hk(ti)xk(t

i ) (5)

where xk(ti ) is the kth filter predicted state es-

timate. The kth filtercomputed residual covari-ance matrix, Ak(ti) is calculated by

Ak(ti) =Hk(ti)Pk(ti )H

Tk (ti)+Rk(ti) (6)

where Pk(ti ) is the kth filter prediction er-

ror covariance. The residual of the jth filterplays a major role in determining pj(ti). Asis evident from (3), the filter with the smallestvalue of rTj (ti)A

1j (ti)rj(ti) assumes the largest

conditional hypothesis probability. Thus, thisalgorithm is consistent with the intuition thatthe residuals of a wellmatched filter should be


4/13

smaller (relative to the filters internally com-puted residual covariance, Aj) than the residualsof a mismatched filter. To allow the estimator toadapt to the changing parameter value, the hy-pothesis conditional probabilities are artificiallybounded below by a small number (0.0005). This

ensures preventing any of them from convergingto zero, which would make it very difficult forthem to change significantly in response to a sub-sequent change in true parameter value.

Structural Model

The fullscale rotor analysis has been carried outusing the software package RAPID/Plus,23 whichis capable of modeling general rotorcraft config-urations, conventional helicopters and tilt-rotors.

RAPID/Plus may handle nonuniform and dissim-ilar blades and is therefore suitable to the cur-rent task. Both rigid and elastic blade analysesare possible. Blade elasticity is modeled usinga built-in modal based analysis for structurallypretwisted spars. This analysis enables includingthe blades axial, leadlag, flap and twist elas-tic deformations, designated by u, v, w and ,respectively. The model also includes fully artic-ulated blades with arbitrary pitch, flap and lagoffsets, root springs and dampers, and a detailedcontrol system mechanism (swashplate, elasticpitch links, pitch horn, etc.), which enables a

study of faults in these components. In this workit is assumed that only one fault occurs. Forthe case of rigid articulated blades, the follow-ing component faults are investigated: pitchlinkdamage, lag damper defect, friction in pitch bear-ing and moisture absorption. The case of a localdamage in hingeless elastic blades is also consid-ered.

The damage detection algorithm consists of 5different models running in parallel 4 damagedrotor models along with the baseline undamagedone.

Damage Identification Logic

The fault detection and identification (FDI) pro-cess is carried out during 5 rotor revolutions (ap-proximately 1 sec) in which all the 5 models runin parallel. Detection based on a 5rev. time in-terval, designated as tp, is termed, in this study,singlerun detection process. The decision logicis based on calculating the fitness probability foreach of the models over an inspection time in-terval (designated as td), which includes only the

last revolution. Let pj(ti) denote the hypothe-sis conditional probability of the jth model at adiscrete time ti (3), and qj refer to the fitness

probability of the jth model. Then

qj =

ttd

pj(t)Jk=1

ttd

pk(t)(7)

Let qmax be defined as

qmax maxj{1,2,...,J}

{qj} (8)

The model associated with qmax is said to de-scribe the true damaged behavior in the bestmanner.

In order to provide a comprehensive view ofthe statistical nature of the results, a MonteCarlo analysis24 is carried out, where the samedamaged case is repeated. For each one of thetested cases, the MonteCarlo procedure contin-ues until no change occurs in the model found tobe the most fitting, and its identification prob-

ability, or a limit of 150 runs is reached. Thisprocedure results in estimated probability val-ues for the singlerun process. When the truecase is the case of no damage, the singlerunfalse alarm rate, designated by pFA, is calculated.Singleshot detection and identification proba-bilities result for each one of the cases where afault occurs. These probabilities are designatedby pDand pIrespectively.

