Research ArticleA Method for Aileron Actuator Fault Diagnosis Based onPCA and PGC-SVM

Wei-Li Qin1 Wen-Jin Zhang1 and Chen Lu2

1School of Reliability and Systems Engineering Beihang University Beijing 100191 China2Science amp Technology on Reliability amp Environmental Engineering Laboratory Beijing 100191 China

Correspondence should be addressed to Chen Lu luchenbuaaeducn

Received 20 October 2015 Revised 25 December 2015 Accepted 29 December 2015

Academic Editor Wen-Hsiang Hsieh

Copyright copy 2016 Wei-Li Qin et al This 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

Aileron actuators are pivotal components for aircraft flight control system Thus the fault diagnosis of aileron actuators is vital inthe enhancement of the reliability and fault tolerant capability This paper presents an aileron actuator fault diagnosis approachcombining principal component analysis (PCA) grid search (GS) 10-fold cross validation (CV) and one-versus-one supportvector machine (SVM) This method is referred to as PGC-SVM and utilizes the direct drive valve input force motor current anddisplacement feedback signal to realize fault detection and location First several common faults of aileron actuators which includeforce motor coil break sensor coil break cylinder leakage and amplifier gain reduction are extracted from the fault quadrantaldiagram the corresponding fault mechanisms are analyzed Second the data feature extraction is performed with dimensionreduction using PCA Finally the GS and CV algorithms are employed to train a one-versus-one SVM for fault classification thusobtaining the optimalmodel parameters and assuring the generalization of the trained SVM respectively To verify the effectivenessof the proposed approach four types of faults are introduced into the simulation model established by AMESim and SimulinkTheresults demonstrate its desirable diagnostic performance which outperforms that of the traditional SVM by comparison

1 Introduction

The aileron actuator which is used to control the aircraftrsquosrolling movement is a pivotal component for the flight con-trol system of aircraft [1]The faults of aileron actuator whichinclude force motor coil break sensor coil break actuatorcylinder leakage and amplifier gain reduction may cause aseries of consequences fromcontrol systemperformance deg-radation to irretrievable economic loss and personal casual-ties Therefore it is utmost important to research on the faultdetection of aileron actuators

Many fault diagnosis approaches have been used andproposed for classification of system health monitoring datasuch as decision tree induction Bayesian-based classificationneural networks genetic algorithms and fuzzy set classifiers[2] Zhao and Su [3] proposed a novel fault diagnosismethod for power transformer insulation based on a decisiontree Ozev et al [4] presented a parametric fault diagnosisapproach for analogRF circuits based on a Bayesian frame-work Zang and Imregun [5] performed structural damage

detection via artificial neural networks He et al [6] usedimmune genetic algorithm to build amathematical model forfault diagnosis of a modern power system Altunok et al [7]presented a damage pattern recognition approach based onfuzzy set theory However most of thesemethods are compu-tationally expensive and their classification accuracy is highlydepending on the sample size Besides with these methodssome faults such as hydraulic pump fault and external leakagefault can hardly be diagnosed

Model-based fault detection anddiagnosis (FDD) schemeis another important way for FDDof aileron actuators Henryet al [8] built an aileron servo-loop model and presented an119867minus

119867infin

-based solution fitted with the structure of AIRBUSin-service monitoring systems Vanek et al [9] founded areliable linear parameter-varying (LPV) model of the aircraftand performed two inherently different fault detection andisolation designs for aileron and elevator Gheorghe et al [10]presented a simple model-based approach for fault detectionin both runaway case and jamming case and yielded a morethan good performance under real flight test Goupil and

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 4807250 12 pageshttpdxdoiorg10115520164807250

2 Shock and Vibration

Command OutputAmplifier Direct drive valve CylinderPID

Direct drive valveinput Force motor current

Displacement sensor

Actuator cylinder displacement

Displacement sensorAmplifier

Direct drive valve displacement

Figure 1 Closed-loop control system of aileron actuator

Marcos [11] built a generic aircraft model and representativefault scenarios and threw light upon both traditional andadvanced model-based FDD approaches Efimov et al [12]presented a hybrid observer solution associated with thein-service A380 decision-making rules to solve oscillatoryfailure case in aircraft system

Support vector machines (SVMs) which were originallyintroduced by Vapnik have been successful for solving classi-fication and function estimation problems Characterized byconvex optimization problems (typically quadratic program-ming) SVM models are capable of obtaining global mini-mum avoiding the trap of local minimum brought by thegreedy algorithm in other methods And the ultimate deci-sion function of SVM is determined by instead of the wholesample a few support vectors so that computational complex-ity is reduced and the curse of dimensionality is shunnedBesides SVM has the advantage of dealing with nonlinearsystems while aileron actuator happens to be a typical non-linear system SVM is a classical binary classifier and in orderto solve multiclassification problem which is common infault diagnosis since there are generally more than two failuremodes many SVM algorithms are proposed to constructthe multiclassification classifiers The algorithms adopted inactual application can be divided into two types [13] (1)the first type is one-time solution method (2) combiningmany binary SVMsubclassifiers to achievemulticlassificationSVM the second type includes one-versus-rest one-versus-one DDAGSVM and binary-tree SVMThe research relatedshows that one-versus-one SVM can be more suitable toactual application because of its comparatively fast trainingspeed and good classification accuracy [13ndash16]

This paper adopts multiclassification algorithm of one-versus-one SVM to design the classifier for the aileron actu-ator fault diagnosis In addition the paper uses grid searchto optimize two important parameters 119862 and 120574 of one-versus-one SVM and Principle Component Analysis (PCA)to reduce dimension In traditional SVM the following pro-cedures are usually used (1) transform data to the format ofSVMpackage (2) randomly try a few kernels and parameters(3) test the model Due to the poor parameter selectionand original data complexity the classification accuracy isrelatively unsatisfactory and the training speed is sometimesintolerable However the biggest problem is that there willbe unclassifiable regions in traditional SVMThe one-versus-one SVM manages to avoid this problem and with the help

of PCA and grid search the data complexity and parameterselection problems are solved Hence compared to thetraditional SVM the method proposed through case studyyields a higher classification accuracy and a faster trainingspeedwhile external leakage fault can be effectively diagnosedby the method Generally the most important thing to do inaeronautical engineering is to performan early fault detectionto switch as soon as possible on a redundant actuator Onceproperly trained on ground using historical data the pro-posed algorithm can achieve fault classification as fast as 01sim1 s each timeWith the development Flight Control Computer(FCC) its constraints such as low computational load andrestricted symbol library will not be a problem for relativelycomplex algorithms in the future On that basis high faultclassification accuracy will be a bonus since correspondingmaintenance preparation can be done before the landing ofthe aircraft and thus efficiency is improved

The remainder of the paper is organized as follows InSection 2 a joint simulation model of aileron actuator basedon AMESim and Simulink is set up In Section 3 the faultsof aileron actuator are analyzed and injected into the modelIn Section 4 a detailed description of the proposed methodis presented In Section 5 the effectiveness of the proposedapproach is demonstrated and the results of experimentalare presented and discussed Finally the conclusion of theresearch will be given

2 Setup of Aileron Actuator

The aileron actuator consists of a hydraulic pump an electro-hydraulic servo valve a cylinder a PID controller two elec-tronic amplifiers and two displacement sensors The controlloop includes two position feedbacksmdashdirect drive valvedisplacement and actuator cylinder displacement as is shownin Figure 1 In this figure the signals used for fault detectionare marked with red ball

The simulation model of the aileron actuator is estab-lished with MATLAB Simulink and AMESim [17] Simulinkdeveloped by MathWorks is the visual simulation environ-ment in MATLAB Thanks to its convenient graphic modelmodules such as linearnonlinear modules continuousdis-crete modules and advanced control toolboxes it is quitefit for control loop modeling However it could not han-dle hydraulic modeling lacking corresponding modulesAMESim developed by Imagine is a hydraulicmechanical

Shock and Vibration 3

LoadIFM

1

Aerodynamic loads

Sine wave1

Sine wave

2000

Manual switch1

Manual switch

Fromworkspace1

Fromworkspace

Gain2

Gain4

Gain1

Gain

Gain5

Gain3

Systeminput

Amplifier fault injection

K-

K-

K-

Clock1

Clock

Switch1

Switch

PID(s)

PID controller

Sensor fault injection

AMESim interface

AMESimHydraulicServoLoad

RAM_XRAM_F

S-functionAdd

Scope

+minus

+minus

+minus

SimData matTo file

y1

y2

K-

Figure 2 Control part of aileron actuator in Simulink

P

Y

X

Aerodynamicloads

Internal leakage

RAM_XRAM_F

IFMLoadControlPart

Simulink interface

Pump fault

Valve blockage

External leakage

Aerodynamic loads

P T

A B

ChCh

F

F

X

MM++

Figure 3 Mechanical part of aileron actuator in AMESim

system modeling simulation and analysis software Withabundant parameterized hydraulic modules the hydraulicpart of the aileron actuator can be easily founded Howeverthere are relatively few control modules in AMESim Withthe combination of Simulink andAMESim the advantages ofthese two can be fully utilized and thereby a relatively goodmodel of aileron actuator is promising The control part of

the aileron actuator established in Simulink environment isshown in Figure 2 themechanical part of the aileron actuatoris shown in Figure 3 The mechanical part of the aileronactuator established in AMESim is converted to a Simulink119878-Function and the 119878-Function can be imported to SimulinkThe physical parameters of the key components are describedin Tables 1ndash9

4 Shock and Vibration

Table 1 Elementary hydraulic properties

FP04-1 all real parameters Unit ValueDensity kgm3 850Bulk modulus Bar 17000Slope of bulk modulus [bar] in function of pressure [bar] (in percentage) Null 0Absolute viscosity cP 51Absolute viscosity of airgas cP 002Saturation pressure (for dissolved airgas) Bar 0Airgas content 01Temperature degC 40Temperature 1198791 degC 40Kinematic viscosity at (119875atm 1198791) cSt 5647Temperature 1198792 degC 100Kinematic viscosity at (119875atm 1198792) cSt 971Coefficient for temperature viscosity characteristic Null 200Polytropic index for airgasvapor content Null 14(Advanced user) High saturated vapor pressure Bar minus05(Advanced user) Low saturated vapor pressure Bar minus06(Advanced user) Absolute viscosity of vapor cP 002(Advanced user) Effective molecular mass of vapor Null 200(Advanced user) Airgas density at atmospheric pressure 0 degC kgm3 12

Table 2 Parameters of pressure source

PS00-1 all real parameters Unit ValueTime at which duty cycle starts s 0Pressure at start of stage 1 Bar 210Pressure at end of stage 1 Bar 210Duration of stage 1 s 1e + 06

One leakageviscous frictionmodule which is utilized forcylinder internal leakage fault injection [18] and two pistonmodules constitute the simulation model of the hydrauliccylinder of the aileron actuator

In this paper the aileron actuator works at normal tem-perature 40∘C which is shown as a part of elementaryhydraulic properties in Table 1 And the kinematic viscositywill decrease when temperature increases

Under normal condition the pressure of the pump asshown in Table 2 is 210 bar

Under normal condition the pressure drops and the flowrate at maximum valve opening as shown in Table 3 is 20 barand 150 Lmin

Under normal condition the clearance diameter asshown in Table 4 is set to 1119890minus05mm And it will be increasedin order to inject the internal leakage fault

The chamber length at zero displacement the rod diame-ter and the piston diameter as shown in Table 5 are 150mm30mm and 90mm

The gain for signal output as shown inTable 6 is set to be 1The mass and displacement module whose parameters

are shown in Table 7 is adopted to confine the hydrauliccylinderrsquos movement scope

The spring damper whose parameters are shown inTable 8 is adopted for simulation of the dampof aerodynamicloads

In Table 9 list the parameters of flow control valve

3 Fault Analysis and Injection

According to statistical maintenance data main faults of anaileron actuator include amplifier fault sensor fault leakagefault external leakage fault pump fault and valve fault whichare listed in Table 10

Failure mode effects and criticality analysis (FMECA) isa bottom-up inductive analytical method for fault analysisAccording to the FMECAs of hydraulic system made by Liet al [19] and Balaban et al [20] these faults can be roughlydivided into four quadrants depending on their criticalityand frequency As shown in Figure 4 the first-quadrant faultsare high-frequency and high-criticality so that normally theyhave to be considered in design phase The second-quadrantfaults currently dealing with visual inspection are high-fre-quency but low-criticality The third-quadrant faults are low-frequency and low-criticality and thus are dismissed takingcost into consideration The fourth-quadrant faults whichneed constant monitoring are low-frequency but high-criti-cality

To demonstrate the approach presented in this paper fourfaults including electronic faults and mechanical faults wereintroduced into the simulation model and listed in Table 11

The faults listed in Tables 10 and 11 were introduced intothe simulationmodel by changing several specific parametersof the fault component and these components were markedwith red box in Figures 2 and 3 The details of fault injectionwere listed in Table 12 The parameter of force motor fault

Shock and Vibration 5

Table 3 Parameters of servo valve

SV00-1 all real parameters Unit ValuePorts P to A flow rate at maximum valve opening Lmin 150Ports P to A corresponding pressure drop Bar 20Ports P to A critical flow number (laminar rarr turbulent) Null 1000Ports B to T flow rate at maximum valve opening Lmin 150Ports B to T corresponding pressure drop Bar 20Ports B to T critical flow number (laminar rarr turbulent) Null 1000Ports P to B flow rate at maximum valve opening Lmin 150Ports P to B corresponding pressure drop Bar 20Ports P to B critical flow number (laminar rarr turbulent) Null 1000Ports A to T flow rate at maximum valve opening Lmin 150Ports A to T corresponding pressure drop Bar 20Ports A to T critical flow number (laminar rarr turbulent) Null 1000Working density for pressure drop measurement kgm3 850Working kinematic viscosity for pressure drop measurement cSt 60Valve rated current mA 1Valve natural frequency Hz 500Valve damping ratio Null 08Deadband as fraction of spool travel Null 0

Table 4 Parameters of leakage and viscous friction module

BAF11-1 all real parameters Unit ValueExternal piston diameter mm 90Clearance on diameter mm 1e minus 05Length of contact mm 30

Table 5 Parameters of piston modules

BAP11-1 all real parameters Unit ValuePiston diameter mm 90Rod diameter mm 30Chamber length at zero displacement mm 150

Table 6 Parameters of displacement sensor

DT000-1 all real parameters Unit ValueOffset to be subtracted from displacement M 0Gain for signal output 1m 1

Table 7 Parameters of mass and displacement module

MAS005-1 all real parameters Unit ValueMass kg 10Coefficient of viscous friction N(ms) 5000Coefficient of windage N(ms)2 0Coulomb friction force N 1000Stiction force N 1000Lower displacement limit m minus015Higher displacement limit m 015Inclination (+90 port 1 lowest minus90 port 1 highest) Degree 0

