Fault Detection and Severity Analysis of Servo Valves Using ...

Fault Detection and Severity Analysis of Servo Valves UsingRecurrence Quantification Analysis

M. Samadani1, C. A. Kitio Kwuimy2, and C. Nataraj3

1,2,3 Department of Mechanical Engineering, Villanova University, Villanova, PA, 19085, [email protected]

[email protected]@villanova.edu

ABSTRACT

This paper presents the application of recurrence plots (RPs)and recurrence quantification analysis (RQA) in model-baseddiagnostics of nonlinear systems. A detailed nonlinear math-ematical model of a servo electro-hydraulic system has beenused to demonstrate the procedure. Two faults have beenconsidered associated with the servo valve including the in-creased friction between spool and sleeve and the degradationof the permanent magnet of the valve armature. The faultshave been simulated in the system by the variation of the cor-responding parameters in the model and the effect of thesefaults on the RPs and RQA parameters has been investigated.A regression-based artificial neural network has been finallydeveloped and trained using the RQA parameters to estimatethe original values of the faulty parameters and identify theseverity of the faults in the system.

1. INTRODUCTION

Servo valves are complex electro-hydraulic systems whichconsist of very precise and sensitive components. A smallchange in the dimensions, metallurgical characteristics, orother parameters of these components can produce instabil-ity, error or even failure in the performance of the system.Hence, it is important to utilize effective algorithms and tech-niques to constantly monitor the performance of such systemsand identify faults that can appear in them along with locationand severity of the faults. Due to highly nonlinear character-istics of servo valves, it is essential to use techniques that canperform effectively in different domains of the nonlinear re-sponse.

In this paper, we introduce the application of recurrence plots(RPs) and recurrence quantification analysis (RQA) in model-based diagnostics of servo valves. The approach is general

Mohsen Samadani et al. This is an open-access article distributed under theterms of the Creative Commons Attribution 3.0 United States License, whichpermits unrestricted use, distribution, and reproduction in any medium, pro-vided the original author and source are credited.

though and can be applied to any complex nonlinear system.Model-based fault detection approaches can be classified intothree main categories of parity relation (Chow & Willsky,1984; Gertler, 1997; Gertler & Singer, 1990), observer/filter-based (Frank & Ding, 1997; Patton, Frank, & Clarke, 1989)and parameter estimation (Isermann, 1982, 1984) methods.In parameter estimation method which is the main scope ofthis research, the parameters of the defective system are es-timated and compared with the original parameters of thehealthy system. The changes in parameter values are in manycases directly related to the defects. Therefore, this knowl-edge facilitates the fault diagnostics task. The parameter esti-mation technique has been used by many researchers for thedetection of the faults in complex systems such as jet engines,rolling element bearings, DC motors, etc. (Baskiotis, Ray-mond, & Rault, 1979; Kappaganthu & Nataraj, 2011a; Liu,Zhang, Liu, & Yang, 2000). More information about param-eter estimation based fault detection can be found in (Frank,Ding, & Koppen-Seliger, 2000; Isermann, 1997, 2005a, 2005b).

In general, nonlinear dynamic systems can exhibit diversephenomena including multi-periodic, quasi-periodic and chaoticresponses, as well as bifurcation and limit cycles. Many stud-ies have reported the emergence of these complex nonlin-ear phenomena in industrial machinery originating from de-fects or due to their nonlinear nature (Sankaravelu, Noah,& Burger, 1994; Mevel & Guyader, 1993; Kappaganthu &Nataraj, 2011b). The prevailing parameter estimation meth-ods are based on system identification techniques which aremostly suitable for linear systems and are not effective whenthe system response includes complex nonlinear phenomena.Moreover, the available methods require a pre-specified rangefor the initial guess of the parameter values which might notalways be available in practice.

This paper presents the initial investigation of a new approachfor parameter estimation-based diagnostics of nonlinear sys-tems, based on the extracted information from the nonlin-ear response. Our main thesis is that the nonlinear dynamic

1

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response of practical systems contains valuable informationabout the system including knowledge that could be used todevelop an effective diagnostics framework. In an earlierwork (Samadani, Kwuimy, & Nataraj, 2014, 2013) we pre-sented an approach to extract information and features fromthe phase plane plot of the response in the periodic domain.The present paper extends that approach to systems with evenmore complex nonlinearities including quasi-periodicity us-ing more advanced nonlinear dynamic analysis tools. Theanalysis in this paper is based on the recurrence propertiesof the system output in its reconstructed state space. In manycases, the phase space has dimensions higher than three whichcan only be visualized by projection into the two or three-dimensional sub-spaces. However, recurrence plots enable usto visualize and investigate certain aspects of the phase spacetrajectory in a two dimensional representation. The methodof recurrence plots is a strong and effective tool for analy-sis of complex systems which has already been used for faultidentification and diagnostics of nonlinear systems (Kwuimy,Samadani, Kappaganthu, & Nataraj, 2015). However, this isthe first effort to use this method in a model-based approachto estimate the parameters of the system for fault diagnostics.