Statistical Experiment

The overall false alarm and detection probabili-ties can be controlled using a well designed sta-tistical experiment. Let H0 and H1 denote thehypotheses of no damage and damage, re-spectively. Assume that N is the total numberof singlerun repetitions and n is the number ofruns in which damage was detected. A decisioncriterion is defined as follows

nH1

H0

nD (9)

where nD is a predetermined threshold. When

the true undamaged case is not detected, a falsealarm results (Type I error). The false alarmprobability is calculated using the following ex-pression

PFA P(H1|H0) =N

i=nD

N

i

piFA(1pFA)

Ni

(10)When true damage is not detected, a missed de-

tection (or type II error) occurs. This probabilityis calculated as follows

PMD= 1 PD P(H0|H1) =nD1i=1

N

i

(1 pD)

ipNiD (11)


5/13

A detector operating characteristics (DOC) plot,showing PD vs PFA can be constructed. Usingthis plot, the total number of runs and the thresh-old level can be tuned to achieve an overall lowfalse alarm rate combined with a high detectionprobability.

Rotor component FDI results

Tip response measurements

Consider a typical fullscale articulated 2 bladedfixed shaft rotor with rigid blades, whose prop-erties are listed in Table 1. Forward flight con-ditions (= 0.3) were simulated including trimcommands.

Table 1: Rotor properties.

Radius 7.1 mChord 0.76 mBlade twist angle 9 degBaseline pitch link stiffness 106 N/mBaseline leadlag damper 3000 NmsBaseline pitch damper 10 NmsMass per unit length 20 Kg/mAngular velocity 34 rad/s

A parametric study was carried out, investigat-

ing the influence of various damage levels, for thefaults mentioned in the previous section, com-bined with several noise levels. As mentionedabove, only one fault may occur in one of theblades. Five damage levels were examined (ex-cept for the lag damper fault which has only 3damage levels), along with five noise levels. Thenoise levels presented in the following figures aredimensional, where displacement noise is mea-sured in meters and pitch angle noise is measuredin radians. The measurements taken are tip re-sponse of the two blades (tip flap and leadlagdisplacements along with the tip pitch angle).

Pitch link damage is manifested as a stiffnessreduction caused by a crack. The damage spec-trum includes five levels which vary from 10%stiffness reduction to 30%. Lag damper damageis modeled by reducing the damping coefficient by50%, 60% and 68% (leadlag stability margin).Pitch bearing friction is modeled by an increasein the pitch damping coefficient at the blade root.Five levels are considered: an increase by a fac-tor of 4 up to a factor of 8. Moisture absorption(for the case of a composite blade) is manifestedby an increase in the blade mass per unit length,

from 2% mass increase up to 4% (five levels).Since the performance of any FDI algorithm

is based on differences between the various dam-

aged cases under consideration, an example ofmeasurement differences is presented in Fig. 2.The tip flap displacement difference is shown inFig. 2(a), and Fig. 2(b) shows the leadlag dis-placement differences. The differences are calcu-lated for all damaged models with respect to the

baseline undamaged tip response. Clearly, pitchlink damage results in a relatively large responsedifference and is, therefore, expected to be eas-ily detectable. However, the lag damper damagecauses hardly any difference in the observables,suggesting detection difficulties.

Figs. 37 show the singlerun probability con-tours, estimated using a MonteCarlo analysisconsisting of a maximum of 150 runs. Figs. 3(a),3(b) present the detection and identificationprobability contours for a pitch link fault, respec-tively. The relatively high probability values in-

dicate that this fault is easily detected and iden-tified. Moreover, a low noise level combined witha high damage level produce better detection andidentification results, as can be expected frombeforehand. An interesting phenomenon is re-vealed where the detection probability decreasesas the noise level increases, until a certain pointwhere the former starts to increase. The reasonis that for high noise levels, the differences be-tween the models are masked by the noise, ren-dering similar probabilities (around 0.2) to all themodels. Therefore, theoretically, the detectionprobability, consists of the probability sum of all4 damaged models, tends to rise to a value ofapproximately 0.8. This phenomenon is demon-strated in Figs. 4(a), 5(a) and Fig. 6(a) as well.Figs. 4(a), 4(b) shows the probability contoursfor the lag damper damage. Clearly, this dam-age case is less detectable. As seen from the fig-ures, the detection and identification probabili-ties are not sensitive to the damage level. This isbecause relatively small lag damping values ex-ist even in the undamaged case. Figs. 5(a), 5(b)shows the probability contours for the pitch fric-tion case. As shown, this fault is also relatively