Table 8 Parameters of spring damper

SD000-1 all real parameters Unit ValueSpring rate Nm 1e + 06Displacement giving zero spring force m 0Damper rating N(ms) 10000

Table 9 Parameters of flow control valve

OR0000 all real parameters Unit ValueCharacteristic flow rate Lmin 1Corresponding pressure drop bar 1Equivalent orifice diameter mm 1e minus 05Maximum flow coefficient null 07Critical flow number (laminar rarr turbulent) Null 1000

is set to 0 indicating force motor coil break the parameterof sensor fault is set to 0 indicating sensor coil break theparameter of leakage fault is set to 5 instead of the default nor-mal value 1119890 minus 5 indicating 556 leakage since the diameterof the valve is 90mm the parameter of amplifier fault is setto 15 instead of the default normal value 50 indicating 70signal transmitting loss All the faults were introduced intothe simulation model in advance of stimulation

4 Methodology

The proposed method in the paper consists of two majorparts the model training using historical data and the real-time diagnosis using real-time data In model training part

6 Shock and Vibration

Table 10 Fault analysis of aileron actuator

Object Fault mode Fault cause Fault phenomenon

Direct drivingvalve

Force motor coil shutoff Force motor coil break Force motor has no power output the position ofvalve element is constantly in the neutral position

Blockage Oil pollution Null bias increases frequency response decreasessystem is unstable

Valve element stuck Oil pollutionSlide valve distortion

The direct driving valve output constant flow thesystem pressure decreases

Valve leakageEdge abrasionRadial valve elementabrasion

Null bias increases gain of system decreasessystem pressure decreases flow noise increases

Null bias out-of-tolerance Inaccurate zero setting Bias exists when DDV is at null positionDisplacementsensor

Coil break Cable break Sensor has no outputConstant bias Iron core of sensor loose Displacement bias

Actuatorcylinder

External leakage Sealing washers failHydraulic leakage

The speed of moving parts decreases systempressure decreases

Internal leakage out-of- toleranceCylinder abrasionOil in high pressure areaflow into low pressure area

The speed of moving parts decreases systempressure decreases vibration and noise appear

Electronicamplifier Gain reduction Internal faults of electronic

amplifier Magnification notably decreases

Table 11 Fault mode and details

Number Fault mode Fault type Details Quadrant1 Force motor fault Mechanical fault Force motor coil break I2 Sensor fault Electronic fault Sensor coil break I3 Leakage fault Mechanical fault Actuator cylinder leakage run out of tolerance II4 Amplifier fault Electronic fault Amplifier gain reduction IV

Faultfrequency

High

Low

Sensor bias

Oil filter blockbreak

SOV leakageSOV diode break

Valve element stuck

Amplifier gain reduction

Sensor coil break

Force motor coil break

Minor MajorFault

criticality

III

III IV

Actuator cylinderleakage

Hydraulic cylinderleakage

Figure 4 Aileron actuator fault quadrantal diagram

three steps are conducted Firstly historical data which inc-lude DDV input force motor current DDV displacementand actuator cylinder displacement are corrupted by whitenoise with signal-noise ratio to be 20 dB in MATLAB Thenthe corrupted data are truncated into a number of datasegments according to the data period And the mean rootmean square (RMS) peak-to-peak value (ppV) and kurtosis

of these data segments are calculated and normalized respec-tively Hence 16-dimensional primitive inputs shown inTable 13 are obtained It is worthmentioning that the dimen-sions of the primitive inputs are not specially chosen since thekey fault information will be automatically extracted by PCAThe flow chart of first step is shown in Figure 5 SecondlyPCA is utilized to conduct dimension reduction and noisereduction and thus the reduced inputs for the SVMmodel aregot Thirdly the reduced inputs are input to the SVM modelfor parameter optimization using grid search Once the opti-mal parameters for the SVMmodel are searched the trainedmodel is prepared for the real-time diagnosis In Real-timediagnosis real-time data are acquired by sensors deployed onthe air craft The same data preprocess as in model trainingpart is conducted and the classification result is returned bythe trained SVM model Fault report would be generatedfor the pilot or ground control station if the classificationresults meet a certain fault criterion The flow chart of themethod is shown in Figure 6

41 PCA Invented by Karl Pearson PCA adopts orthogonalmapping to map a set of possibly correlated variables to prin-cipal components that are linearly uncorrelated The greatestvariance lies on the first principal component the secondgreatest variance on the second principal component and soon

Shock and Vibration 7

Table 12 Fault injection details

Test number Fault mode Fault componentChanged

parameter for faultinjection (unit)

Parameter(normal)

Parameter(fault)

1 Force motor fault Force motor FMC gain 1 02 Sensor fault Displacement sensor Signal output (1m) 1 0

3 Leakage fault Actuator cylinderFlow control valveequivalent orificediameter (mm)

1119890 minus 5 5

4 Amplifier fault Electronic amplifier Gain 50 15

Corrupted by whitenoise

Signal-noise ratio 20dB

DDV inputor

force motor currentor

DDV displacementor

actuator displacement

Data segments

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

Normalization

Primitive inputs

Figure 5 Flow chart of data preprocess

Here is a data matrix 119883 whose 119899 rows are 119899 differentrepetition of the experiment and whose 119901 columns are 119901

different parameters 119883 = (119883(1)

119883(119894)

119883(119899)

)119879 119883(119894)

=

(1199091

119909119901

)(119894)

The scores of new vector of principal com-ponents t

(119894)

= (1199051

119905119901

)(119894)

119894 = 1 2 119899 where 119894 isordinal number of the row are given through a mathematicaltransformation defined by 119901-dimensional vectors of weightsw(119896)

= (1199081

119908119901

)119879

(119896) 119896 = 1 2 119901 where 119896 is the ordinal

number of the principal component The equation is shownas below

119905119896(119894)

= X(119894)

sdot w(119896)

(1)

where 119905119896(119894)

is the 119896th component of 119883(119894)

and thus the max-imum possible variance from 119883 is inherited by t with eachvector of weight w constrained as a unit vector

Thefirst component of a data vectorX(119894)

can then be givenas a score 119905

1(119894)

= X(119894)

sdot w(1)

in the transformed coordinateswhere w

(1)

has to satisfy

w(1)

= argmaxw=1

sum

119894

(1199051

)2

(119894)

= argmaxw=1

Xw2

= argmaxw=1

w119879X119879Xw

(2)

8 Shock and Vibration

Model training Real-time diagnosis

Historicaldata

Data preprocess

Primitiveinputs

PCA

Reducedinputs

Grid search

Gridparameters

10-fold crossvalidation

Optimalparameters

Trainedmodel

Data acquisition

Data process

Fault diagnosis

Normal Sensor fault

Force motor fault

Amplifier fault

Leakage fault

Alarmcriterion

Fault report

Figure 6 Flow chart of fault diagnosis

Table 13 Primitive inputs for SVMmodel

Model input Features ObjectInput 1

Mean

Direct drive valve inputInput 2 Force motor currentInput 3 Direct drive valve displacementInput 4 Actuator cylinder displacementInput 5

RMS

Direct drive valve inputInput 6 Force motor currentInput 7 Direct drive valve displacementInput 8 Actuator cylinder displacementInput 9

ppV

Direct drive valve inputInput 10 Force motor currentInput 11 Direct drive valve displacementInput 12 Actuator cylinder displacementInput 13

Kurtosis

Direct drive valve inputInput 14 Force motor currentInput 15 Direct drive valve displacementInput 16 Actuator cylinder displacement

and the 119896th component can be found by subtracting the first119896 minus 1 principal components from X

X119896

= X minus

119896minus1

sum

119904=1

Xw(119904)

w119879(119904)

(3)

and then finding the weight vector which extracts the maxi-mum variance from this new data matrix

w(119896)

= argmaxw=1

10038171003817100381710038171003817X119896

w10038171003817100381710038171003817

2

= argmaxw=1

w119879X119879119896

X119879119896

w (4)

the 119896th component of a data vector X(119894)

can then be given asa score 119905

119896(119894)

= X(119894)

sdot w(119896)

in the transformed coordinates

The full principal component decomposition of X cantherefore be given as

T = XW (5)

whereW is a 119901-by-119901matrix whose columns are the eigenvec-tors of X119879X

42 Grid Search and CV Grid search executes exhaustivesearching through an artificially selected parameter set of cer-tain learning algorithms A typical soft-margin SVMclassifierequipped with an RBF kernel has two parameters that needto be tuned a regularization constant 119862 and a kernel hyperparameter 120574 The goal of grid search is to identify good pair(119862 120574) so that the classifier can accurately predict unknowndata Exponentially growing sequences of 119862 and 120574 (eg 119862 =

2minus5

2minus3

215 120574 = 2

minus15

2minus13

23

) are recommended byHsu et al [21]

In contrast with other optimization algorithms such asgenetic algorithm and particle swarm algorithm the gridsearch is straightforward but seems naive However thereare two motivations why I prefer the simple grid-searchapproach One is that psychologically we may not feel safeto use methods which avoid doing an exhaustive parametersearch by approximations or heuristics The other reason isthat the computational time required to find good parametersby grid search is not muchmore than that by advancedmeth-ods since there are only two parameters in this case Further-more the grid search can be easily parallelized because each(119862 120574) is independent Many of advanced methods are itera-tive processes for example walking along a path which canbe hard to parallelize

And the performance of the pair is assessed by crossvalidation on the training set The training set is divided into

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

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Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 Shock and Vibration

Command OutputAmplifier Direct drive valve CylinderPID

Direct drive valveinput Force motor current

Displacement sensor

Actuator cylinder displacement

Displacement sensorAmplifier

Direct drive valve displacement

Figure 1 Closed-loop control system of aileron actuator

Marcos [11] built a generic aircraft model and representativefault scenarios and threw light upon both traditional andadvanced model-based FDD approaches Efimov et al [12]presented a hybrid observer solution associated with thein-service A380 decision-making rules to solve oscillatoryfailure case in aircraft system

Support vector machines (SVMs) which were originallyintroduced by Vapnik have been successful for solving classi-fication and function estimation problems Characterized byconvex optimization problems (typically quadratic program-ming) SVM models are capable of obtaining global mini-mum avoiding the trap of local minimum brought by thegreedy algorithm in other methods And the ultimate deci-sion function of SVM is determined by instead of the wholesample a few support vectors so that computational complex-ity is reduced and the curse of dimensionality is shunnedBesides SVM has the advantage of dealing with nonlinearsystems while aileron actuator happens to be a typical non-linear system SVM is a classical binary classifier and in orderto solve multiclassification problem which is common infault diagnosis since there are generally more than two failuremodes many SVM algorithms are proposed to constructthe multiclassification classifiers The algorithms adopted inactual application can be divided into two types [13] (1)the first type is one-time solution method (2) combiningmany binary SVMsubclassifiers to achievemulticlassificationSVM the second type includes one-versus-rest one-versus-one DDAGSVM and binary-tree SVMThe research relatedshows that one-versus-one SVM can be more suitable toactual application because of its comparatively fast trainingspeed and good classification accuracy [13ndash16]

This paper adopts multiclassification algorithm of one-versus-one SVM to design the classifier for the aileron actu-ator fault diagnosis In addition the paper uses grid searchto optimize two important parameters 119862 and 120574 of one-versus-one SVM and Principle Component Analysis (PCA)to reduce dimension In traditional SVM the following pro-cedures are usually used (1) transform data to the format ofSVMpackage (2) randomly try a few kernels and parameters(3) test the model Due to the poor parameter selectionand original data complexity the classification accuracy isrelatively unsatisfactory and the training speed is sometimesintolerable However the biggest problem is that there willbe unclassifiable regions in traditional SVMThe one-versus-one SVM manages to avoid this problem and with the help

of PCA and grid search the data complexity and parameterselection problems are solved Hence compared to thetraditional SVM the method proposed through case studyyields a higher classification accuracy and a faster trainingspeedwhile external leakage fault can be effectively diagnosedby the method Generally the most important thing to do inaeronautical engineering is to performan early fault detectionto switch as soon as possible on a redundant actuator Onceproperly trained on ground using historical data the pro-posed algorithm can achieve fault classification as fast as 01sim1 s each timeWith the development Flight Control Computer(FCC) its constraints such as low computational load andrestricted symbol library will not be a problem for relativelycomplex algorithms in the future On that basis high faultclassification accuracy will be a bonus since correspondingmaintenance preparation can be done before the landing ofthe aircraft and thus efficiency is improved

The remainder of the paper is organized as follows InSection 2 a joint simulation model of aileron actuator basedon AMESim and Simulink is set up In Section 3 the faultsof aileron actuator are analyzed and injected into the modelIn Section 4 a detailed description of the proposed methodis presented In Section 5 the effectiveness of the proposedapproach is demonstrated and the results of experimentalare presented and discussed Finally the conclusion of theresearch will be given

2 Setup of Aileron Actuator

The aileron actuator consists of a hydraulic pump an electro-hydraulic servo valve a cylinder a PID controller two elec-tronic amplifiers and two displacement sensors The controlloop includes two position feedbacksmdashdirect drive valvedisplacement and actuator cylinder displacement as is shownin Figure 1 In this figure the signals used for fault detectionare marked with red ball

The simulation model of the aileron actuator is estab-lished with MATLAB Simulink and AMESim [17] Simulinkdeveloped by MathWorks is the visual simulation environ-ment in MATLAB Thanks to its convenient graphic modelmodules such as linearnonlinear modules continuousdis-crete modules and advanced control toolboxes it is quitefit for control loop modeling However it could not han-dle hydraulic modeling lacking corresponding modulesAMESim developed by Imagine is a hydraulicmechanical

Shock and Vibration 3

LoadIFM

1

Aerodynamic loads

Sine wave1

Sine wave

2000

Manual switch1

Manual switch

Fromworkspace1

Fromworkspace

Gain2

Gain4

Gain1

Gain

Gain5

Gain3

Systeminput

Amplifier fault injection

K-

K-

K-

Clock1

Clock

Switch1

Switch

PID(s)