A detailed nonlinear mathematical model has been used tosimulate the performance of the electro-hydraulic system. Theanalyses have been performed on the output flow of the servovalve. Three different electrical current signals including aperiodic, a bi-periodic and a quasi-periodic signal have beeninput to the servo valve to investigate the performance of thealgorithm in various nonlinear domains. RQA parametershave been obtained from the reconstructed phase space andused as the response features to identify dynamical changesin the system. Finally, an artificial neural network has beentrained for mapping of the feature space to the parameterspace.

The remaining parts of this paper are organized as follows.In section 2, a detailed mathematical model of the electro-hydraulic valve has been derived. In section 3, the definitionof recurrence plots and RQA parameters have been provided.Section 4 describes the diagnostics algorithm along with theanalyses and subsequent discussions. The conclusion is madein section 5.

2. MODELING OF THE ELECTRO-HYDRAULIC SERVOSYSTEM

A detailed dynamical model of a two-stage servo valve with amechanical feedback has been used in the analyses. This sys-tem is shown in Fig. 1. Only the final equations are presentedhere. The detailed explanation of formulae can be found in(Samadani, Behbahani, & Nataraj, 2013; Rabie, 2009; Gordic,Babic, & Jovicic, 2004). The definition of system states andparameters along with the nominal values of the parametershave been presented in the nomenclature.

Neglecting the effect of the magnetic hysteresis, the net torqueon the armature is given by the following expression.

Figure 1. Functional schematic of the electro-hydraulicservo system [18]

T = Kiie (1)

where the coefficient Ki can be calculated by:

Ki =NλpµoAL

2x2o

(2)

The motion of the armature and the elements attached to it isdescribed by the following equations:

T = Jd2θ

dt2+ fθ

dθ

dt+KT θ + TL + TP + TF (3)

TP =π

4d2f (P2 − P1)Lf (4)

The feedback torque depends on the displacement of the spooland the angle of the flapper and can be given by:

TF = FSLS = KS(LSθ + x)LS (5)

The rotational displacement of the flapper is limited mechan-ically by the jet nozzles. When the flapper reaches any of theside jet nozzles, a counter torque TL is applied on it whichcan be calculated by the following equation:

2


TL =

{0, |xf | < xi

Rsdθdt − (|xf | − xi)KLfLf sign(xf ), |xf | > xi

(6)

The flow rates through the flapper valve restrictions are givenby the following equations:

Q1 = CDAo

√2

ρ(Ps − P1) = C12

√(Ps − P1) (7)

Q2 = CDAo

√2

ρ(Ps − P2) = C12

√(Ps − P2) (8)

Q3 = Cdπdf (xi + xf )√

2ρ (P1 − P3)

= C34(xi + xf )√(P1 − P3)

(9)

Q4 = Cdπdf (xi − xf )√

2ρ (P2 − P3)

= C34(xi − xf )√(P2 − P3)

(10)

xf = Lfθ (11)

Q5 = CdAs

√2

ρ(P3 − PT ) = C5

√(P3 − PT ) (12)

By using the continuity equation for the chambers of the flap-per valve, the following expressions can be deduced:

Q1 −Q3 +Asdx

dt=

Vo −Asx

B

dP1

dt(13)

Q2 −Q4 −Asdx

dt=

Vo +Asx

B

dP2

dt(14)

Q3 +Q4 −Q5 =V3

B

dP3

dt(15)

The motion of the spool is governed by the following equa-tions.

As(P2 − P1) = msd2x

dt2+ fs

dx

dt+ Fj + Fs (16)

Fj =

(

ρQ2b

CcAb+

ρQ2d

CcAd

)sign(x) for x > 0

(ρQ2

a

CcAa+

ρQ2c

CcAc

)sign(x) for x < 0

(17)

Ignoring the effect of transmission lines between the valveand the symmetrical hydraulic cylinder, the flow rates throughthe valve restriction areas are given by:

Qa = CdAa(x)

√2

ρ(PA − PT ) (18)

Qb = CdAb(x)

√2

ρ(Ps − PA) (19)

Qc = CdAc(x)

√2

ρ(Ps − PB) (20)

Qd = CdAd(x)

√2

ρ(PB − PT ) (21)

The area of the valve restrictions are given by:

{ Aa = Ac = ωcfor x ≥ 0

Ab = Ad = ω√(x2 + c2)

(22)

{Aa = Ac = ω

√(x2 + c2)

for x ≤ 0Ab = Ad = ωc

(23)

Considering the internal leakage and neglecting the externalleakage, the following equations can be obtained by applyingthe continuity equation to the cylinder chambers.