easy to detect and identify. Figs. 6(a), 6(b) showsthe probability contours for the moisture absorp-tion case. In this case, the probability rangeis well covered. Fig. 7 presents the false alarmrate contours. Since all 5 models are included, ateach damage level all 4 faulty models assume thecorresponding damage value. For example dam-age level 1 means 10% pitch link stiffness reduc-tion, 50% lag damping reduction, pitch frictionincrease of a factor of 4 and 2% mass increasedue to moisture absorption. For high noise lev-els the false alarm approaches 0.8, as theoreticalanalysis predicts.

A statistical experiment composed of severalrepetitions of a singlerun process enables some


6/13

0 45 90 135 180 225 270 315 3600.2

0.15

0.1

0.05

0

0.05

0.1

0.15

w

[m]

Pitch linkLag damperPitch frictionMoisture

(a) Tip flap differences w

0 45 90 135 180 225 270 315 3600.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

0.01

v

[m]


(b) Tip leadlag differences v

Figure 2: Blade tip response differences

10 15 20 25 30

104

103

PitchLink Stiffness Reduction [%]

NoiseLevel[m]

0.99

0.980.970

.96

0.95

0.94

0.93

0.92

0.91

(a) Detection results

10 15 20 25 30

104

103


NoiseLevel[m]

0.9

0.8

0.7

0.60.

(b) Identification results

Figure 3: Pitch link damage results

50 55 60 65

104

103

Lag Damping Reduction [%]

NoiseLevel[

m]

0.9

0.8

0.7

0.6

0.5

0.4

0.

30.5

0.6

0.7

0.

(a) Detection results

50 55 60 65

104

103


NoiseLevel[

m] 0.1

0.2

0.30.4

0.5

0.6

0.7

0.8

0.9

(b) Identification results

Figure 4: Lag damper damage results


7/13


8/13

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PFA

PD

N=2N=3N=5N=10

pFA=0.1

pD

=0.8

nD

nD=2

3

(a) Experiment results for a noise level of= 104m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PFA

PD

N=20

N=50

N=100

N=200

N=400

nD

nD=10

24

46

89

pFA=0.4

pD=0.5

(b) Experiment results for a noise level of = 103m

Figure 8: Detector operating characteristics examples

of runs is needed (N400).Let the required overall false alarm and detec-

tion rates assume acceptable representative val-ues of 0.05 and 0.95, respectively. Using theabove statistical experiment, the number of rep-etitions (N) can also be presented as contours,for each fault under consideration. The contourlines in Fig. 9 constitute the smallest value of Nrequired to meet those rates.

Nonrotating hub load measure-

ments

Consider the same rotor as in the previous sec-tion. In this case, only one damage level is con-sidered. A 5% stiffness reduction for the pitchlink damage, 68% lag damping reduction, pitchfriction which results in a pitch damping increaseof factor 1.5 and 0.5% mass increase for the mois-ture absorption case. Note that all these damagelevels are lower that the levels presented in theprevious section. Moreover, a much higher mea-surement noise level is induced, with standarddeviations of 1 [KN] and 1 [KN-m] for the forceand moment measurements, respectively.Two load differences are shown in Fig. 10 as anexample. Fig. 10(a) demonstrates the normal-ized hub force differences in the lateral direc-tion (Fy), and Fig. 10(b) shows the normalizedpitching moment differences (My). The mois-ture absorption case clearly results in larger dif-ferences, indicating high detectability. The otherdamage cases produce load differences boundedby 1 of the noise.

The singlerun identification probability timehistories, for the various damage cases, are shownin Fig. 11. These results indicate that the model

associated with the highest probability is indeedthe correct one. Moreover, during the decisiontime interval td, the probability results are quitedecisive, suggesting that a MonteCarlo analysisis not needed. The high probability values ( 1)indicates that the statistical experiment is alsounnecessary.