PID controller

Sensor fault injection

AMESim interface

AMESimHydraulicServoLoad

RAM_XRAM_F

S-functionAdd

Scope

+minus

+minus

+minus

SimData matTo file

y1

y2

K-

Figure 2 Control part of aileron actuator in Simulink

P

Y

X

Aerodynamicloads

Internal leakage

RAM_XRAM_F

IFMLoadControlPart

Simulink interface

Pump fault

Valve blockage

External leakage

Aerodynamic loads

P T

A B

ChCh

F

F

X

MM++

Figure 3 Mechanical part of aileron actuator in AMESim

system modeling simulation and analysis software Withabundant parameterized hydraulic modules the hydraulicpart of the aileron actuator can be easily founded Howeverthere are relatively few control modules in AMESim Withthe combination of Simulink andAMESim the advantages ofthese two can be fully utilized and thereby a relatively goodmodel of aileron actuator is promising The control part of

the aileron actuator established in Simulink environment isshown in Figure 2 themechanical part of the aileron actuatoris shown in Figure 3 The mechanical part of the aileronactuator established in AMESim is converted to a Simulink119878-Function and the 119878-Function can be imported to SimulinkThe physical parameters of the key components are describedin Tables 1ndash9

4 Shock and Vibration

Table 1 Elementary hydraulic properties

FP04-1 all real parameters Unit ValueDensity kgm3 850Bulk modulus Bar 17000Slope of bulk modulus [bar] in function of pressure [bar] (in percentage) Null 0Absolute viscosity cP 51Absolute viscosity of airgas cP 002Saturation pressure (for dissolved airgas) Bar 0Airgas content 01Temperature degC 40Temperature 1198791 degC 40Kinematic viscosity at (119875atm 1198791) cSt 5647Temperature 1198792 degC 100Kinematic viscosity at (119875atm 1198792) cSt 971Coefficient for temperature viscosity characteristic Null 200Polytropic index for airgasvapor content Null 14(Advanced user) High saturated vapor pressure Bar minus05(Advanced user) Low saturated vapor pressure Bar minus06(Advanced user) Absolute viscosity of vapor cP 002(Advanced user) Effective molecular mass of vapor Null 200(Advanced user) Airgas density at atmospheric pressure 0 degC kgm3 12

Table 2 Parameters of pressure source

PS00-1 all real parameters Unit ValueTime at which duty cycle starts s 0Pressure at start of stage 1 Bar 210Pressure at end of stage 1 Bar 210Duration of stage 1 s 1e + 06

One leakageviscous frictionmodule which is utilized forcylinder internal leakage fault injection [18] and two pistonmodules constitute the simulation model of the hydrauliccylinder of the aileron actuator

In this paper the aileron actuator works at normal tem-perature 40∘C which is shown as a part of elementaryhydraulic properties in Table 1 And the kinematic viscositywill decrease when temperature increases

Under normal condition the pressure of the pump asshown in Table 2 is 210 bar

Under normal condition the pressure drops and the flowrate at maximum valve opening as shown in Table 3 is 20 barand 150 Lmin

Under normal condition the clearance diameter asshown in Table 4 is set to 1119890minus05mm And it will be increasedin order to inject the internal leakage fault

The chamber length at zero displacement the rod diame-ter and the piston diameter as shown in Table 5 are 150mm30mm and 90mm

The gain for signal output as shown inTable 6 is set to be 1The mass and displacement module whose parameters

are shown in Table 7 is adopted to confine the hydrauliccylinderrsquos movement scope

The spring damper whose parameters are shown inTable 8 is adopted for simulation of the dampof aerodynamicloads

In Table 9 list the parameters of flow control valve

3 Fault Analysis and Injection

According to statistical maintenance data main faults of anaileron actuator include amplifier fault sensor fault leakagefault external leakage fault pump fault and valve fault whichare listed in Table 10

Failure mode effects and criticality analysis (FMECA) isa bottom-up inductive analytical method for fault analysisAccording to the FMECAs of hydraulic system made by Liet al [19] and Balaban et al [20] these faults can be roughlydivided into four quadrants depending on their criticalityand frequency As shown in Figure 4 the first-quadrant faultsare high-frequency and high-criticality so that normally theyhave to be considered in design phase The second-quadrantfaults currently dealing with visual inspection are high-fre-quency but low-criticality The third-quadrant faults are low-frequency and low-criticality and thus are dismissed takingcost into consideration The fourth-quadrant faults whichneed constant monitoring are low-frequency but high-criti-cality

To demonstrate the approach presented in this paper fourfaults including electronic faults and mechanical faults wereintroduced into the simulation model and listed in Table 11

The faults listed in Tables 10 and 11 were introduced intothe simulationmodel by changing several specific parametersof the fault component and these components were markedwith red box in Figures 2 and 3 The details of fault injectionwere listed in Table 12 The parameter of force motor fault

Shock and Vibration 5

Table 3 Parameters of servo valve

SV00-1 all real parameters Unit ValuePorts P to A flow rate at maximum valve opening Lmin 150Ports P to A corresponding pressure drop Bar 20Ports P to A critical flow number (laminar rarr turbulent) Null 1000Ports B to T flow rate at maximum valve opening Lmin 150Ports B to T corresponding pressure drop Bar 20Ports B to T critical flow number (laminar rarr turbulent) Null 1000Ports P to B flow rate at maximum valve opening Lmin 150Ports P to B corresponding pressure drop Bar 20Ports P to B critical flow number (laminar rarr turbulent) Null 1000Ports A to T flow rate at maximum valve opening Lmin 150Ports A to T corresponding pressure drop Bar 20Ports A to T critical flow number (laminar rarr turbulent) Null 1000Working density for pressure drop measurement kgm3 850Working kinematic viscosity for pressure drop measurement cSt 60Valve rated current mA 1Valve natural frequency Hz 500Valve damping ratio Null 08Deadband as fraction of spool travel Null 0

Table 4 Parameters of leakage and viscous friction module

BAF11-1 all real parameters Unit ValueExternal piston diameter mm 90Clearance on diameter mm 1e minus 05Length of contact mm 30

Table 5 Parameters of piston modules

BAP11-1 all real parameters Unit ValuePiston diameter mm 90Rod diameter mm 30Chamber length at zero displacement mm 150

Table 6 Parameters of displacement sensor

DT000-1 all real parameters Unit ValueOffset to be subtracted from displacement M 0Gain for signal output 1m 1

Table 7 Parameters of mass and displacement module

MAS005-1 all real parameters Unit ValueMass kg 10Coefficient of viscous friction N(ms) 5000Coefficient of windage N(ms)2 0Coulomb friction force N 1000Stiction force N 1000Lower displacement limit m minus015Higher displacement limit m 015Inclination (+90 port 1 lowest minus90 port 1 highest) Degree 0

Table 8 Parameters of spring damper

SD000-1 all real parameters Unit ValueSpring rate Nm 1e + 06Displacement giving zero spring force m 0Damper rating N(ms) 10000

Table 9 Parameters of flow control valve

OR0000 all real parameters Unit ValueCharacteristic flow rate Lmin 1Corresponding pressure drop bar 1Equivalent orifice diameter mm 1e minus 05Maximum flow coefficient null 07Critical flow number (laminar rarr turbulent) Null 1000

is set to 0 indicating force motor coil break the parameterof sensor fault is set to 0 indicating sensor coil break theparameter of leakage fault is set to 5 instead of the default nor-mal value 1119890 minus 5 indicating 556 leakage since the diameterof the valve is 90mm the parameter of amplifier fault is setto 15 instead of the default normal value 50 indicating 70signal transmitting loss All the faults were introduced intothe simulation model in advance of stimulation

4 Methodology

The proposed method in the paper consists of two majorparts the model training using historical data and the real-time diagnosis using real-time data In model training part

6 Shock and Vibration

Table 10 Fault analysis of aileron actuator

Object Fault mode Fault cause Fault phenomenon

Direct drivingvalve

Force motor coil shutoff Force motor coil break Force motor has no power output the position ofvalve element is constantly in the neutral position

Blockage Oil pollution Null bias increases frequency response decreasessystem is unstable

Valve element stuck Oil pollutionSlide valve distortion

The direct driving valve output constant flow thesystem pressure decreases

Valve leakageEdge abrasionRadial valve elementabrasion

Null bias increases gain of system decreasessystem pressure decreases flow noise increases

Null bias out-of-tolerance Inaccurate zero setting Bias exists when DDV is at null positionDisplacementsensor

Coil break Cable break Sensor has no outputConstant bias Iron core of sensor loose Displacement bias

Actuatorcylinder

External leakage Sealing washers failHydraulic leakage

The speed of moving parts decreases systempressure decreases

Internal leakage out-of- toleranceCylinder abrasionOil in high pressure areaflow into low pressure area

The speed of moving parts decreases systempressure decreases vibration and noise appear

Electronicamplifier Gain reduction Internal faults of electronic

amplifier Magnification notably decreases

Table 11 Fault mode and details

Number Fault mode Fault type Details Quadrant1 Force motor fault Mechanical fault Force motor coil break I2 Sensor fault Electronic fault Sensor coil break I3 Leakage fault Mechanical fault Actuator cylinder leakage run out of tolerance II4 Amplifier fault Electronic fault Amplifier gain reduction IV

Faultfrequency

High

Low

Sensor bias

Oil filter blockbreak

SOV leakageSOV diode break

Valve element stuck

Amplifier gain reduction

Sensor coil break

Force motor coil break

Minor MajorFault

criticality

III

III IV

Actuator cylinderleakage

Hydraulic cylinderleakage

Figure 4 Aileron actuator fault quadrantal diagram

three steps are conducted Firstly historical data which inc-lude DDV input force motor current DDV displacementand actuator cylinder displacement are corrupted by whitenoise with signal-noise ratio to be 20 dB in MATLAB Thenthe corrupted data are truncated into a number of datasegments according to the data period And the mean rootmean square (RMS) peak-to-peak value (ppV) and kurtosis

of these data segments are calculated and normalized respec-tively Hence 16-dimensional primitive inputs shown inTable 13 are obtained It is worthmentioning that the dimen-sions of the primitive inputs are not specially chosen since thekey fault information will be automatically extracted by PCAThe flow chart of first step is shown in Figure 5 SecondlyPCA is utilized to conduct dimension reduction and noisereduction and thus the reduced inputs for the SVMmodel aregot Thirdly the reduced inputs are input to the SVM modelfor parameter optimization using grid search Once the opti-mal parameters for the SVMmodel are searched the trainedmodel is prepared for the real-time diagnosis In Real-timediagnosis real-time data are acquired by sensors deployed onthe air craft The same data preprocess as in model trainingpart is conducted and the classification result is returned bythe trained SVM model Fault report would be generatedfor the pilot or ground control station if the classificationresults meet a certain fault criterion The flow chart of themethod is shown in Figure 6

41 PCA Invented by Karl Pearson PCA adopts orthogonalmapping to map a set of possibly correlated variables to prin-cipal components that are linearly uncorrelated The greatestvariance lies on the first principal component the secondgreatest variance on the second principal component and soon

Shock and Vibration 7

Table 12 Fault injection details

Test number Fault mode Fault componentChanged

parameter for faultinjection (unit)

Parameter(normal)

Parameter(fault)

1 Force motor fault Force motor FMC gain 1 02 Sensor fault Displacement sensor Signal output (1m) 1 0

3 Leakage fault Actuator cylinderFlow control valveequivalent orificediameter (mm)

1119890 minus 5 5

4 Amplifier fault Electronic amplifier Gain 50 15

Corrupted by whitenoise

Signal-noise ratio 20dB

DDV inputor

force motor currentor

DDV displacementor

actuator displacement

Data segments

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

Normalization

Primitive inputs

Figure 5 Flow chart of data preprocess

Here is a data matrix 119883 whose 119899 rows are 119899 differentrepetition of the experiment and whose 119901 columns are 119901

different parameters 119883 = (119883(1)

119883(119894)

119883(119899)

)119879 119883(119894)

=

(1199091

119909119901

)(119894)

The scores of new vector of principal com-ponents t

(119894)

= (1199051

119905119901

)(119894)

119894 = 1 2 119899 where 119894 isordinal number of the row are given through a mathematicaltransformation defined by 119901-dimensional vectors of weightsw(119896)

= (1199081

119908119901

)119879

(119896) 119896 = 1 2 119901 where 119896 is the ordinal

number of the principal component The equation is shownas below

119905119896(119894)

= X(119894)

sdot w(119896)

(1)

where 119905119896(119894)

is the 119896th component of 119883(119894)

and thus the max-imum possible variance from 119883 is inherited by t with eachvector of weight w constrained as a unit vector

Thefirst component of a data vectorX(119894)

can then be givenas a score 119905

1(119894)

= X(119894)

sdot w(1)

in the transformed coordinateswhere w

(1)

has to satisfy

w(1)

= argmaxw=1

sum

119894

(1199051

)2

(119894)

= argmaxw=1

Xw2

= argmaxw=1

w119879X119879Xw

(2)

8 Shock and Vibration

Model training Real-time diagnosis

Historicaldata

Data preprocess

Primitiveinputs

PCA

Reducedinputs

Grid search

Gridparameters

10-fold crossvalidation

Optimalparameters

Trainedmodel

Data acquisition

Data process

Fault diagnosis

Normal Sensor fault

Force motor fault

Amplifier fault

Leakage fault

Alarmcriterion

Fault report

Figure 6 Flow chart of fault diagnosis

Table 13 Primitive inputs for SVMmodel

Model input Features ObjectInput 1

Mean

Direct drive valve inputInput 2 Force motor currentInput 3 Direct drive valve displacementInput 4 Actuator cylinder displacementInput 5

RMS

Direct drive valve inputInput 6 Force motor currentInput 7 Direct drive valve displacementInput 8 Actuator cylinder displacementInput 9

ppV

Direct drive valve inputInput 10 Force motor currentInput 11 Direct drive valve displacementInput 12 Actuator cylinder displacementInput 13

Kurtosis

Direct drive valve inputInput 14 Force motor currentInput 15 Direct drive valve displacementInput 16 Actuator cylinder displacement

and the 119896th component can be found by subtracting the first119896 minus 1 principal components from X

X119896

= X minus

119896minus1

sum

119904=1

Xw(119904)

w119879(119904)

(3)

and then finding the weight vector which extracts the maxi-mum variance from this new data matrix

w(119896)

= argmaxw=1

10038171003817100381710038171003817X119896

w10038171003817100381710038171003817

2

= argmaxw=1

w119879X119879119896

X119879119896

w (4)

the 119896th component of a data vector X(119894)

can then be given asa score 119905

119896(119894)

= X(119894)

sdot w(119896)

in the transformed coordinates

The full principal component decomposition of X cantherefore be given as

T = XW (5)

whereW is a 119901-by-119901matrix whose columns are the eigenvec-tors of X119879X

42 Grid Search and CV Grid search executes exhaustivesearching through an artificially selected parameter set of cer-tain learning algorithms A typical soft-margin SVMclassifierequipped with an RBF kernel has two parameters that needto be tuned a regularization constant 119862 and a kernel hyperparameter 120574 The goal of grid search is to identify good pair(119862 120574) so that the classifier can accurately predict unknowndata Exponentially growing sequences of 119862 and 120574 (eg 119862 =