Qb −Qa −APdy

dt− (PA − PB)

Ri=

(Vc +Apy)

B

dPA

dt(24)

Qc−Qad+APdy

dt− (PA − PB)

Ri=

(Vc −Apy)

B

dPB

dt(25)

Finally, the equation of motion for the cylinder piston is givenby:

AP (PA − PB) = mpd2y

dt2+ fP

dy

dt+Kby (26)

2.1. Servo Valve Faults

Various faults leading to parameter changes can appear in aservo valve. Three of the common defects in servo valves are:

• Change of magneto-motive force of the permanent mag-net λp over time, which leads to the change of Ki

• Change of spool friction coefficient fs, due to clearancevariations or contamination

3


• Decrease in the diameter of nozzles df due to contami-nation or residuals

Sensitivity analyses show that the change of df does not sig-nificantly affect the dynamics of the system and hence, cannotbe captured by dynamical analysis, unless the contaminationblocks the nozzles completely. In this research, we assumethe first two faults and use the response of the system in orderto identify changes in those parameters. We suppose that onecan measure the position of cylinder and the output flow ofthe valve.

3. RECURRENCE PLOTS AND RECURRENCE QUANTIFI-CATION ANALYSIS

The recurrence plots analysis for time series is based on theanalysis of a matrix R whose elements are defined as:

Rij =

{1, Φi ≈ Φj ,

0, Φi = Φj ,, i, j = 1...N, (27)

where Φi = (ϕ1i, ϕ2i, ..., ϕmi) is a state vector the dimensionof m, N is the length of the time series, i and j are relatedrespectively to the row and column of the matrix, and Φi ≈Φj means equality up to an error ϵ.

If only a time series is available, the state vector Φ can bereconstructed by using delay embedding theorem (Takens,1981; Abarbanel, 1996; Fontaine, Dia, & Renner, 2011; Kwuimy,Samadani, & Nataraj, 2014). In this paper, the state vector hasbeen reconstructed from the output flow of the valve. Thisis done in two steps: The first step consists of estimating theprescribed time lag T and the second step would be the evalu-ation of the embedded dimension m. In practice, if u(i) is theavailable time series, the value of T corresponds to the firstminimum of the average mutual information between the val-ues of u(i) and u(i+T ), and the embedding dimension can bededuced from the method of false nearness neighbor (Takens,1981; Abarbanel, 1996; Kantz & Schreiber, 2004; Kwuimyet al., 2014). Once the values of T and m are obtained, thestate vector Φ can be reconstructed by:

Φ = (u(i), u(i+ T ), . . . , u(i+ T (m− 1)) (28)

The elements of the matrix R are thus obtained by compar-ing the state of the system at time i and j with a thresholdprecision ϵ. Thus, formally, one has:

Rij = θ(ϵ− ||Φi −Φj ||), (29)

with ||.|| been the Euclidian norm (L2-norm) and θ(y) is theheaviside function defined as:

θ(y) = 1 for y > 0 and θ(y) = 0 for y < 0

Once we have the R matrix, the RP graph is obtained by plot-ting the Rij points in the i and j plane with different colors.By definition, RP graphs are always symmetric (Rij = Rji)and always have a central diagonal.

In order to go beyond the qualitative impression given byRPs, complexity measures have been developed that quantifythe structures of RPs and are called recurrence quantificationanalysis (RQA) (Zbilut, Thomasson, & Webber, 2002). Inthis paper, we use the following RQA parameters to quantifythe RP of the system under various fault conditions.

• Recurrence rate (RR)

The recurrence rate is the simplest RQA parameter whichmeasures the density of recurrence points in a recurrenceplot.

RR =1

N2

N∑i,j=1

Ri,j(ϵ) (30)

• Determinism (DET )

The determinism is the percentage of recurrence pointswhich form diagonal lines in the recurrence plot of min-imal length ℓmin.

DET =

∑Nℓ=ℓmin

ℓP (ℓ)∑Nℓ=1 ℓP (ℓ)

(31)

where P (ℓ) is the frequency distribution of the lengths ℓof the diagonal lines.