Detection of a blade local

stiffness defect based on

hub load measurements

Consider a hingeless fixed shaft rotor with elas-tic blades, with the properties listed in Table 1.The blade beamwise and chordwise stiffnessesand torsional rigidity are: EIb = 7.6 104 Nm2,EIc = 12 105 Nm

2, GJ= 8.6 104 Nm2, respec-tively. The blade local damage, discussed in thissection, is a crack at a specific location alongthe span. This crack is simulated by reducingthe stiffnesses (bending stiffnesses and torsional

rigidity) at a particular finite element in the bladestructural model, as illustrated in Fig. 12.

Damaged section

Undeformed

Deformed

uv

w

Figure 12: A damaged elastic blade


9/13

10 15 20 25 30

104

103


NoiseL

evel[m]

3

5

10

20

50

PFA=0.05

PD

=0.95

(a) Pitch link fault

50 55 60 65

104

103


NoiseL

evel[m]

20

50

100

200

400

PFA=0.05

PD

=0.95

(b) Lag damper fault

4 5 6 7 8

104

103

Pitch Friction Increase Factor

NoiseLevel[m]

3

5

10

20

PFA=0.05

PD

=0.95

(c) Pitch friction fault

2 2.5 3 3.5 4

104

103

Moisture Absorption [%mass]

NoiseLevel[m]

3

5

10

20

50

100

200

400

PFA=0.05

PD

=0.95

(d) Moisture absorption fault

Figure 9: The required number of runs (N)

0 90 180 270 3600.08

0.06

0.04

0.02

0

0.02

0.04

0.06

0.08

Fy

/W

3

3


(a) Normalized lateral force differences Fy/W

0 90 180 270 3600.2

0.15

0.1

0.05

0

0.05

0.1

0.15

0.2

My

/Q

3

3


(b) Normalized pitching moment differences My/Q

Figure 10: Nonrotating hub load differences


10/13

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Revs.

Probability

No damagePitch linkLag damperPitch frictionMoisture

td

(a) No damage case

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability

Revs.


td

(b) Pitch link fault

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Revs.

Probability


td

(c) Lag damper fault

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Revs.

Probability


td

(d) Pitch friction fault

0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Revs.

Probability


td

(e) Moisture absorption fault

Figure 11: Singlerun identification probability time history


11/13

In this study, the damage intensity is modeledby a 5% stiffness reduction. Hub loads are mea-sured with standard deviations of 1 [KN] and 1[KN-m] for the force and moment measurements,

respectively. Four filters are constructed, basedon 4 models in which the damage location x, mea-sured from the hub, assumes 4 discrete normal-ized values: x/R= 0.15, 0.35, 0.55, 0.75. The 5thfilter simulates the undamaged case. The truedamage, also simulated as a 5% stiffnesses reduc-tion, is supposed to occur at a discrete locationx/R= 0.1, 0.2, 0.3 . . . 0.9. (Note that the true lo-cation is never identical to one of the modeledlocations).Fig. 13 gives an example of the damaged case loaddifferences with respect to the undamaged loads.As can be expected from beforehand, the damagelocated near the root results in the largest differ-ence. As the damage location approaches the tip,the differences diminish.

Table 2 summarizes the singlerun results,which indicate good identification capability. Inmost cases, the model in which the damage loca-tion is closest to the true location, indeed receivesthe highest fitness probability. The case wherethe true damage occurs near the tip (x/R= 0.9,marked in red) results in a misseddetection. Ascan be expected, this case constitutes a very dif-ficult problem and requires special treatment.

Table 2: Identification results.