2minus5

2minus3

215 120574 = 2

minus15

2minus13

23

) are recommended byHsu et al [21]

In contrast with other optimization algorithms such asgenetic algorithm and particle swarm algorithm the gridsearch is straightforward but seems naive However thereare two motivations why I prefer the simple grid-searchapproach One is that psychologically we may not feel safeto use methods which avoid doing an exhaustive parametersearch by approximations or heuristics The other reason isthat the computational time required to find good parametersby grid search is not muchmore than that by advancedmeth-ods since there are only two parameters in this case Further-more the grid search can be easily parallelized because each(119862 120574) is independent Many of advanced methods are itera-tive processes for example walking along a path which canbe hard to parallelize

And the performance of the pair is assessed by crossvalidation on the training set The training set is divided into

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

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Active and Passive Electronic Components

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 3

LoadIFM

1

Aerodynamic loads

Sine wave1

Sine wave

2000

Manual switch1

Manual switch

Fromworkspace1

Fromworkspace

Gain2

Gain4

Gain1

Gain

Gain5

Gain3

Systeminput

Amplifier fault injection

K-

K-

K-

Clock1

Clock

Switch1

Switch

PID(s)

PID controller

Sensor fault injection

AMESim interface

AMESimHydraulicServoLoad

RAM_XRAM_F

S-functionAdd

Scope

+minus

+minus

+minus

SimData matTo file

y1

y2

K-

Figure 2 Control part of aileron actuator in Simulink

P

Y

X

Aerodynamicloads

Internal leakage

RAM_XRAM_F

IFMLoadControlPart

Simulink interface

Pump fault

Valve blockage

External leakage

Aerodynamic loads

P T

A B

ChCh

F

F

X

MM++

Figure 3 Mechanical part of aileron actuator in AMESim

system modeling simulation and analysis software Withabundant parameterized hydraulic modules the hydraulicpart of the aileron actuator can be easily founded Howeverthere are relatively few control modules in AMESim Withthe combination of Simulink andAMESim the advantages ofthese two can be fully utilized and thereby a relatively goodmodel of aileron actuator is promising The control part of

the aileron actuator established in Simulink environment isshown in Figure 2 themechanical part of the aileron actuatoris shown in Figure 3 The mechanical part of the aileronactuator established in AMESim is converted to a Simulink119878-Function and the 119878-Function can be imported to SimulinkThe physical parameters of the key components are describedin Tables 1ndash9

4 Shock and Vibration

Table 1 Elementary hydraulic properties

FP04-1 all real parameters Unit ValueDensity kgm3 850Bulk modulus Bar 17000Slope of bulk modulus [bar] in function of pressure [bar] (in percentage) Null 0Absolute viscosity cP 51Absolute viscosity of airgas cP 002Saturation pressure (for dissolved airgas) Bar 0Airgas content 01Temperature degC 40Temperature 1198791 degC 40Kinematic viscosity at (119875atm 1198791) cSt 5647Temperature 1198792 degC 100Kinematic viscosity at (119875atm 1198792) cSt 971Coefficient for temperature viscosity characteristic Null 200Polytropic index for airgasvapor content Null 14(Advanced user) High saturated vapor pressure Bar minus05(Advanced user) Low saturated vapor pressure Bar minus06(Advanced user) Absolute viscosity of vapor cP 002(Advanced user) Effective molecular mass of vapor Null 200(Advanced user) Airgas density at atmospheric pressure 0 degC kgm3 12

Table 2 Parameters of pressure source

PS00-1 all real parameters Unit ValueTime at which duty cycle starts s 0Pressure at start of stage 1 Bar 210Pressure at end of stage 1 Bar 210Duration of stage 1 s 1e + 06

One leakageviscous frictionmodule which is utilized forcylinder internal leakage fault injection [18] and two pistonmodules constitute the simulation model of the hydrauliccylinder of the aileron actuator

In this paper the aileron actuator works at normal tem-perature 40∘C which is shown as a part of elementaryhydraulic properties in Table 1 And the kinematic viscositywill decrease when temperature increases

Under normal condition the pressure of the pump asshown in Table 2 is 210 bar

Under normal condition the pressure drops and the flowrate at maximum valve opening as shown in Table 3 is 20 barand 150 Lmin

Under normal condition the clearance diameter asshown in Table 4 is set to 1119890minus05mm And it will be increasedin order to inject the internal leakage fault

The chamber length at zero displacement the rod diame-ter and the piston diameter as shown in Table 5 are 150mm30mm and 90mm

The gain for signal output as shown inTable 6 is set to be 1The mass and displacement module whose parameters

are shown in Table 7 is adopted to confine the hydrauliccylinderrsquos movement scope

The spring damper whose parameters are shown inTable 8 is adopted for simulation of the dampof aerodynamicloads

In Table 9 list the parameters of flow control valve

3 Fault Analysis and Injection

According to statistical maintenance data main faults of anaileron actuator include amplifier fault sensor fault leakagefault external leakage fault pump fault and valve fault whichare listed in Table 10

Failure mode effects and criticality analysis (FMECA) isa bottom-up inductive analytical method for fault analysisAccording to the FMECAs of hydraulic system made by Liet al [19] and Balaban et al [20] these faults can be roughlydivided into four quadrants depending on their criticalityand frequency As shown in Figure 4 the first-quadrant faultsare high-frequency and high-criticality so that normally theyhave to be considered in design phase The second-quadrantfaults currently dealing with visual inspection are high-fre-quency but low-criticality The third-quadrant faults are low-frequency and low-criticality and thus are dismissed takingcost into consideration The fourth-quadrant faults whichneed constant monitoring are low-frequency but high-criti-cality

To demonstrate the approach presented in this paper fourfaults including electronic faults and mechanical faults wereintroduced into the simulation model and listed in Table 11

The faults listed in Tables 10 and 11 were introduced intothe simulationmodel by changing several specific parametersof the fault component and these components were markedwith red box in Figures 2 and 3 The details of fault injectionwere listed in Table 12 The parameter of force motor fault

Shock and Vibration 5

Table 3 Parameters of servo valve

SV00-1 all real parameters Unit ValuePorts P to A flow rate at maximum valve opening Lmin 150Ports P to A corresponding pressure drop Bar 20Ports P to A critical flow number (laminar rarr turbulent) Null 1000Ports B to T flow rate at maximum valve opening Lmin 150Ports B to T corresponding pressure drop Bar 20Ports B to T critical flow number (laminar rarr turbulent) Null 1000Ports P to B flow rate at maximum valve opening Lmin 150Ports P to B corresponding pressure drop Bar 20Ports P to B critical flow number (laminar rarr turbulent) Null 1000Ports A to T flow rate at maximum valve opening Lmin 150Ports A to T corresponding pressure drop Bar 20Ports A to T critical flow number (laminar rarr turbulent) Null 1000Working density for pressure drop measurement kgm3 850Working kinematic viscosity for pressure drop measurement cSt 60Valve rated current mA 1Valve natural frequency Hz 500Valve damping ratio Null 08Deadband as fraction of spool travel Null 0

Table 4 Parameters of leakage and viscous friction module

BAF11-1 all real parameters Unit ValueExternal piston diameter mm 90Clearance on diameter mm 1e minus 05Length of contact mm 30

Table 5 Parameters of piston modules

BAP11-1 all real parameters Unit ValuePiston diameter mm 90Rod diameter mm 30Chamber length at zero displacement mm 150

Table 6 Parameters of displacement sensor

DT000-1 all real parameters Unit ValueOffset to be subtracted from displacement M 0Gain for signal output 1m 1

Table 7 Parameters of mass and displacement module

MAS005-1 all real parameters Unit ValueMass kg 10Coefficient of viscous friction N(ms) 5000Coefficient of windage N(ms)2 0Coulomb friction force N 1000Stiction force N 1000Lower displacement limit m minus015Higher displacement limit m 015Inclination (+90 port 1 lowest minus90 port 1 highest) Degree 0

Table 8 Parameters of spring damper

SD000-1 all real parameters Unit ValueSpring rate Nm 1e + 06Displacement giving zero spring force m 0Damper rating N(ms) 10000

Table 9 Parameters of flow control valve

OR0000 all real parameters Unit ValueCharacteristic flow rate Lmin 1Corresponding pressure drop bar 1Equivalent orifice diameter mm 1e minus 05Maximum flow coefficient null 07Critical flow number (laminar rarr turbulent) Null 1000

is set to 0 indicating force motor coil break the parameterof sensor fault is set to 0 indicating sensor coil break theparameter of leakage fault is set to 5 instead of the default nor-mal value 1119890 minus 5 indicating 556 leakage since the diameterof the valve is 90mm the parameter of amplifier fault is setto 15 instead of the default normal value 50 indicating 70signal transmitting loss All the faults were introduced intothe simulation model in advance of stimulation

4 Methodology

The proposed method in the paper consists of two majorparts the model training using historical data and the real-time diagnosis using real-time data In model training part

6 Shock and Vibration

Table 10 Fault analysis of aileron actuator

Object Fault mode Fault cause Fault phenomenon

Direct drivingvalve

Force motor coil shutoff Force motor coil break Force motor has no power output the position ofvalve element is constantly in the neutral position

Blockage Oil pollution Null bias increases frequency response decreasessystem is unstable

Valve element stuck Oil pollutionSlide valve distortion

The direct driving valve output constant flow thesystem pressure decreases

Valve leakageEdge abrasionRadial valve elementabrasion

Null bias increases gain of system decreasessystem pressure decreases flow noise increases

Null bias out-of-tolerance Inaccurate zero setting Bias exists when DDV is at null positionDisplacementsensor

Coil break Cable break Sensor has no outputConstant bias Iron core of sensor loose Displacement bias

Actuatorcylinder

External leakage Sealing washers failHydraulic leakage

The speed of moving parts decreases systempressure decreases

Internal leakage out-of- toleranceCylinder abrasionOil in high pressure areaflow into low pressure area

The speed of moving parts decreases systempressure decreases vibration and noise appear

Electronicamplifier Gain reduction Internal faults of electronic

amplifier Magnification notably decreases

Table 11 Fault mode and details

Number Fault mode Fault type Details Quadrant1 Force motor fault Mechanical fault Force motor coil break I2 Sensor fault Electronic fault Sensor coil break I3 Leakage fault Mechanical fault Actuator cylinder leakage run out of tolerance II4 Amplifier fault Electronic fault Amplifier gain reduction IV

Faultfrequency

High

Low

Sensor bias

Oil filter blockbreak

SOV leakageSOV diode break

Valve element stuck

Amplifier gain reduction

Sensor coil break

Force motor coil break

Minor MajorFault

criticality

III

III IV

Actuator cylinderleakage

Hydraulic cylinderleakage

Figure 4 Aileron actuator fault quadrantal diagram

three steps are conducted Firstly historical data which inc-lude DDV input force motor current DDV displacementand actuator cylinder displacement are corrupted by whitenoise with signal-noise ratio to be 20 dB in MATLAB Thenthe corrupted data are truncated into a number of datasegments according to the data period And the mean rootmean square (RMS) peak-to-peak value (ppV) and kurtosis

of these data segments are calculated and normalized respec-tively Hence 16-dimensional primitive inputs shown inTable 13 are obtained It is worthmentioning that the dimen-sions of the primitive inputs are not specially chosen since thekey fault information will be automatically extracted by PCAThe flow chart of first step is shown in Figure 5 SecondlyPCA is utilized to conduct dimension reduction and noisereduction and thus the reduced inputs for the SVMmodel aregot Thirdly the reduced inputs are input to the SVM modelfor parameter optimization using grid search Once the opti-mal parameters for the SVMmodel are searched the trainedmodel is prepared for the real-time diagnosis In Real-timediagnosis real-time data are acquired by sensors deployed onthe air craft The same data preprocess as in model trainingpart is conducted and the classification result is returned bythe trained SVM model Fault report would be generatedfor the pilot or ground control station if the classificationresults meet a certain fault criterion The flow chart of themethod is shown in Figure 6

41 PCA Invented by Karl Pearson PCA adopts orthogonalmapping to map a set of possibly correlated variables to prin-cipal components that are linearly uncorrelated The greatestvariance lies on the first principal component the secondgreatest variance on the second principal component and soon

Shock and Vibration 7

Table 12 Fault injection details

Test number Fault mode Fault componentChanged

parameter for faultinjection (unit)

Parameter(normal)

Parameter(fault)

1 Force motor fault Force motor FMC gain 1 02 Sensor fault Displacement sensor Signal output (1m) 1 0

3 Leakage fault Actuator cylinderFlow control valveequivalent orificediameter (mm)

1119890 minus 5 5

4 Amplifier fault Electronic amplifier Gain 50 15

Corrupted by whitenoise

Signal-noise ratio 20dB

DDV inputor

force motor currentor

DDV displacementor

actuator displacement

Data segments

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

Normalization

Primitive inputs

Figure 5 Flow chart of data preprocess

Here is a data matrix 119883 whose 119899 rows are 119899 differentrepetition of the experiment and whose 119901 columns are 119901

different parameters 119883 = (119883(1)

119883(119894)

119883(119899)

)119879 119883(119894)

=

(1199091

119909119901

)(119894)

The scores of new vector of principal com-ponents t

(119894)

= (1199051

119905119901

)(119894)

119894 = 1 2 119899 where 119894 isordinal number of the row are given through a mathematicaltransformation defined by 119901-dimensional vectors of weightsw(119896)

= (1199081

119908119901

)119879

(119896) 119896 = 1 2 119901 where 119896 is the ordinal

number of the principal component The equation is shownas below

119905119896(119894)

= X(119894)

sdot w(119896)

(1)

where 119905119896(119894)

is the 119896th component of 119883(119894)

and thus the max-imum possible variance from 119883 is inherited by t with eachvector of weight w constrained as a unit vector

Thefirst component of a data vectorX(119894)

can then be givenas a score 119905

1(119894)

= X(119894)

sdot w(1)

in the transformed coordinateswhere w

(1)

has to satisfy

w(1)

= argmaxw=1

sum

119894

(1199051

)2

(119894)

= argmaxw=1

Xw2

= argmaxw=1

w119879X119879Xw

(2)

8 Shock and Vibration

Model training Real-time diagnosis

Historicaldata

Data preprocess

Primitiveinputs

PCA

Reducedinputs

Grid search

Gridparameters

10-fold crossvalidation

Optimalparameters

Trainedmodel

Data acquisition

Data process

Fault diagnosis

Normal Sensor fault

Force motor fault

Amplifier fault

Leakage fault

Alarmcriterion

Fault report

Figure 6 Flow chart of fault diagnosis

Table 13 Primitive inputs for SVMmodel

Model input Features ObjectInput 1

Mean

Direct drive valve inputInput 2 Force motor currentInput 3 Direct drive valve displacementInput 4 Actuator cylinder displacementInput 5