• Laminarity (LAM )

In the same way, the amount of recurrence points form-ing vertical lines can be quantified by laminarity.

LAM =

∑Nv=vmin

vP (v)∑Nv=1 vP (v)

(32)

where P (v) is the frequency distribution of the lengths vof the vertical lines, which have at least a length of vmin.

• Average length of the diagonal lines (L)

L is related with the predictability time of the dynami-cal system.

L =

∑Nℓ=ℓmin

ℓP (ℓ)∑Nℓ=ℓmin

P (ℓ)(33)

• Trapping Time (TT )

The trapping time measures the average length of the ver-tical lines.

4


TT =

∑Nv=vmin

vP (v)∑Nv=vmin

P (v)(34)

• Entropy (ENTR)

The probability that a diagonal line has exactly lengthℓ can be estimated with p(ℓ) = P (ℓ)∑N

ℓ=ℓminP (ℓ)

. ENTR

is the Shannon entropy of this probability which reflectsthe complexity of the RP in respect of the diagonal lines.

ENTR = −N∑

ℓ=ℓmin

p(ℓ) ln p(ℓ) (35)

4. FAULT DIAGNOSTICS AND SEVERITY ANALYSIS

A standard procedure to identify faults and dynamical changesin systems is to input a pre-specified signal to the system, ob-tain the response and compare the signatures of the responsewith the ones of the system response in healthy conditions.Here we have input an electrical current signal to the servovalve, and measured the output flow of the valve. The statespace of the system has then been reconstructed from the out-put flow signal and the effect of the parameter changes onthe response has been evaluated using the defined recurrencequantification parameters.

In order to investigate the effectiveness of the approach in var-ious domains of the nonlinear response, three different signalshave been input to the servo valve including:

• Periodic input signal

i = 0.01 sin 50t

• Bi-periodic input signal

i = 0.01 sin 50t+ 0.005 sin 75t

• Quasi-periodic input signal

i = 0.01 sin 50t+ 0.005 sin 50πt

To better understand the effect of dynamical changes in re-currence point of view, the performance of the system is firstanalyzed and presented under three sample fault cases includ-ing:

• Healthy system

• Fault 1: Ki decreased by %50

• Fault 2: fs increased by %500

Figure 2 shows the output flow of the valve versus time, cor-responding to the three input cases, for the three sample faultscenarios.

0 0.2 0.4 0.6 0.8 1

−5

0

5

x 10−5

Out

put f

low

(m

3 /s)

0 0.2 0.4 0.6 0.8 1

−5

0

5

x 10−5

Out

put f

low

(m

3 /s)

0 0.2 0.4 0.6 0.8 1

−5

0

5

x 10−5

Out

put f

low

(m

3 /s)

Time (sec)

Healthy Fault 1 Fault 2

(a)

(b)

(c)

Figure 2. Time response of the system for (a): periodic, (b):bi-periodic and (c):quai-periodic inputs to the servo valve for

three fault cases

In order to obtain the recurrence matrix and plots, we need toreconstruct the state space from the output flow time series.As discussed earlier, the appropriate time lag for the recon-struction of the state space corresponds to the first minimumin the average mutual information of the signal. Using thismethod, the time lag was determined to be T=50. By applica-tion of the method of false nearest neighbors, we found thatthe minimum embedding dimension for the system is d=2.

Figure 3 shows the recurrence plots of the reconstructed statespace, for the three inputs and the three sample fault scenar-ios.

As can be seen, the plots consist of complicated patterns whichare hard to interpret. In addition, there is little differencebetween them for the three fault cases, which is not easilydetectable. Hence, we need quantitative measures to extractinformation from these plots.

Table 1 shows the computed RQA parameters for all ninecases. In this table p, bp, and qp correspond to the responseof the system to the periodic, bi-periodic and quasi-periodicinput signals, respectively. As can be seen, even though thedifference of the recurrence plots for the three fault cases ishardly detectable by eye, RQA parameters can easily distin-guish the differences and detect the alternations in the signal.