True damage Identified Identificationlocation location probability

No damage No damage 0.990.1 0.15 0.990.2 0.15 0.990.3 0.35 0.910.4 0.35 0.890.5 0.55 0.630.6 0.55 0.99

0.7 0.75 0.990.8 0.75 0.970.9 No Damage 0.90

Conclusions

A modelbased damage detection algorithm fora helicopter rotor, using an adaptive estimationtechnique, incorporating noisy measurements, ispresented. The coupled blade-fuselage dynamic

behavior is introduced using the RAPID/Pluspackage where finite element model of the bladeis utilized. A set of Kalman filters is constructed

0 90 180 270 3600.015

0.01

0.005

0

0.005

0.01

0.015

0.02

Fy

/W

x/R=0.15

x/R=0.35

x/R=0.55

x/R=0.75

(a) Normalized lateral force differences Fy/W

0 90 180 270 3600.08

0.06

0.04

0.02

0

0.02

0.04

0.06

0.08

My

/Q

x/R=0.15

x/R=0.35

x/R=0.55

x/R=0.75

(b) Normalized pitching moment differences My/Q

Figure 13: Nonrotating hub load differences

to simulate various rotor faults. The proposedmethod also enables sensors of various types to

be implemented.

The algorithm presented constitutes a new ap-proach towards damage detection in mechanicalsystems. Contrary to other modelbased dam-age detection methods in helicopter rotors, suchas methods based on neural networks, this ap-proach requires no training stage. Moreover, thisalgorithm treats measurement and process noiseinherently, accounting for the noisy rotor envi-ronment and modeling uncertainties. Combinedwith the modelbased feature, the proposed al-

gorithm eliminates the need for a training stageand enables a wide range of flight regimes. Thedamage detection capability is tested in various


12/13

cases. In general, for low noise levels, this ap-proach produces excellent results. The illustra-tive rotor faults considered in this work demon-strate several levels of detectability. Pitch linkdamage and pitch bearing friction were found tobe highly detectable, for both sets of measure-

ments considered. This emerges from the rela-tively high response sensitivity to pitch changes.On the contrary, lag damper damage was hardto detect using blade tip response measurements,since small damping values are present. Lagdamping changes, in this case, have a small effecton the overall rotor response. The detectability ofthis type of damage was shown to increase signifi-cantly using hub load measurements. Blade mois-ture absorption detectability is also quite high. Incases of poor singlerun performance, the statis-tical experiment suggested, enables sustaining a

low false alarm rate combined with a high detec-tion capability. The case of a blade local damagewas also investigated. It was shown that, usingnoisy hub load measurements, this approach iscapable of detecting, and, in most cases, correctlylocating small stiffness changes along the span.The significant advantage of the proposed ap-proach arises from the filtering process enablingprobabilistic determination based on relativelylittle information. Introducing an external ex-citation in this case would probably increasedamage detectability since the transient sys-tem response will provide additional information.Moreover, other sensor types like fuselage vibra-tion measurements (in trimmed flight) are ex-pected to enhance detection capability. Thesetopics are currently under investigation.

References

1 Linder, D. K. and Kirby, G., Location andEstimation of Damage in a Beam Using Iden-tification Algorithms, AIAA/ASME Adap-tive Structures Forum, Washington, D.C.,April 2122 1994.

2 Kahl, K. and Sirkis, J. S., Damage Detectionin Beam Structures Using Subspace RotationAlgorithm with Strain Data, AIAA Journal,Vol. 34, No. 12, December 1996, pp. 26092614.

3 Ostachowicz, W. M. and Krawczuk, M.,Analysis of the Effect of Cracks on the Nat-ural Frequencies of a Cantilever Beam, Jour-nal of Sound and Vibration, Vol. 150, No. 2,1991, pp. 191201.

4 Sundermeyer, J. N. and Weaver, R. L., OnCrack Identification and Characterization Ina Beam by NonLinear Vibration Analysis,

Journal of Sound and Vibration, Vol. 183,No. 5, 1995, pp. 857871.

5 Yuen, M. M. F., A Numerical Study of theEigenparameters of a Damaged Cantilever,Journal of Sound and Vibration, Vol. 103,

No. 3, 1985, pp. 301310.

6 Kiddy, J. and Pines, D., Eigenstructure As-signment Technique for Damage Detection inRotating Structure, AIAA Journal, Vol. 36,No. 9, September 1998, pp. 16801685.

7 Kiddy, J. and Pines, D., The Effects of Aero-dynamic Damping on Damage Detection inHelicopter Main Rotor Blades, 54th AnnualForum of the American Helicopter Society,Montreal, Canada, May 2527 1999.