RMS

Direct drive valve inputInput 6 Force motor currentInput 7 Direct drive valve displacementInput 8 Actuator cylinder displacementInput 9

ppV

Direct drive valve inputInput 10 Force motor currentInput 11 Direct drive valve displacementInput 12 Actuator cylinder displacementInput 13

Kurtosis

Direct drive valve inputInput 14 Force motor currentInput 15 Direct drive valve displacementInput 16 Actuator cylinder displacement

and the 119896th component can be found by subtracting the first119896 minus 1 principal components from X

X119896

= X minus

119896minus1

sum

119904=1

Xw(119904)

w119879(119904)

(3)

and then finding the weight vector which extracts the maxi-mum variance from this new data matrix

w(119896)

= argmaxw=1

10038171003817100381710038171003817X119896

w10038171003817100381710038171003817

2

= argmaxw=1

w119879X119879119896

X119879119896

w (4)

the 119896th component of a data vector X(119894)

can then be given asa score 119905

119896(119894)

= X(119894)

sdot w(119896)

in the transformed coordinates

The full principal component decomposition of X cantherefore be given as

T = XW (5)

whereW is a 119901-by-119901matrix whose columns are the eigenvec-tors of X119879X

42 Grid Search and CV Grid search executes exhaustivesearching through an artificially selected parameter set of cer-tain learning algorithms A typical soft-margin SVMclassifierequipped with an RBF kernel has two parameters that needto be tuned a regularization constant 119862 and a kernel hyperparameter 120574 The goal of grid search is to identify good pair(119862 120574) so that the classifier can accurately predict unknowndata Exponentially growing sequences of 119862 and 120574 (eg 119862 =

2minus5

2minus3

215 120574 = 2

minus15

2minus13

23

) are recommended byHsu et al [21]

In contrast with other optimization algorithms such asgenetic algorithm and particle swarm algorithm the gridsearch is straightforward but seems naive However thereare two motivations why I prefer the simple grid-searchapproach One is that psychologically we may not feel safeto use methods which avoid doing an exhaustive parametersearch by approximations or heuristics The other reason isthat the computational time required to find good parametersby grid search is not muchmore than that by advancedmeth-ods since there are only two parameters in this case Further-more the grid search can be easily parallelized because each(119862 120574) is independent Many of advanced methods are itera-tive processes for example walking along a path which canbe hard to parallelize

And the performance of the pair is assessed by crossvalidation on the training set The training set is divided into

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

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DistributedSensor Networks

International Journal of

4 Shock and Vibration

Table 1 Elementary hydraulic properties

FP04-1 all real parameters Unit ValueDensity kgm3 850Bulk modulus Bar 17000Slope of bulk modulus [bar] in function of pressure [bar] (in percentage) Null 0Absolute viscosity cP 51Absolute viscosity of airgas cP 002Saturation pressure (for dissolved airgas) Bar 0Airgas content 01Temperature degC 40Temperature 1198791 degC 40Kinematic viscosity at (119875atm 1198791) cSt 5647Temperature 1198792 degC 100Kinematic viscosity at (119875atm 1198792) cSt 971Coefficient for temperature viscosity characteristic Null 200Polytropic index for airgasvapor content Null 14(Advanced user) High saturated vapor pressure Bar minus05(Advanced user) Low saturated vapor pressure Bar minus06(Advanced user) Absolute viscosity of vapor cP 002(Advanced user) Effective molecular mass of vapor Null 200(Advanced user) Airgas density at atmospheric pressure 0 degC kgm3 12

Table 2 Parameters of pressure source

PS00-1 all real parameters Unit ValueTime at which duty cycle starts s 0Pressure at start of stage 1 Bar 210Pressure at end of stage 1 Bar 210Duration of stage 1 s 1e + 06

One leakageviscous frictionmodule which is utilized forcylinder internal leakage fault injection [18] and two pistonmodules constitute the simulation model of the hydrauliccylinder of the aileron actuator

In this paper the aileron actuator works at normal tem-perature 40∘C which is shown as a part of elementaryhydraulic properties in Table 1 And the kinematic viscositywill decrease when temperature increases

Under normal condition the pressure of the pump asshown in Table 2 is 210 bar

Under normal condition the pressure drops and the flowrate at maximum valve opening as shown in Table 3 is 20 barand 150 Lmin

Under normal condition the clearance diameter asshown in Table 4 is set to 1119890minus05mm And it will be increasedin order to inject the internal leakage fault

The chamber length at zero displacement the rod diame-ter and the piston diameter as shown in Table 5 are 150mm30mm and 90mm

The gain for signal output as shown inTable 6 is set to be 1The mass and displacement module whose parameters

are shown in Table 7 is adopted to confine the hydrauliccylinderrsquos movement scope

The spring damper whose parameters are shown inTable 8 is adopted for simulation of the dampof aerodynamicloads

In Table 9 list the parameters of flow control valve

3 Fault Analysis and Injection

According to statistical maintenance data main faults of anaileron actuator include amplifier fault sensor fault leakagefault external leakage fault pump fault and valve fault whichare listed in Table 10

Failure mode effects and criticality analysis (FMECA) isa bottom-up inductive analytical method for fault analysisAccording to the FMECAs of hydraulic system made by Liet al [19] and Balaban et al [20] these faults can be roughlydivided into four quadrants depending on their criticalityand frequency As shown in Figure 4 the first-quadrant faultsare high-frequency and high-criticality so that normally theyhave to be considered in design phase The second-quadrantfaults currently dealing with visual inspection are high-fre-quency but low-criticality The third-quadrant faults are low-frequency and low-criticality and thus are dismissed takingcost into consideration The fourth-quadrant faults whichneed constant monitoring are low-frequency but high-criti-cality

To demonstrate the approach presented in this paper fourfaults including electronic faults and mechanical faults wereintroduced into the simulation model and listed in Table 11

The faults listed in Tables 10 and 11 were introduced intothe simulationmodel by changing several specific parametersof the fault component and these components were markedwith red box in Figures 2 and 3 The details of fault injectionwere listed in Table 12 The parameter of force motor fault

Shock and Vibration 5

Table 3 Parameters of servo valve

SV00-1 all real parameters Unit ValuePorts P to A flow rate at maximum valve opening Lmin 150Ports P to A corresponding pressure drop Bar 20Ports P to A critical flow number (laminar rarr turbulent) Null 1000Ports B to T flow rate at maximum valve opening Lmin 150Ports B to T corresponding pressure drop Bar 20Ports B to T critical flow number (laminar rarr turbulent) Null 1000Ports P to B flow rate at maximum valve opening Lmin 150Ports P to B corresponding pressure drop Bar 20Ports P to B critical flow number (laminar rarr turbulent) Null 1000Ports A to T flow rate at maximum valve opening Lmin 150Ports A to T corresponding pressure drop Bar 20Ports A to T critical flow number (laminar rarr turbulent) Null 1000Working density for pressure drop measurement kgm3 850Working kinematic viscosity for pressure drop measurement cSt 60Valve rated current mA 1Valve natural frequency Hz 500Valve damping ratio Null 08Deadband as fraction of spool travel Null 0

Table 4 Parameters of leakage and viscous friction module

BAF11-1 all real parameters Unit ValueExternal piston diameter mm 90Clearance on diameter mm 1e minus 05Length of contact mm 30

Table 5 Parameters of piston modules

BAP11-1 all real parameters Unit ValuePiston diameter mm 90Rod diameter mm 30Chamber length at zero displacement mm 150

Table 6 Parameters of displacement sensor

DT000-1 all real parameters Unit ValueOffset to be subtracted from displacement M 0Gain for signal output 1m 1

Table 7 Parameters of mass and displacement module

MAS005-1 all real parameters Unit ValueMass kg 10Coefficient of viscous friction N(ms) 5000Coefficient of windage N(ms)2 0Coulomb friction force N 1000Stiction force N 1000Lower displacement limit m minus015Higher displacement limit m 015Inclination (+90 port 1 lowest minus90 port 1 highest) Degree 0

Table 8 Parameters of spring damper

SD000-1 all real parameters Unit ValueSpring rate Nm 1e + 06Displacement giving zero spring force m 0Damper rating N(ms) 10000

Table 9 Parameters of flow control valve

OR0000 all real parameters Unit ValueCharacteristic flow rate Lmin 1Corresponding pressure drop bar 1Equivalent orifice diameter mm 1e minus 05Maximum flow coefficient null 07Critical flow number (laminar rarr turbulent) Null 1000

is set to 0 indicating force motor coil break the parameterof sensor fault is set to 0 indicating sensor coil break theparameter of leakage fault is set to 5 instead of the default nor-mal value 1119890 minus 5 indicating 556 leakage since the diameterof the valve is 90mm the parameter of amplifier fault is setto 15 instead of the default normal value 50 indicating 70signal transmitting loss All the faults were introduced intothe simulation model in advance of stimulation

4 Methodology

The proposed method in the paper consists of two majorparts the model training using historical data and the real-time diagnosis using real-time data In model training part

6 Shock and Vibration

Table 10 Fault analysis of aileron actuator

Object Fault mode Fault cause Fault phenomenon

Direct drivingvalve

Force motor coil shutoff Force motor coil break Force motor has no power output the position ofvalve element is constantly in the neutral position

Blockage Oil pollution Null bias increases frequency response decreasessystem is unstable

Valve element stuck Oil pollutionSlide valve distortion

The direct driving valve output constant flow thesystem pressure decreases

Valve leakageEdge abrasionRadial valve elementabrasion

Null bias increases gain of system decreasessystem pressure decreases flow noise increases

Null bias out-of-tolerance Inaccurate zero setting Bias exists when DDV is at null positionDisplacementsensor

Coil break Cable break Sensor has no outputConstant bias Iron core of sensor loose Displacement bias

Actuatorcylinder

External leakage Sealing washers failHydraulic leakage

The speed of moving parts decreases systempressure decreases

Internal leakage out-of- toleranceCylinder abrasionOil in high pressure areaflow into low pressure area

The speed of moving parts decreases systempressure decreases vibration and noise appear

Electronicamplifier Gain reduction Internal faults of electronic

amplifier Magnification notably decreases

Table 11 Fault mode and details

Number Fault mode Fault type Details Quadrant1 Force motor fault Mechanical fault Force motor coil break I2 Sensor fault Electronic fault Sensor coil break I3 Leakage fault Mechanical fault Actuator cylinder leakage run out of tolerance II4 Amplifier fault Electronic fault Amplifier gain reduction IV

Faultfrequency

High

Low

Sensor bias

Oil filter blockbreak

SOV leakageSOV diode break

Valve element stuck

Amplifier gain reduction

Sensor coil break

Force motor coil break

Minor MajorFault

criticality

III

III IV

Actuator cylinderleakage

Hydraulic cylinderleakage

Figure 4 Aileron actuator fault quadrantal diagram

three steps are conducted Firstly historical data which inc-lude DDV input force motor current DDV displacementand actuator cylinder displacement are corrupted by whitenoise with signal-noise ratio to be 20 dB in MATLAB Thenthe corrupted data are truncated into a number of datasegments according to the data period And the mean rootmean square (RMS) peak-to-peak value (ppV) and kurtosis

of these data segments are calculated and normalized respec-tively Hence 16-dimensional primitive inputs shown inTable 13 are obtained It is worthmentioning that the dimen-sions of the primitive inputs are not specially chosen since thekey fault information will be automatically extracted by PCAThe flow chart of first step is shown in Figure 5 SecondlyPCA is utilized to conduct dimension reduction and noisereduction and thus the reduced inputs for the SVMmodel aregot Thirdly the reduced inputs are input to the SVM modelfor parameter optimization using grid search Once the opti-mal parameters for the SVMmodel are searched the trainedmodel is prepared for the real-time diagnosis In Real-timediagnosis real-time data are acquired by sensors deployed onthe air craft The same data preprocess as in model trainingpart is conducted and the classification result is returned bythe trained SVM model Fault report would be generatedfor the pilot or ground control station if the classificationresults meet a certain fault criterion The flow chart of themethod is shown in Figure 6

41 PCA Invented by Karl Pearson PCA adopts orthogonalmapping to map a set of possibly correlated variables to prin-cipal components that are linearly uncorrelated The greatestvariance lies on the first principal component the secondgreatest variance on the second principal component and soon

Shock and Vibration 7

Table 12 Fault injection details

Test number Fault mode Fault componentChanged

parameter for faultinjection (unit)

Parameter(normal)

Parameter(fault)

1 Force motor fault Force motor FMC gain 1 02 Sensor fault Displacement sensor Signal output (1m) 1 0

3 Leakage fault Actuator cylinderFlow control valveequivalent orificediameter (mm)

1119890 minus 5 5

4 Amplifier fault Electronic amplifier Gain 50 15

Corrupted by whitenoise

Signal-noise ratio 20dB

DDV inputor

force motor currentor

DDV displacementor

actuator displacement

Data segments

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

Normalization

Primitive inputs

Figure 5 Flow chart of data preprocess

Here is a data matrix 119883 whose 119899 rows are 119899 differentrepetition of the experiment and whose 119901 columns are 119901

different parameters 119883 = (119883(1)

119883(119894)

119883(119899)

)119879 119883(119894)

=

(1199091

119909119901

)(119894)

The scores of new vector of principal com-ponents t

(119894)

= (1199051

119905119901

)(119894)

119894 = 1 2 119899 where 119894 isordinal number of the row are given through a mathematicaltransformation defined by 119901-dimensional vectors of weightsw(119896)

= (1199081

119908119901

)119879

(119896) 119896 = 1 2 119901 where 119896 is the ordinal

number of the principal component The equation is shownas below

119905119896(119894)

= X(119894)

sdot w(119896)

(1)

where 119905119896(119894)

is the 119896th component of 119883(119894)

and thus the max-imum possible variance from 119883 is inherited by t with eachvector of weight w constrained as a unit vector

Thefirst component of a data vectorX(119894)

can then be givenas a score 119905

1(119894)

= X(119894)

sdot w(1)

in the transformed coordinateswhere w

(1)

has to satisfy

w(1)

= argmaxw=1

sum

119894

(1199051

)2

(119894)

= argmaxw=1

Xw2

= argmaxw=1

w119879X119879Xw

(2)

8 Shock and Vibration

Model training Real-time diagnosis

Historicaldata

Data preprocess

Primitiveinputs

PCA

Reducedinputs

Grid search

Gridparameters

10-fold crossvalidation

Optimalparameters

Trainedmodel

Data acquisition

Data process

Fault diagnosis

Normal Sensor fault

Force motor fault

Amplifier fault

Leakage fault

Alarmcriterion

Fault report

Figure 6 Flow chart of fault diagnosis

Table 13 Primitive inputs for SVMmodel

Model input Features ObjectInput 1

Mean

Direct drive valve inputInput 2 Force motor currentInput 3 Direct drive valve displacementInput 4 Actuator cylinder displacementInput 5