5


(a)

(b)

(c)

Figure 3. From left to right: Recurrence plots for periodic, bi-periodic and quasi-periodic inputs to the valve (a): Healthysystem (b): Fault 1 (c): Fault 2

Table 1. RQA parameters for three defect cases

Defect-free Defect 1 Defect 2

RQA Parameter p bp qp p bp qp p bp qp

RR 0.0269 0.0160 0.0071 0.0269 0.0159 0.0070 0.0266 0.0160 0.0081DET 0.9997 0.9994 0.9589 0.9997 0.9996 0.9589 0.9994 0.9996 0.9772LAM 0.9999 0.9993 0.9548 0.9999 0.9993 0.9530 0.9997 0.9992 0.9790L 107.1795 102.6667 5.6023 87.2343 95.2610 5.5580 103.0904 104.3878 6.7376TT 7.4741 7.7383 4.4261 7.4741 7.7383 4.4261 7.4678 7.7575 4.9349

ENTR 3.7933 3.9199 1.9403 3.7933 3.9199 1.9403 3.8093 3.9572 2.2226

6


4.1. Mapping of Features to Parameters

So far we have illustrated how the response of the systemis affected with the change of parameters and how it can bedetected by using the RQA parameters. We were able to mea-sure and represent these influences by quantitative criteria. Incontrast to this, the diagnostics problem is the inverse prob-lem, where we would like to predict the system parametersgiven its nonlinear response. In order to do that, machinelearning techniques can be used which have been proved tobe effective for diagnostics of machinery (Kankar, Sharma,& Harsha, 2011) and biomedical diagnostics (Jalali et al.,2014). In this paper, an artificial neural network (ANN) hasbeen used. For this purpose, a two-layer feed-forward net-work with ten sigmoid hidden neurons and linear output neu-rons was developed. The inputs used for the training of theneural network were vectors of RQA parameters and the out-puts were vectors of Ki and fs. The data was obtained byrandom selection of the values of Ki and fs in the intervals[0.1,0.6] and [1,100], respectively, simulation of the systemand computation of the response features, i.e. RQA parame-ters, each time. A total number of 100 samples was used fortraining, validation and test of the network.

Figures 4, 5, and 6 show the regression plots of the networkoutputs with respect to targets for training, validation and testsets along the Regression (R) values for each case. For a per-fect fit, the (R) value should be close to 1 and the data in theregression plot should fall along a 45 degree line, where thenetwork outputs are equal to the targets. As can be seen, inthis case, all the points have fallen along the 45 degree lineand the R values are equal to 1, which are representatives ofan accurate mapping of the features space to the parametersspace.

Table 2 shows some samples of the performance of the pa-rameter estimation systems developed with periodic, bi-periodicand quasi-periodic inputs. K∗

i and f∗s represent the estimated

values of Ki and fs. This table shows that the proposedmethod has a very good ability to predict the original param-eters of the system using the defined features, especially withthe periodic input signal.

Table 2. Some examples of the performance of the parameterestimation system

Periodic Bi-periodic Quasi-periodic

Ki fs K∗i f∗

s K∗i f∗

s K∗i f∗

s

0.1 5 0.098 5.879 0.096 6.087 0.123 6.0880.3 50 0.289 50.623 0.275 51.025 0.356 51.6100.6 100 0.591 101.511 0.592 98.410 0.633 102.2140.2 25 0.207 24.234 0.206 25.324 0.227 26.6650.4 2 0.390 2.012 0.384 2.622 0.383 3.0010.5 10 0.512 9.824 0.488 9.357 0.520 9.512

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Ou

tpu

t ~=

1*T

arg

et +

0.0

0083

Training: R=0.99909

DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Ou

tpu

t ~=

1*T

arg

et +

0.0

062

Validation: R=0.9966

DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Ou

tpu

t ~=

0.9

8*T

arg

et +

0.0

13

Test: R=0.99711

DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Ou

tpu

t ~=

1*T

arg

et +

0.0

04

All: R=0.99835

DataFitY = T

Figure 4. Outputs of the artificial neural network withrespect to target values for the periodic input signal

5. CONCLUSION

We used recurrence plots and recurrence quantification anal-ysis for model-based fault detection and diagnostics of anelectro-hydraulic system. It was shown that the nonlinearresponse of the system contains valuable information aboutthe system that can be used for this purpose. The analy-ses were performed with the assumption that only the out-put response of the system (here output flow of the valve) isavailable; and the other states were reconstructed using themethod of time delays. The recurrence plots were producedand the corresponding recurrence analyses were performedon the reconstructed state space of the system. It was shownthat even though the recurrence plots for the system with dif-ferent faults can be similar, the dynamical changes can bedetected by RQA parameters. An artificial neural networkwas trained using the RQA parameters to estimate the faultyparameters of the system. It was shown that RQA parame-ters can be used as effective features for characterizing thenonlinear response of the system even in the multi-periodicor quasi-periodic domain with complex nonlinearities.