8 Ganguli, R. and Chopra, I., Simulation ofHelicopter Rotor-System Structural Damage,Blade Mistracking, Friction and Freeplay,Journal of the American Helicopter Society,Vol. 35, No. 4, July 1998, pp. 591597.

9 Stevens, P. W., Hall, D. L., and Smith, E. C.,A Multidisciplinary Research Approach toRotorcraft Health and Usage Monitoring,52nd Annual Forum of the American Heli-copter Society, Washington, D.C., June 461996.

10 Hass, D. J. and Schaefer, C. G., EmergingTechnologies for Rotor System Health Moni-toring, 52nd Annual Forum of the AmericanHelicopter Society, Washington, D.C., June46 1996.

11 Ganguli, R., Chopra, I., and Hass, D. J., APhisics Based Model for Rotor System HealthMonitoring, 22nd European Rotorcraft Fo-rum, Brighton, UK, September 1996.

12 Yang, M., Chopra, I., and Hass, D. J., Rotor

Sysytem Health Monitoring Using CoupledRotorFuselage Vibration Analysis, 56th An-nual Forum of the American Helicopter Soci-ety, Virginia beach, Virginia, May 24 2000.

13 Larden, B. D., An Analysis of HUMS Vi-bration Diagnostic Capabilities, 53rd An-nual Forum of the American Helicopter So-ciety, Virginia beach, Virginia, April 29May1 1997.

14 Hess, R., Chaffee, M., Page, R., and Rose-berry, K., Realizing an Expandable Open

HUMS Architecture, 56th Annual Forumof the American Helicopter Society, Virginiabeach, Virginia, May 24 2000.


13/13

15 Hass, D. J., Baker, T., Sspracklen, D., andSchaefer, C., Joint Advanced Health andUsage Monitoring System (JAHUMS) Ad-vanced Concept Technology Demonstration(ACTD), 56th Annual Forum of the Amer-ican Helicopter Society, Virginia beach, Vir-

ginia, May 24 2000.

16 Robeson, E., MH47E Structural UsageMonitoring System (SUMS) Fleet Demon-stration Results, 56th Annual Forum of theAmerican Helicopter Society, Virginia beach,Virginia, May 24 2000.

17 Ghoshal, A., Harrison, J., Sundaresan, M. J.,Schulz, M. J., and Pai, P. F., Toward Devel-opement of an Intelligent Rotor System, 56thAnnual Forum of the American Helicopter So-ciety, Virginia beach, Virginia, May 24 2000.

18 Alkahe, J., Rand, O., and Oshman, Y., Dam-age Detection in a Rotating Helicopter BladeUsing an Adaptive Estimator, AIAA Guid-ance, Navigation and Control Conference,Denver, CO, August 1417 2000.

19 Alkahe, J., Rand, O., and Oshman, Y.,Damage Detection in a Helicopter Rotor byAdaptive Estimation, 26th European Rotor-craft Forum, The Hague, The Netherlands,September 2629 2000.

20

Magill, D. T., Optimal Adaptive Estima-tion of Sampled Stochastic Processes, IEEETransactions on Automatic Control, Vol. AC10, No. 4, October 1965, pp. 434439.

21 Maybeck, P. S., Stochastic Models, Estima-tion, and Control, Vol. 2, Academic Press,NY, 1982.

22 Stepaniac, M. J. and Maybeck, P. S.,MMAEbased Control Redistribution Ap-plied to the VISTA F16, IEEE Transactionson Aerospace and Electronic Systems , Vol. 34,

No. 4, October 1998, pp. 12491259.23 Rand, O., RAPID/Plus: Rotorcraft Analy-

sis for Preliminary Design + Aeroelasticity:User Manual, Tech. rep., Haifa, Israel, Jan-uary 1999.

24 Freund, J. E., Modern Elementary Statistics ,PrenticeHall, New Jersey, 6th ed., 1984.

Rotor Health

Documents

Transcript of Rotor Health