RMS

Direct drive valve inputInput 6 Force motor currentInput 7 Direct drive valve displacementInput 8 Actuator cylinder displacementInput 9

ppV

Direct drive valve inputInput 10 Force motor currentInput 11 Direct drive valve displacementInput 12 Actuator cylinder displacementInput 13

Kurtosis

Direct drive valve inputInput 14 Force motor currentInput 15 Direct drive valve displacementInput 16 Actuator cylinder displacement

and the 119896th component can be found by subtracting the first119896 minus 1 principal components from X

X119896

= X minus

119896minus1

sum

119904=1

Xw(119904)

w119879(119904)

(3)

and then finding the weight vector which extracts the maxi-mum variance from this new data matrix

w(119896)

= argmaxw=1

10038171003817100381710038171003817X119896

w10038171003817100381710038171003817

2

= argmaxw=1

w119879X119879119896

X119879119896

w (4)

the 119896th component of a data vector X(119894)

can then be given asa score 119905

119896(119894)

= X(119894)

sdot w(119896)

in the transformed coordinates

The full principal component decomposition of X cantherefore be given as

T = XW (5)

whereW is a 119901-by-119901matrix whose columns are the eigenvec-tors of X119879X

42 Grid Search and CV Grid search executes exhaustivesearching through an artificially selected parameter set of cer-tain learning algorithms A typical soft-margin SVMclassifierequipped with an RBF kernel has two parameters that needto be tuned a regularization constant 119862 and a kernel hyperparameter 120574 The goal of grid search is to identify good pair(119862 120574) so that the classifier can accurately predict unknowndata Exponentially growing sequences of 119862 and 120574 (eg 119862 =

2minus5

2minus3

215 120574 = 2

minus15

2minus13

23

) are recommended byHsu et al [21]

In contrast with other optimization algorithms such asgenetic algorithm and particle swarm algorithm the gridsearch is straightforward but seems naive However thereare two motivations why I prefer the simple grid-searchapproach One is that psychologically we may not feel safeto use methods which avoid doing an exhaustive parametersearch by approximations or heuristics The other reason isthat the computational time required to find good parametersby grid search is not muchmore than that by advancedmeth-ods since there are only two parameters in this case Further-more the grid search can be easily parallelized because each(119862 120574) is independent Many of advanced methods are itera-tive processes for example walking along a path which canbe hard to parallelize

And the performance of the pair is assessed by crossvalidation on the training set The training set is divided into

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

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DistributedSensor Networks

International Journal of

Shock and Vibration 5

Table 3 Parameters of servo valve

SV00-1 all real parameters Unit ValuePorts P to A flow rate at maximum valve opening Lmin 150Ports P to A corresponding pressure drop Bar 20Ports P to A critical flow number (laminar rarr turbulent) Null 1000Ports B to T flow rate at maximum valve opening Lmin 150Ports B to T corresponding pressure drop Bar 20Ports B to T critical flow number (laminar rarr turbulent) Null 1000Ports P to B flow rate at maximum valve opening Lmin 150Ports P to B corresponding pressure drop Bar 20Ports P to B critical flow number (laminar rarr turbulent) Null 1000Ports A to T flow rate at maximum valve opening Lmin 150Ports A to T corresponding pressure drop Bar 20Ports A to T critical flow number (laminar rarr turbulent) Null 1000Working density for pressure drop measurement kgm3 850Working kinematic viscosity for pressure drop measurement cSt 60Valve rated current mA 1Valve natural frequency Hz 500Valve damping ratio Null 08Deadband as fraction of spool travel Null 0

Table 4 Parameters of leakage and viscous friction module

BAF11-1 all real parameters Unit ValueExternal piston diameter mm 90Clearance on diameter mm 1e minus 05Length of contact mm 30

Table 5 Parameters of piston modules

BAP11-1 all real parameters Unit ValuePiston diameter mm 90Rod diameter mm 30Chamber length at zero displacement mm 150

Table 6 Parameters of displacement sensor

DT000-1 all real parameters Unit ValueOffset to be subtracted from displacement M 0Gain for signal output 1m 1

Table 7 Parameters of mass and displacement module

MAS005-1 all real parameters Unit ValueMass kg 10Coefficient of viscous friction N(ms) 5000Coefficient of windage N(ms)2 0Coulomb friction force N 1000Stiction force N 1000Lower displacement limit m minus015Higher displacement limit m 015Inclination (+90 port 1 lowest minus90 port 1 highest) Degree 0

Table 8 Parameters of spring damper

SD000-1 all real parameters Unit ValueSpring rate Nm 1e + 06Displacement giving zero spring force m 0Damper rating N(ms) 10000

Table 9 Parameters of flow control valve

OR0000 all real parameters Unit ValueCharacteristic flow rate Lmin 1Corresponding pressure drop bar 1Equivalent orifice diameter mm 1e minus 05Maximum flow coefficient null 07Critical flow number (laminar rarr turbulent) Null 1000

is set to 0 indicating force motor coil break the parameterof sensor fault is set to 0 indicating sensor coil break theparameter of leakage fault is set to 5 instead of the default nor-mal value 1119890 minus 5 indicating 556 leakage since the diameterof the valve is 90mm the parameter of amplifier fault is setto 15 instead of the default normal value 50 indicating 70signal transmitting loss All the faults were introduced intothe simulation model in advance of stimulation

4 Methodology

The proposed method in the paper consists of two majorparts the model training using historical data and the real-time diagnosis using real-time data In model training part

6 Shock and Vibration

Table 10 Fault analysis of aileron actuator

Object Fault mode Fault cause Fault phenomenon

Direct drivingvalve

Force motor coil shutoff Force motor coil break Force motor has no power output the position ofvalve element is constantly in the neutral position

Blockage Oil pollution Null bias increases frequency response decreasessystem is unstable

Valve element stuck Oil pollutionSlide valve distortion

The direct driving valve output constant flow thesystem pressure decreases

Valve leakageEdge abrasionRadial valve elementabrasion

Null bias increases gain of system decreasessystem pressure decreases flow noise increases

Null bias out-of-tolerance Inaccurate zero setting Bias exists when DDV is at null positionDisplacementsensor

Coil break Cable break Sensor has no outputConstant bias Iron core of sensor loose Displacement bias

Actuatorcylinder

External leakage Sealing washers failHydraulic leakage

The speed of moving parts decreases systempressure decreases

Internal leakage out-of- toleranceCylinder abrasionOil in high pressure areaflow into low pressure area

The speed of moving parts decreases systempressure decreases vibration and noise appear

Electronicamplifier Gain reduction Internal faults of electronic

amplifier Magnification notably decreases

Table 11 Fault mode and details

Number Fault mode Fault type Details Quadrant1 Force motor fault Mechanical fault Force motor coil break I2 Sensor fault Electronic fault Sensor coil break I3 Leakage fault Mechanical fault Actuator cylinder leakage run out of tolerance II4 Amplifier fault Electronic fault Amplifier gain reduction IV

Faultfrequency

High

Low

Sensor bias

Oil filter blockbreak

SOV leakageSOV diode break

Valve element stuck

Amplifier gain reduction

Sensor coil break

Force motor coil break

Minor MajorFault

criticality

III

III IV

Actuator cylinderleakage

Hydraulic cylinderleakage

Figure 4 Aileron actuator fault quadrantal diagram

three steps are conducted Firstly historical data which inc-lude DDV input force motor current DDV displacementand actuator cylinder displacement are corrupted by whitenoise with signal-noise ratio to be 20 dB in MATLAB Thenthe corrupted data are truncated into a number of datasegments according to the data period And the mean rootmean square (RMS) peak-to-peak value (ppV) and kurtosis

of these data segments are calculated and normalized respec-tively Hence 16-dimensional primitive inputs shown inTable 13 are obtained It is worthmentioning that the dimen-sions of the primitive inputs are not specially chosen since thekey fault information will be automatically extracted by PCAThe flow chart of first step is shown in Figure 5 SecondlyPCA is utilized to conduct dimension reduction and noisereduction and thus the reduced inputs for the SVMmodel aregot Thirdly the reduced inputs are input to the SVM modelfor parameter optimization using grid search Once the opti-mal parameters for the SVMmodel are searched the trainedmodel is prepared for the real-time diagnosis In Real-timediagnosis real-time data are acquired by sensors deployed onthe air craft The same data preprocess as in model trainingpart is conducted and the classification result is returned bythe trained SVM model Fault report would be generatedfor the pilot or ground control station if the classificationresults meet a certain fault criterion The flow chart of themethod is shown in Figure 6

41 PCA Invented by Karl Pearson PCA adopts orthogonalmapping to map a set of possibly correlated variables to prin-cipal components that are linearly uncorrelated The greatestvariance lies on the first principal component the secondgreatest variance on the second principal component and soon

Shock and Vibration 7

Table 12 Fault injection details

Test number Fault mode Fault componentChanged

parameter for faultinjection (unit)

Parameter(normal)

Parameter(fault)

1 Force motor fault Force motor FMC gain 1 02 Sensor fault Displacement sensor Signal output (1m) 1 0

3 Leakage fault Actuator cylinderFlow control valveequivalent orificediameter (mm)

1119890 minus 5 5

4 Amplifier fault Electronic amplifier Gain 50 15

Corrupted by whitenoise

Signal-noise ratio 20dB

DDV inputor

force motor currentor

DDV displacementor

actuator displacement

Data segments

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

Normalization

Primitive inputs

Figure 5 Flow chart of data preprocess

Here is a data matrix 119883 whose 119899 rows are 119899 differentrepetition of the experiment and whose 119901 columns are 119901

different parameters 119883 = (119883(1)

119883(119894)

119883(119899)

)119879 119883(119894)

=

(1199091

119909119901

)(119894)

The scores of new vector of principal com-ponents t

(119894)

= (1199051

119905119901

)(119894)

119894 = 1 2 119899 where 119894 isordinal number of the row are given through a mathematicaltransformation defined by 119901-dimensional vectors of weightsw(119896)

= (1199081

119908119901

)119879

(119896) 119896 = 1 2 119901 where 119896 is the ordinal

number of the principal component The equation is shownas below

119905119896(119894)

= X(119894)

sdot w(119896)

(1)

where 119905119896(119894)

is the 119896th component of 119883(119894)

and thus the max-imum possible variance from 119883 is inherited by t with eachvector of weight w constrained as a unit vector

Thefirst component of a data vectorX(119894)

can then be givenas a score 119905

1(119894)

= X(119894)

sdot w(1)

in the transformed coordinateswhere w

(1)

has to satisfy

w(1)

= argmaxw=1

sum

119894

(1199051

)2

(119894)

= argmaxw=1

Xw2

= argmaxw=1

w119879X119879Xw

(2)

8 Shock and Vibration

Model training Real-time diagnosis

Historicaldata

Data preprocess

Primitiveinputs

PCA

Reducedinputs

Grid search

Gridparameters

10-fold crossvalidation

Optimalparameters

Trainedmodel

Data acquisition

Data process

Fault diagnosis

Normal Sensor fault

Force motor fault

Amplifier fault

Leakage fault

Alarmcriterion

Fault report

Figure 6 Flow chart of fault diagnosis

Table 13 Primitive inputs for SVMmodel

Model input Features ObjectInput 1

Mean

Direct drive valve inputInput 2 Force motor currentInput 3 Direct drive valve displacementInput 4 Actuator cylinder displacementInput 5

RMS

Direct drive valve inputInput 6 Force motor currentInput 7 Direct drive valve displacementInput 8 Actuator cylinder displacementInput 9

ppV

Direct drive valve inputInput 10 Force motor currentInput 11 Direct drive valve displacementInput 12 Actuator cylinder displacementInput 13

Kurtosis

Direct drive valve inputInput 14 Force motor currentInput 15 Direct drive valve displacementInput 16 Actuator cylinder displacement

and the 119896th component can be found by subtracting the first119896 minus 1 principal components from X

X119896

= X minus

119896minus1

sum

119904=1

Xw(119904)

w119879(119904)

(3)

and then finding the weight vector which extracts the maxi-mum variance from this new data matrix

w(119896)

= argmaxw=1

10038171003817100381710038171003817X119896

w10038171003817100381710038171003817

2

= argmaxw=1

w119879X119879119896

X119879119896

w (4)

the 119896th component of a data vector X(119894)

can then be given asa score 119905

119896(119894)

= X(119894)

sdot w(119896)

in the transformed coordinates

The full principal component decomposition of X cantherefore be given as

T = XW (5)

whereW is a 119901-by-119901matrix whose columns are the eigenvec-tors of X119879X

42 Grid Search and CV Grid search executes exhaustivesearching through an artificially selected parameter set of cer-tain learning algorithms A typical soft-margin SVMclassifierequipped with an RBF kernel has two parameters that needto be tuned a regularization constant 119862 and a kernel hyperparameter 120574 The goal of grid search is to identify good pair(119862 120574) so that the classifier can accurately predict unknowndata Exponentially growing sequences of 119862 and 120574 (eg 119862 =

2minus5

2minus3

215 120574 = 2

minus15

2minus13

23

) are recommended byHsu et al [21]

In contrast with other optimization algorithms such asgenetic algorithm and particle swarm algorithm the gridsearch is straightforward but seems naive However thereare two motivations why I prefer the simple grid-searchapproach One is that psychologically we may not feel safeto use methods which avoid doing an exhaustive parametersearch by approximations or heuristics The other reason isthat the computational time required to find good parametersby grid search is not muchmore than that by advancedmeth-ods since there are only two parameters in this case Further-more the grid search can be easily parallelized because each(119862 120574) is independent Many of advanced methods are itera-tive processes for example walking along a path which canbe hard to parallelize

And the performance of the pair is assessed by crossvalidation on the training set The training set is divided into

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Shock and Vibration

Table 10 Fault analysis of aileron actuator

Object Fault mode Fault cause Fault phenomenon

Direct drivingvalve

Force motor coil shutoff Force motor coil break Force motor has no power output the position ofvalve element is constantly in the neutral position

Blockage Oil pollution Null bias increases frequency response decreasessystem is unstable

Valve element stuck Oil pollutionSlide valve distortion

The direct driving valve output constant flow thesystem pressure decreases

Valve leakageEdge abrasionRadial valve elementabrasion

Null bias increases gain of system decreasessystem pressure decreases flow noise increases

Null bias out-of-tolerance Inaccurate zero setting Bias exists when DDV is at null positionDisplacementsensor

Coil break Cable break Sensor has no outputConstant bias Iron core of sensor loose Displacement bias