In this study, the proposed method was only applied to numer-ical data obtained from the mathematical model of the sys-tem. Although the results were promising, there is no guar-antee that we can obtain the same prediction accuracy for realexperimental data. Hence, it is of importance to confirm theeffectiveness of the approach with experimental analysis. Inaddition, only two parametric defects (defects due to changeof parameter values) were considered in this paper, whereasin real world applications we might have multiple paramet-

7


0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Ou

tpu

t ~=

0.9

9*T

arg

et +

0.0

053

Training: R=0.99676

DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

TargetO

utp

ut

~= 0

.94*

Tar

get

+ 0

.031


DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Ou

tpu

t ~=

0.9

4*T

arg

et +

0.0

34

Test: R=0.98857

DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Ou

tpu

t ~=

0.9

7*T

arg

et +

0.0

15

All: R=0.99472

DataFitY = T

Figure 5. Outputs of the artificial neural network withrespect to target values for the bi-periodic input signal

ric defects in the system or even defects of the type that canchange the structure of the mathematical model of the sys-tem. The present method can be extended with using moredynamical and statistical features in order to be able to char-acterize the system response and diagnose the faults in suchconditions, which is currently the focus of our research.

ACKNOWLEDGMENT

This work is supported by the US Office of Naval Researchunder the grant ONR N00014-13-1-0485. We deeply appre-ciate this support. Thanks are due to Mr Anthony Seman IIIof ONR.

NOMENCLATUREa Width of spool edges m 4e-03A Area of air gap m2

A5 Drain orifice area m2

ALArea of the flow between spooland sleeve edges m2

Ao Orifice area m2

Aa′ , Ab′ ,Ac′ , andAd′

Spool valve restrictions areas m2

AP Piston area m2 7e-04As Spool cross-sectional area m2

b Width of sleeve slots m 4e-03B Bulk modulus of oil Pa 1.5e09c Spool radial clearance m 2e-06Cc Contraction coefficient

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Out

put ~

= 0.

99*T

arge

t + 0

.007

Training: R=0.99415

DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Out

put ~

= 1*

Tar

get +

−0.

023


DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Out

put ~

= 1*

Tar

get +

−0.

0046

Test: R=0.9834

DataFitY = T

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Target

Out

put ~

= 1*

Tar

get +

−0.

0015

All: R=0.99238

DataFitY = T

Figure 6. Outputs of the artificial neural network withrespect to target values for the quasi-periodic input signal

Cd and CD Discharge coefficients 0.661df Flapper nozzle diameter m 5e-04d5 Diameter of return orifice m 6e-04ds Spool diameter m 4.6e-03fθ Armature damping coefficient Nms/rad 0.002Fj Hydraulic momentum force Nfp Piston friction coefficient Ns/m 1000fs Spool friction coefficient Ns/m 3.05

FsForce acting at the extremity ofthe feedback spring N

HMagneto-motive force per unitlength A/m

ib Feedback current Aic Control current Aie Torque motor input current A

JMoment of inertia of rotatingpart Nms2 5e-07

Kb Load coefficient N/m 0KFB Feedback gain A/m 1KLf Equivalent flapper seat stiffness N/m 1e6Ki Current-torque gain Nm/A 0.559Ks Stiffness of the feedback spring N/m 900KT Stiffness of flexure tube Nm/rad 10.68

K Rotational angle-torque gain Nm/rad 9.45e-4L Armature length m 0.029Lf Flapper length m 0.009

LsLength of the feedback springand flapper

m 0.03

8


Lsp Length of spool land m 1.5e-02mp Piston mass kg 5ms Spool mass kg 0.2

P1Pressure in the left side of theflapper valve Pa

P2Pressure in the right side of theflapper valve Pa

P3Pressure in the flapper valvereturn chamber Pa

PA and PB Hydraulic cylinder pressures PaPs Supply pressure Pa 1.2e7PT Return line pressure Pa 0Q Flow rate m3/sQ1 Flow rate in the left orifice m3/sQ2 Flow rate in the right orifice m3/sQ3 Left flapper nozzle flow rate m3/sQ4 Right flapper nozzle flow rate m3/sQ5 Flapper valve drain flow rate m3/sQa, Qb,Qc, and Qd