Actuatorcylinder

External leakage Sealing washers failHydraulic leakage

The speed of moving parts decreases systempressure decreases

Internal leakage out-of- toleranceCylinder abrasionOil in high pressure areaflow into low pressure area

The speed of moving parts decreases systempressure decreases vibration and noise appear

Electronicamplifier Gain reduction Internal faults of electronic

amplifier Magnification notably decreases

Table 11 Fault mode and details

Number Fault mode Fault type Details Quadrant1 Force motor fault Mechanical fault Force motor coil break I2 Sensor fault Electronic fault Sensor coil break I3 Leakage fault Mechanical fault Actuator cylinder leakage run out of tolerance II4 Amplifier fault Electronic fault Amplifier gain reduction IV

Faultfrequency

High

Low

Sensor bias

Oil filter blockbreak

SOV leakageSOV diode break

Valve element stuck

Amplifier gain reduction

Sensor coil break

Force motor coil break

Minor MajorFault

criticality

III

III IV

Actuator cylinderleakage

Hydraulic cylinderleakage

Figure 4 Aileron actuator fault quadrantal diagram

three steps are conducted Firstly historical data which inc-lude DDV input force motor current DDV displacementand actuator cylinder displacement are corrupted by whitenoise with signal-noise ratio to be 20 dB in MATLAB Thenthe corrupted data are truncated into a number of datasegments according to the data period And the mean rootmean square (RMS) peak-to-peak value (ppV) and kurtosis

of these data segments are calculated and normalized respec-tively Hence 16-dimensional primitive inputs shown inTable 13 are obtained It is worthmentioning that the dimen-sions of the primitive inputs are not specially chosen since thekey fault information will be automatically extracted by PCAThe flow chart of first step is shown in Figure 5 SecondlyPCA is utilized to conduct dimension reduction and noisereduction and thus the reduced inputs for the SVMmodel aregot Thirdly the reduced inputs are input to the SVM modelfor parameter optimization using grid search Once the opti-mal parameters for the SVMmodel are searched the trainedmodel is prepared for the real-time diagnosis In Real-timediagnosis real-time data are acquired by sensors deployed onthe air craft The same data preprocess as in model trainingpart is conducted and the classification result is returned bythe trained SVM model Fault report would be generatedfor the pilot or ground control station if the classificationresults meet a certain fault criterion The flow chart of themethod is shown in Figure 6

41 PCA Invented by Karl Pearson PCA adopts orthogonalmapping to map a set of possibly correlated variables to prin-cipal components that are linearly uncorrelated The greatestvariance lies on the first principal component the secondgreatest variance on the second principal component and soon

Shock and Vibration 7

Table 12 Fault injection details

Test number Fault mode Fault componentChanged

parameter for faultinjection (unit)

Parameter(normal)

Parameter(fault)

1 Force motor fault Force motor FMC gain 1 02 Sensor fault Displacement sensor Signal output (1m) 1 0

3 Leakage fault Actuator cylinderFlow control valveequivalent orificediameter (mm)

1119890 minus 5 5

4 Amplifier fault Electronic amplifier Gain 50 15

Corrupted by whitenoise

Signal-noise ratio 20dB

DDV inputor

force motor currentor

DDV displacementor

actuator displacement

Data segments

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

Normalization

Primitive inputs

Figure 5 Flow chart of data preprocess

Here is a data matrix 119883 whose 119899 rows are 119899 differentrepetition of the experiment and whose 119901 columns are 119901

different parameters 119883 = (119883(1)

119883(119894)

119883(119899)

)119879 119883(119894)

=

(1199091

119909119901

)(119894)

The scores of new vector of principal com-ponents t

(119894)

= (1199051

119905119901

)(119894)

119894 = 1 2 119899 where 119894 isordinal number of the row are given through a mathematicaltransformation defined by 119901-dimensional vectors of weightsw(119896)

= (1199081

119908119901

)119879

(119896) 119896 = 1 2 119901 where 119896 is the ordinal

number of the principal component The equation is shownas below

119905119896(119894)

= X(119894)

sdot w(119896)

(1)

where 119905119896(119894)

is the 119896th component of 119883(119894)

and thus the max-imum possible variance from 119883 is inherited by t with eachvector of weight w constrained as a unit vector

Thefirst component of a data vectorX(119894)

can then be givenas a score 119905

1(119894)

= X(119894)

sdot w(1)

in the transformed coordinateswhere w

(1)

has to satisfy

w(1)

= argmaxw=1

sum

119894

(1199051

)2

(119894)

= argmaxw=1

Xw2

= argmaxw=1

w119879X119879Xw

(2)

8 Shock and Vibration

Model training Real-time diagnosis

Historicaldata

Data preprocess

Primitiveinputs

PCA

Reducedinputs

Grid search

Gridparameters

10-fold crossvalidation

Optimalparameters

Trainedmodel

Data acquisition

Data process

Fault diagnosis

Normal Sensor fault

Force motor fault

Amplifier fault

Leakage fault

Alarmcriterion

Fault report

Figure 6 Flow chart of fault diagnosis

Table 13 Primitive inputs for SVMmodel

Model input Features ObjectInput 1

Mean

Direct drive valve inputInput 2 Force motor currentInput 3 Direct drive valve displacementInput 4 Actuator cylinder displacementInput 5

RMS

Direct drive valve inputInput 6 Force motor currentInput 7 Direct drive valve displacementInput 8 Actuator cylinder displacementInput 9

ppV

Direct drive valve inputInput 10 Force motor currentInput 11 Direct drive valve displacementInput 12 Actuator cylinder displacementInput 13

Kurtosis

Direct drive valve inputInput 14 Force motor currentInput 15 Direct drive valve displacementInput 16 Actuator cylinder displacement

and the 119896th component can be found by subtracting the first119896 minus 1 principal components from X

X119896

= X minus

119896minus1

sum

119904=1

Xw(119904)

w119879(119904)

(3)

and then finding the weight vector which extracts the maxi-mum variance from this new data matrix

w(119896)

= argmaxw=1

10038171003817100381710038171003817X119896

w10038171003817100381710038171003817

2

= argmaxw=1

w119879X119879119896

X119879119896

w (4)

the 119896th component of a data vector X(119894)

can then be given asa score 119905

119896(119894)

= X(119894)

sdot w(119896)

in the transformed coordinates

The full principal component decomposition of X cantherefore be given as

T = XW (5)

whereW is a 119901-by-119901matrix whose columns are the eigenvec-tors of X119879X

42 Grid Search and CV Grid search executes exhaustivesearching through an artificially selected parameter set of cer-tain learning algorithms A typical soft-margin SVMclassifierequipped with an RBF kernel has two parameters that needto be tuned a regularization constant 119862 and a kernel hyperparameter 120574 The goal of grid search is to identify good pair(119862 120574) so that the classifier can accurately predict unknowndata Exponentially growing sequences of 119862 and 120574 (eg 119862 =

2minus5

2minus3

215 120574 = 2

minus15

2minus13

23

) are recommended byHsu et al [21]

In contrast with other optimization algorithms such asgenetic algorithm and particle swarm algorithm the gridsearch is straightforward but seems naive However thereare two motivations why I prefer the simple grid-searchapproach One is that psychologically we may not feel safeto use methods which avoid doing an exhaustive parametersearch by approximations or heuristics The other reason isthat the computational time required to find good parametersby grid search is not muchmore than that by advancedmeth-ods since there are only two parameters in this case Further-more the grid search can be easily parallelized because each(119862 120574) is independent Many of advanced methods are itera-tive processes for example walking along a path which canbe hard to parallelize

And the performance of the pair is assessed by crossvalidation on the training set The training set is divided into

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 7

Table 12 Fault injection details

Test number Fault mode Fault componentChanged

parameter for faultinjection (unit)

Parameter(normal)

Parameter(fault)

1 Force motor fault Force motor FMC gain 1 02 Sensor fault Displacement sensor Signal output (1m) 1 0

3 Leakage fault Actuator cylinderFlow control valveequivalent orificediameter (mm)

1119890 minus 5 5

4 Amplifier fault Electronic amplifier Gain 50 15

Corrupted by whitenoise

Signal-noise ratio 20dB

DDV inputor

force motor currentor

DDV displacementor

actuator displacement

Data segments

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

MeanRMSppV

Kurtosis

Normalization

Primitive inputs

Figure 5 Flow chart of data preprocess

Here is a data matrix 119883 whose 119899 rows are 119899 differentrepetition of the experiment and whose 119901 columns are 119901

different parameters 119883 = (119883(1)

119883(119894)

119883(119899)

)119879 119883(119894)

=

(1199091

119909119901

)(119894)

The scores of new vector of principal com-ponents t

(119894)

= (1199051

119905119901

)(119894)

119894 = 1 2 119899 where 119894 isordinal number of the row are given through a mathematicaltransformation defined by 119901-dimensional vectors of weightsw(119896)

= (1199081

119908119901

)119879

(119896) 119896 = 1 2 119901 where 119896 is the ordinal

number of the principal component The equation is shownas below

119905119896(119894)

= X(119894)

sdot w(119896)

(1)

where 119905119896(119894)

is the 119896th component of 119883(119894)

and thus the max-imum possible variance from 119883 is inherited by t with eachvector of weight w constrained as a unit vector

Thefirst component of a data vectorX(119894)

can then be givenas a score 119905

1(119894)

= X(119894)

sdot w(1)

in the transformed coordinateswhere w

(1)

has to satisfy

w(1)

= argmaxw=1

sum

119894

(1199051

)2

(119894)

= argmaxw=1

Xw2

= argmaxw=1

w119879X119879Xw

(2)

8 Shock and Vibration

Model training Real-time diagnosis

Historicaldata

Data preprocess

Primitiveinputs

PCA

Reducedinputs

Grid search

Gridparameters

10-fold crossvalidation

Optimalparameters

Trainedmodel

Data acquisition

Data process

Fault diagnosis

Normal Sensor fault

Force motor fault

Amplifier fault

Leakage fault

Alarmcriterion

Fault report

Figure 6 Flow chart of fault diagnosis

Table 13 Primitive inputs for SVMmodel

Model input Features ObjectInput 1

Mean

Direct drive valve inputInput 2 Force motor currentInput 3 Direct drive valve displacementInput 4 Actuator cylinder displacementInput 5

RMS

Direct drive valve inputInput 6 Force motor currentInput 7 Direct drive valve displacementInput 8 Actuator cylinder displacementInput 9

ppV

Direct drive valve inputInput 10 Force motor currentInput 11 Direct drive valve displacementInput 12 Actuator cylinder displacementInput 13

Kurtosis

Direct drive valve inputInput 14 Force motor currentInput 15 Direct drive valve displacementInput 16 Actuator cylinder displacement

and the 119896th component can be found by subtracting the first119896 minus 1 principal components from X

X119896

= X minus

119896minus1

sum

119904=1

Xw(119904)

w119879(119904)

(3)

and then finding the weight vector which extracts the maxi-mum variance from this new data matrix

w(119896)

= argmaxw=1

10038171003817100381710038171003817X119896

w10038171003817100381710038171003817

2

= argmaxw=1

w119879X119879119896

X119879119896

w (4)

the 119896th component of a data vector X(119894)

can then be given asa score 119905

119896(119894)

= X(119894)

sdot w(119896)

in the transformed coordinates

The full principal component decomposition of X cantherefore be given as

T = XW (5)

whereW is a 119901-by-119901matrix whose columns are the eigenvec-tors of X119879X

42 Grid Search and CV Grid search executes exhaustivesearching through an artificially selected parameter set of cer-tain learning algorithms A typical soft-margin SVMclassifierequipped with an RBF kernel has two parameters that needto be tuned a regularization constant 119862 and a kernel hyperparameter 120574 The goal of grid search is to identify good pair(119862 120574) so that the classifier can accurately predict unknowndata Exponentially growing sequences of 119862 and 120574 (eg 119862 =

2minus5

2minus3

215 120574 = 2

minus15

2minus13

23

) are recommended byHsu et al [21]

In contrast with other optimization algorithms such asgenetic algorithm and particle swarm algorithm the gridsearch is straightforward but seems naive However thereare two motivations why I prefer the simple grid-searchapproach One is that psychologically we may not feel safeto use methods which avoid doing an exhaustive parametersearch by approximations or heuristics The other reason isthat the computational time required to find good parametersby grid search is not muchmore than that by advancedmeth-ods since there are only two parameters in this case Further-more the grid search can be easily parallelized because each(119862 120574) is independent Many of advanced methods are itera-tive processes for example walking along a path which canbe hard to parallelize

And the performance of the pair is assessed by crossvalidation on the training set The training set is divided into

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Shock and Vibration

Model training Real-time diagnosis

Historicaldata

Data preprocess

Primitiveinputs

PCA

Reducedinputs

Grid search

Gridparameters

10-fold crossvalidation

Optimalparameters

Trainedmodel

Data acquisition

Data process

Fault diagnosis

Normal Sensor fault

Force motor fault

Amplifier fault

Leakage fault

Alarmcriterion

Fault report

Figure 6 Flow chart of fault diagnosis

Table 13 Primitive inputs for SVMmodel

Model input Features ObjectInput 1

Mean

Direct drive valve inputInput 2 Force motor currentInput 3 Direct drive valve displacementInput 4 Actuator cylinder displacementInput 5

RMS

Direct drive valve inputInput 6 Force motor currentInput 7 Direct drive valve displacementInput 8 Actuator cylinder displacementInput 9

ppV

Direct drive valve inputInput 10 Force motor currentInput 11 Direct drive valve displacementInput 12 Actuator cylinder displacementInput 13

Kurtosis

Direct drive valve inputInput 14 Force motor currentInput 15 Direct drive valve displacementInput 16 Actuator cylinder displacement

and the 119896th component can be found by subtracting the first119896 minus 1 principal components from X

X119896

= X minus

119896minus1

sum

119904=1

Xw(119904)

w119879(119904)

(3)

and then finding the weight vector which extracts the maxi-mum variance from this new data matrix

w(119896)

= argmaxw=1

10038171003817100381710038171003817X119896

w10038171003817100381710038171003817

2

= argmaxw=1

w119879X119879119896

X119879119896

w (4)

the 119896th component of a data vector X(119894)

can then be given asa score 119905

119896(119894)

= X(119894)

sdot w(119896)

in the transformed coordinates

The full principal component decomposition of X cantherefore be given as

T = XW (5)

whereW is a 119901-by-119901matrix whose columns are the eigenvec-tors of X119879X

42 Grid Search and CV Grid search executes exhaustivesearching through an artificially selected parameter set of cer-tain learning algorithms A typical soft-margin SVMclassifierequipped with an RBF kernel has two parameters that needto be tuned a regularization constant 119862 and a kernel hyperparameter 120574 The goal of grid search is to identify good pair(119862 120574) so that the classifier can accurately predict unknowndata Exponentially growing sequences of 119862 and 120574 (eg 119862 =

2minus5

2minus3

215 120574 = 2

minus15

2minus13

23

) are recommended byHsu et al [21]

In contrast with other optimization algorithms such asgenetic algorithm and particle swarm algorithm the gridsearch is straightforward but seems naive However thereare two motivations why I prefer the simple grid-searchapproach One is that psychologically we may not feel safeto use methods which avoid doing an exhaustive parametersearch by approximations or heuristics The other reason isthat the computational time required to find good parametersby grid search is not muchmore than that by advancedmeth-ods since there are only two parameters in this case Further-more the grid search can be easily parallelized because each(119862 120574) is independent Many of advanced methods are itera-tive processes for example walking along a path which canbe hard to parallelize

And the performance of the pair is assessed by crossvalidation on the training set The training set is divided into

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

V equal-sized subsets in V-fold cross validation In propersequence each subset is used for test while other Vminus1 subsetsare used for classifier training Hence V prediction resultsare obtained and the percentage of data correctly classifiedis the final cross validation accuracy Rodriguez et al [22]conducted a sensitivity analysis for cross validation and found10-fold cross validation is a practical method

43 One-versus-One SVM One-versus-one SVM is pro-posed by Knerr et al [23] that transform the 119899-classificationproblem into 119899(119899 minus 1)2 two-classification problem One-versus-one SVM adopts the voting method to get respec-tively the number of votes that the sample 119909 belongs to eachclassification In the end 119909 belongs to the classification inwhich the number of votes is the largest Hsu and Lin [24]compared one-versus-one SVM one-versus-all SVM andDAG-SVM and the results showed that one-versus-one SVMmay be more suitable for practical use

In order to construct the subclassifier for class 119894 and 119895 takethe sample of class 119894 and class 119895 from the original sample as thetraining sample for two-classification problem the optimalproblem is shown as follows

min120596

119894119895119887

119894119895120585

119894119895

1

2(120596119894119895

)119879

120596119894119895

+ 119862

119894

sum

119895=1

120585119894119895

119894

(120596119894119895

)119879

(6)

Corresponding decisive plane is

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

ge 1 minus 120585119894119895

119894

if 119910119905

= 119894

(120596119894119895

)119879

120601 (119909119905

) + 119887119894119895

le minus1 + 120585119894119895

119894

if 119910119905

= 119895 120585119894119895

119894

ge 0

(7)

where 120596119894119895 is the coefficient of the hyperplane between classes119894 and 119895 119887119894119895 is the intercept of the hyperplane between classes 119894and 119895120601(119909

119905

) is themap of the sample119909119905

in the high-dimensionspace 119862 is error penalty factor which reflects the valueddegree of sample outliers and adjusts the proportion betweenthe incredible range and empirical risk of SVM networkmodel and 120585

119894119895

119894

is the fitting error variable

44 Alarm Criterion With the continuous development ofFCC the limitation of FCC will be kept pushing Once thecomputational limits were broken and complex algorithmcould also achieve practically fast fault detection then inorder to reduce false alarm rate to the greatest extent three-alarm criterion listed below can be attempted

Criterion 1 (two consecutive classification results concur) Iftwo consecutive classification results concur then the classi-fication results are validated and the corresponding fault canbe reported

Criterion 2 (two out of three consecutive classification resultsconcur) If the first two consecutive classification results dif-fer and yet two out of three consecutive classification resultsconcur then the classification results are validated and thecorresponding fault denoted by the two same classificationresults can be reported

Table 14 Contribution rate of principal component

Principalcomponent Eigenvalue Contribution

rateCumulative

contribution rate1 40114 8344 83442 01995 415 87593 01339 279 90384 01257 261 92995 01048 218 95176ndash16 lt01 lt2 gt9517

Table 15 The cross validation rate and test rate with regard to dif-ferent dimension of inputs

Dimension CV rate Test rate1 7673 76752 8208 83053 8937 89874 9663 96505 9888 9901

Criterion 3 (none of three consecutive classification resultsconcur) If three consecutive classification results all differthen the diagnosis fails and the diagnosis-fail report will besubmitted

5 Fault Diagnosis and Result Analysis

In this simulation case the amplitude of system input is2mm the frequency of system input is 05Hz the samplingrate is 200 Ss and the sampling time is 20 s Accordingly thefeatures which include mean RMS ppV and kurtosis areextracted every 200 points The data obtained are consideredas the historical data to train the model Once trained themodel can be used to detect faults every 200 points (lessthan 1 s depending on the real-time sampling rate) in real-time diagnosis The extracted features at different workingconditions are listed in Figure 7 from which it is clear to seethat different working conditions result in different featureamplitude so that fault classification using these features ispositively tenable

The results of PCA for the 16-dimensional primitiveinputs are shown in Table 14 and Figure 8 from which it isclear to see that the first three principal components occupyup to 100 cumulative contribution rate and that the inputsdimension may even be reduced to just 1-dimension depend-ing on the ultimate test rate of the trained model

As shown in Table 15 using just the first principal compo-nent to train the model the trained modelrsquos cross validationrate is 7673 and test rate is 7675 which implies overre-duction and information loss Using first five principal com-ponents to train the model the trained modelrsquos cross valida-tion rate is increased up to 9888 and test rate to 9901close to 1 which is more than good so the reduced inputs canbe determined as three-dimensional

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

Mean

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

minus6

minus4

minus2

0

2A

mpl

itude

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Root mean square

DDV inputDDV displacement

ACT displacementForce motor current

1

2

3

4

5

6

Am

plitu

de

Time (s)

0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

DDV inputDDV displacement

ACT displacementForce motor current

Peak-to-peak value

0

5

10

15

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

Normal Leakagefault

Amplifierfault

Sensorfault

Force motorfault

Kurtosis

135

14

145

15

155

16

Am

plitu

de

Time (s)0 020 20 0 20 0 20 0 20

DDV inputDDV displacement

ACT displacementForce motor current

Figure 7 Features extracted

Table 16 Comparison between traditional SVM and PGC-SVM

Method Time cost Classification accuracyParameters optimization Training

General SVM days even months 15884 s 8187PGC-SVM 8h 20mins 08989 s 9888

There are two parameters penalty factor 119862 and kernelparameter 120574 to be optimized in one-versus-one SVM usingRBF kernel which is shown below

119870(119909 1199091015840

) = exp (12057410038171003817100381710038171003817119909 minus 1199091015840

10038171003817100381710038171003817

2

) (8)

The exponentially growing sequences of parameter pairs(119862 120574) are adopted in grid search and the contour of parameterpairs is shown in Figure 9 The best pair (119862 = 4096 120574 =

1) whose cross validation accuracy was up to 9887 wasobtained

The final results shown in Table 16 indicated that thePGC-SVM proposed in the paper outperformed traditionalSVM in both time cost (Pentium(R) Dual-Core CPU T4500 230GHz) and classification accuracy

6 Conclusions

This paper presents an aileron actuator fault diagnosisapproach combining principal component analysis (PCA)

1 2 3 4 50

Result of PCA

Principal component

9038 9299 9517

415 279 261 218

87598344

102030405060708090

100

Con

trib

utio

n ra

te (

)

0102030405060708090100

Cum

ulat

ive c

ontr

ibut

ion

rate

()

Figure 8 Result of PCA

grid search (GS) 10-fold cross validation (CV) and one-versus-one support vector machine (SVM)The classificationaccuracy is good enough for the diagnosis of the main faultsof aileron actuatorswhich include forcemotor coil break sen-sor coil break actuator cylinder leakage and amplifier gain

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

minus5 0 5 10 1580

82

84

86

88

90

92

94

96

98

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

2

C = 4096 120574 = 1

Best log2(C) = 12 log2(120574) = 0 accuracy = 9887

log2

(120574)

log2(C)

Figure 9 Grid search for model with PCA

reduction Compared to the traditional SVM the PGC-SVMdemands less time for both parameters optimization andmodel training The performance of the proposed algorithmis fast enough for fault detection to switch as soon as possibleon a redundant actuator The high classification accuracy ofactuator faults gives the algorithm a bonus that maintenanceefficiency can be promoted since maintenance preparationcan be done before the landing of aircraft Hence thealgorithm presented in the paper shows a great potential onceit passed the rigorous test of real FCC

Obviously the future work lies in the field validation ofthe proposed algorithm And in practice the field data areoften severely corrupted by various data noise that may influ-ence the performance of the algorithm so that noise immu-nity of the proposed algorithm should also be consideredBesides the method still has some room for improvementmdashthe computational resource consumption can be compressedfurther and detection delay can be minimized

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Wei-Li Qin and Chen Lu drafted the paper Wei-Li Qin andChen Lu acquired the data Wei-Li Qin analyzed and inter-preted the dataWei-Li Qin andChen Lu critically revised thepaper Chen Lu and Wen-Jin Zhang planned and supervisedthe research

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grants nos 61074083 50705005 and

51105019) and by the Technology Foundation Program ofNational Defense (Grant no Z132013B002)

References

[1] Y Chinniah R Burton S Habibi and E Sampson ldquoIdentifi-cation of the nonlinear friction characteristics in a hydraulicactuator using the extended Kalman filterrdquo Transactions of theCanadian Society for Mechanical Engineering vol 32 no 2 pp121ndash136 2008

[2] I Lopez and N Sarigul-Klijn ldquoA review of uncertainty in flightvehicle structural damage monitoring diagnosis and controlchallenges and opportunitiesrdquo Progress in Aerospace Sciencesvol 46 no 7 pp 247ndash273 2010

[3] F Zhao and H Su ldquoA decision tree approach for powertransformer insulation fault diagnosisrdquo in Proceedings of the 7thWorld Congress on Intelligent Control and Automation (WCICArsquo08) pp 6882ndash6886 IEEE Chongqing China June 2008

[4] S Ozev P K Nikolov and F Liu ldquoParametric fault diagnosisfor analog circuits using a bayesian frameworkrdquo in Proceedingsof the 24th IEEE VLSI Test Symposium IEEE Computer Societypp 272ndash277 Berkeley Calif USA May 2006

[5] C Zang and M Imregun ldquoStructural damage detection usingartificial neural networks and measured FRF data reducedvia principal component projectionrdquo Journal of Sound andVibration vol 242 no 5 pp 813ndash827 2001

[6] L He K-N Jia and Z-Q Fan ldquoThe immune genetic algorithmin fault diagnosis of modern power systemrdquo in Proceedings ofthe 2nd International Conference on Education Technology andComputer (ICETC rsquo10) vol 4 pp V4-26ndashV4-29 IEEE Shang-hai China June 2010

[7] E AltunokMM R Taha D S Epp R LMayes and T J BacaldquoDamage pattern recognition for structural health monitoringusing fuzzy similarity prescriptionrdquo Computer-Aided Civil ampInfrastructure Engineering vol 21 no 8 pp 549ndash560 2006

[8] D Henry J Cieslak A Zolghadri and D Efimov ldquoA non-conservative119867

minus

119867infin

solution for early and robust fault diagno-sis in aircraft control surface servo-loopsrdquo Control EngineeringPractice vol 31 no 1 pp 183ndash199 2014

[9] B Vanek A Edelmayer Z Szabo and J Bokor ldquoBridging thegap between theory andpractice in LPV fault detection for flightcontrol actuatorsrdquoControl Engineering Practice vol 31 no 1 pp171ndash182 2014

[10] A Gheorghe A Zolghadri J Cieslak P Goupil R Dayre andH L Berre ldquoModel-based approaches for fast and robust faultdetection in an aircraft control surface servo loop from theoryto flight testsrdquo IEEE Control Systems Magazine vol 33 pp 20ndash84 2013

[11] P Goupil and A Marcos ldquoThe European ADDSAFE projectindustrial and academic efforts towards advanced fault diagno-sisrdquo Control Engineering Practice vol 31 pp 109ndash125 2014

[12] D Efimov J Cieslak A Zolghadri and D Henry ldquoActuatorfault detection in aircraft systems oscillatory failure case studyrdquoAnnual Reviews in Control vol 37 no 1 pp 180ndash190 2013

[13] T Yaohua G Jinghuai and B Qianzong ldquoNovel selectivesupport vector machine ensemble learning algorithmrdquo Journalof Xirsquoan Jiaotong University vol 42 no 10 pp 1221ndash1225 2008

[14] W Jiang and S Wu ldquoMulti-data fusion fault diagnosis methodbased on SVMand evidence theoryrdquoChinese Journal of ScientificInstrument vol 31 no 8 pp 1738ndash1743 2010

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

[15] X Gu S Yang and S Qian ldquoOn rotary machinersquos multi-classfault recognition based on SVMrdquo in Proceedings of the 26th Chi-nese Control Conference (CCC rsquo07) pp 460ndash463 IEEE HunanChina July 2007

[16] S-L Zhao and Y-C Zhang ldquoSVM classifier based fault diagno-sis of the satellite attitude control systemrdquo in Proceedings of theInternational Conference on Intelligent Computation Technologyand Automation (ICICTA rsquo08) pp 907ndash911 Hunan ChinaOctober 2008

[17] Z Zhao M Jia F Wang and S Wang ldquoIntermittent chaosand sliding window symbol sequence statistics-based early faultdiagnosis for hydraulic pump on hydraulic tube testerrdquoMechan-ical Systems and Signal Processing vol 23 no 5 pp 1573ndash15852009

[18] J Yao G Yang and DMa ldquoInternal leakage fault detection andtolerant control of single-rod hydraulic actuatorsrdquo Mathemat-ical Problems in Engineering vol 2014 Article ID 345345 14pages 2014

[19] P Li Z-H Yuan and F Su ldquoReliability analysis of electro-hydraulic actuator based on fuzzy FMECArdquo Machine Tool ampHydraulics vol 7 pp 178ndash182 2013

[20] E Balaban A Saxena P Bansal K F Goebel P Stoeltingand S Curran ldquoA diagnostic approach for electro-mechanicalactuators in aerospace systemsrdquo in Proceedings of the IEEEAerospace Conference pp 1ndash13 IEEE Big Sky Mont USAMarch 2009

[21] C-W Hsu C-C Chang and C-J Lin A Practical Guide toSupport Vector Classification Department of Computer Scienceamp Information Engineering National Taiwan University 2010

[22] J D Rodriguez A Perez and J A Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis ampMachine Intelligence vol 32no 3 pp 569ndash575 2010

[23] S Knerr L Personnaz and G Dreyfus ldquoSingle-layer learningrevisited a stepwise procedure for building and training aneural networkrdquo in Neurocomputing pp 41ndash50 Springer 1990

[24] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of