Flow rates through the spoolvalve restrictions m3/s

Ri Resistance to internal leakage Ns/m5 1e20

RsFlapper seat dampingcoefficient Nms/rad 5000

TTorque of electromagnetictorque motor Nm

TF Feedback torque Nm

TLTorque due to flapperdisplacement limiter Nm

TPTorque due to the pressureforces Nm

V3Volume of the flapper valvereturn chamber m3 5e-06

VcHalf of the volume of oil fillingthe cylinder m3 1e-04

VoInitial volume of oil in thespool side chamber m3 2e-06

x Spool displacement m

xaDisplacement of the armatureend

m

xfFlapper displacement on thelevel of the jet nozzles

m

xi Flapper displacement limit m 3e-05

xoLength of the air gap in theneutral position of armature

m 3e-04

λ Magneto-motive force A

λpMagneto-motive force of thepermanent magnet A 66.75

µ Permeability Vs/Amµo Permeability of the air Vs/Am 4e-07µr Relative permeabilityρ Oil density kg/m3 867

ω Width of ports on the valvesleeve

m 0.014

θ Armature rotation angle rad

REFERENCES

Abarbanel, H. D. I. (1996). Analysis of observed chaoticdata. Springer, New York.

Baskiotis, C., Raymond, J., & Rault, A. (1979). Parameteridentification and discriminant analysis for jet enginemachanical state diagnosis. In 18th IEEE Conferenceon Decision and Control including the Symposium onAdaptive Processes (Vol. 18, pp. 648–650).

Chow, E., & Willsky, A. (1984). Analytical redundancy andthe design of robust failure detection systems. IEEETransactions on Automatic Control, 29(7), 603–614.

Fontaine, S., Dia, S., & Renner, M. (2011). Nonlinear frictiondynamics on fibrous materials, application to the char-acterization of surface quality. part i: global character-ization of phase spaces. Nonlinear Dynamics, 66(4),625–646.

Frank, P., Ding, S. X., & Koppen-Seliger, B. (2000). Currentdevelopments in the theory of FDI. In Proceedings ofSAFEPROCESS (Vol. 1, pp. 16–27).

Frank, P., & Ding, X. (1997). Survey of robust residual gen-eration and evaluation methods in observer–based faultdetection systems. Journal of Process Control, 7(6),403–424.

Gertler, J. (1997). Fault detection and isolation using par-ity relations. Control Engineering Practice, 5(5), 653–661.

Gertler, J., & Singer, D. (1990). A new structural frameworkfor parity equation–based failure detection and isola-tion. Automatica, 26(2), 381–388.

Gordic, D., Babic, M., & Jovicic, N. (2004). Modellingof spool position feedback servovalves. InternationalJournal of Fluid Power, 5(1), 37–51.

Isermann, R. (1982). Parameter adaptive control algorithms–a tutorial. Automatica, 18(5), 513–528.

Isermann, R. (1984). Process fault detection based on mod-eling and estimation methods–a survey. Automatica,20(4), 387–404.

Isermann, R. (1997). Supervision, fault-detection and fault-diagnosis methods–an introduction. Control Engineer-ing Practice, 5(5), 639–652.

Isermann, R. (2005a). Fault-diagnosis systems: an introduc-tion from fault detection to fault tolerance. Springer.

Isermann, R. (2005b). Model-based fault-detection anddiagnosis–status and applications. Annual Reviews inControl, 29(1), 71–85.

Jalali, A., Buckley, E. M., Lynch, J. M., Schwab, P. J., Licht,D. J., & Nataraj, C. (2014, Jul). Prediction of periven-tricular leukomalacia occurrence in neonates after heartsurgery. IEEE Journal of Biomedical and Health Infor-matics, 18(4), 1453–1460.

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Kankar, P., Sharma, S. C., & Harsha, S. (2011). Fault diag-nosis of ball bearings using machine learning methods.Expert Systems with Applications, 38(3), 1876–1886.

Kantz, H., & Schreiber, T. (2004). Nonlinear time seriesanalysis. Cambridge University Press.

Kappaganthu, K., & Nataraj, C. (2011a). Mutual informa-tion based feature selection from data driven and modelbased techniques for fault detection in rolling elementbearings. In ASME 2011 International Design Engi-neering Technical Conferences and Computers and In-formation in Engineering Conference (pp. 941–953).

Kappaganthu, K., & Nataraj, C. (2011b). Nonlinear mod-eling and analysis of a rolling element bearing with aclearance. Communications in Nonlinear Science andNumerical Simulation, 16(10), 4134–4145.

Kwuimy, C. A. K., Samadani, M., Kappaganthu, K., &Nataraj, C. (2015). Sequential recurrence analysis ofexperimental time series of a rotor response with bear-ing outer race faults. In Vibration engineering and tech-nology of machinery (pp. 683–696). Springer.

Kwuimy, C. A. K., Samadani, M., & Nataraj, C. (2014). Pre-liminary diagnostics of dynamic systems from time se-ries. In Proceedings of the ASME International DesignEngineering Technical Conference.

Liu, X.-Q., Zhang, H.-Y., Liu, J., & Yang, J. (2000). Faultdetection and diagnosis of permanent-magnet DC mo-tor based on parameter estimation and neural network.IEEE Transactions on Industrial Electronics, 47(5),1021–1030.

Mevel, B., & Guyader, J. (1993). Routes to chaos in ballbearings. Journal of Sound and Vibration, 162(3), 471–487.

Patton, R. J., Frank, P. M., & Clarke, R. N. (1989). Faultdiagnosis in dynamic systems: theory and application.Prentice–Hall, Inc.

Rabie, M. (2009). Fluid power engineering. McGraw HillProfessional.

Samadani, M., Behbahani, S., & Nataraj, C. (2013).A reliability-based manufacturing process planningmethod for the components of a complex mechatronicsystem. Applied Mathematical Modelling, 37(24),9829–9845.

Samadani, M., Kwuimy, C. A. K., & Nataraj, C. (2013).Diagnostics of a nonlinear pendulum using computa-tional intelligence. In ASME 2013 Dynamic Systemsand Control Conference.

Samadani, M., Kwuimy, C. A. K., & Nataraj, C. (2014).Model-based fault diagnostics of nonlinear systems us-ing the features of the phase space response. Commu-nications in Nonlinear Science and Numerical Simula-tion.

Sankaravelu, A., Noah, S. T., & Burger, C. P. (1994). Bifur-cation and chaos in ball bearings. ASME Applied Me-

chanics Division–Publications–AMD, 192, 313–313.Takens, F. (1981). Detecting strange attractors in turbulence.

In Dynamical Systems and Turbulence (pp. 366–381).Springer.

Zbilut, J. P., Thomasson, N., & Webber, C. L. (2002). Re-currence quantification analysis as a tool for nonlinearexploration of nonstationary cardiac signals. MedicalEngineering & Physics, 24(1), 53–60.

BIOGRAPHIES

Mohsen Samadani Mohsen received his B.Sc and M.Sc in Me-chanical Engineering from Isfahan University of Technology, Isfa-han, Iran. He is currently a Ph.D. candidate at the Department ofMechanical Engineering at Villanova University. Mohsen has beeninvolved in various research topics including manufacturing tech-nologies, control, vibrations, system dynamics, hydraulic systemsand reliability analysis. His current research interests include dataanalysis, machine learning, nonlinear dynamics and vibrations withapplications to machinery diagnostics and health management. Heis a member of Sigma Xi and ASME and a recipient of Sigma Xibest poster award and PHM doctoral consortium travel award.

Cedrick Kwuimy Prior to joining the Department of MechanicalEngineering at Villanova University in Jan. 2011, Dr. Kwuimyworked in South Africa as a postdoctoral research associate at theAfrican Institute for Mathematical Sciences (2009-2010) and as aResearch and Teaching Assistant (2007-2009) at the Faculty of Sci-ence at the University of Yaounde, Cameroon. He has been involvedin a wide range of research topics including vibration control, non-linear dynamics of self-sustained electromechanical devices, syn-chronization, nonlinear analysis of butterfly valves, and chaos con-trol and prediction in active magnetic bearings. He has over 30 peer-reviewed papers in international journals and conference proceed-ings and serves as a reviewer in high standard journals includingNonlinear Dynamics, Journal of Vibration and Control and Journalof Sound and Vibration. Dr. Kwuimy has supervised three graduateresearch theses at the African Institute for Mathematical Sciencesand is the recipient of Victor Rothschild Fellowships at African In-stitute for Mathematical Sciences and Research.

C. Nataraj Dr. C. Nataraj holds the Mr. and Mrs. Robert F. Mor-tiz, Sr. Endowed Chair Professorship in Engineered Systems at Vil-lanova University. He has a B.S. in Mechanical Engineering fromIndian Institute of Technology, and M.S. and Ph.D. in Engineer-ing Science from Arizona State University. After getting his Ph.D.in 1987, he worked for a year as a research engineer and a part-ner with Trumpler Associates, Inc. He is currently the Chairmanof the Mechanical Engineering Department at Villanova University.Dr. Nataraj was also the founding director of the Center for Non-linear Dynamics and Control in the College Of Engineering. Hehas worked on various research problems in nonlinear dynamic sys-tems with applications to mobile robotics, unmanned vehicles, rotordynamics, vibration, control, and electromagnetic bearings. His re-search has been funded by Office of Naval Research, National Sci-ence Foundation, National Institute of Health and many companies.

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