research article online fault-tolerant onboard aeroengine...

Research ArticleOnline Fault-Tolerant Onboard Aeroengine ModelTuning Structure

Shuiting Ding1 Ye Yuan1 Naiyu Xue2 and Xiaofeng Liu2

1School of Energy and Power Engineering Beijing University of Aeronautics and Astronautics Beijing China2School of Transportation Science and Engineering Beijing University of Aeronautics and Astronautics Beijing China

Correspondence should be addressed to Xiaofeng Liu liuxfbuaaeducn

Received 9 July 2016 Revised 7 October 2016 Accepted 19 October 2016

Academic Editor Kenneth M Sobel

Copyright copy 2016 Shuiting Ding 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

Online onboard aeroengine models (OBEMs) have been widely used in health management fault diagnostics and fault-tolerantcontrol A mismatch between the OBEM and the actual engine may be caused by a variety of factors such as health degradationor sensor fault and may influence the effectiveness of the systems mentioned above However mismatch caused by unpredictablesensor fault is hardly distinguished from that caused by health degradation through the tuning process A fault-tolerant OBEMtuning structure is provided to perform the online tuning function when health degradation and sensor fault coexist This systemincludes three parts that include improved fault diagnostics and isolation (IFDI) a fault-tolerant OBEM tuning system (FTOTS)and a channel switching module IFDI is used to distinguish the cause of mismatch and provide fault information a FTOTS is usedto complete an online tuning process based on information obtained from the IFDI and the channel switching module is used toswitch the working process from the IFDI to the FTOTS Several simulation results show that this system is able to distinguish thecauses of mismatch and complete online tuning in the case of sensor faults

1 Introduction

Aeroengines are operated in harsh environments with hightemperatures pressures and speeds and the deteriorationof components is unavoidable The performance of compo-nents sensors and actuators slowly degrades during regularoperations [1] During actual flight highly condensed sandor salt can accelerate fan or compressor degradation andtropical heat can accelerate turbine degradation [2] Thedamage caused by foreign objects primarily affects the fanand front part of the engine with the extent of the damagedetermined by the geometry angle of impact hardnessand relative speed amongst other factors of the object [3]Volcanic ash may severely affect the hot section of the enginewhile producing no visible damage to the cooler portions inthe front of the engine [3] and ash ingested by the engine canlead to an immediate degradation of engine performance [4]

Unpredictable sensor fault may occur during flight TheKalman filter has proved to be a useful tool in sensor faultdetection and in recent years different diagnostics systemsbased on the Kalman filter have been developed to detect

sensor faults [5ndash12] The fault diagnostics systems are de-signed based on the nondegrade condition of the enginewhich has become a reference health baseline for diagnosticsprocesses and any observed deviations from the measuredoutputs of the reference baseline outputs may be indicative ofa fault However as previously referenced health degradationcauses the outputs of the actual engine to deviate from thereference health baseline When the deviation exceeds acertain level it becomes difficult to distinguish the fault fromthe mismatch that caused the health degradation merely byobserving the measured outputs

In various studies [7ndash9] fault detection and isolation(FDI) based on the Kalman filter have been proven capableof identifying faulty sensor location when health degradationand sensor fault coexist however this diagnostics systemmaylose its effectiveness when the health degradation exceeds acertain level Therefore the diagnostics system based on theKalman filter must be improved to accommodate severelydegraded engines

Onboard aeroengine models (OBEMs) have been com-monly used in recent years to provide information for fault

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2016 Article ID 7904657 15 pageshttpdxdoiorg10115520167904657

2 International Journal of Aerospace Engineering

diagnostics and engine control As advanced control systemshealth monitoring and diagnosis systems with OBEM weredeveloped to improve the performance and safety of aero-engines The NASA Glenn Research Center (GRC) proposedan intelligent engine control system that includes activecontrol health management and fault-tolerant control tech-nologies [13 14] The latest model-based control system usesOBEM to calculate unmeasured outputs such as aeroenginethrust compressor stall and surge [15] In 2006 the GRCintroduced OBEM into the structure of the linear Kalman fil-ter to establish the hybrid Kalman filter (HKF) [16 17] In thefollowing years the HKF was used for engine performanceestimation and sensor fault detection [18 19] Pourbabaee etal introduced the HKF into an FDI to achieve the functionsof sensor fault detection isolation and identification [20 21]

Recently a real-time self-tuning OBEM has been com-bined with a health management structure [22] Simon et alpresented a real-time self-tuning model used for engineperformance monitoring and fault diagnostics [22ndash24] Thismodel is a hybrid model including an OBEM and neuralnetworks Furthermore Volponi et al presented an onlinetuning engine model updated with a Kalman filter [25 26]This kind of an OBEM is able to minimize the mismatchbetween an OBEM and the actual engine and maintain theeffectiveness of the fault diagnostics system However duringthe tuning process the influence of a faulty signal is notconsidered so a tuning system with a fault-tolerant functionmust be developed because an online tuning system mayencounter coexisting health degradation and sensor fault

The following contents of this paper include three sec-tions Section 2 presents a general description of fault-tolerant tuning structures and the development of differentparts including the improved fault diagnostics and isolation(IFDI) fault-tolerantOBEM tuning system (FTOTS) and thechannel switching module Section 3 includes the simulationresults which were used to prove the effectiveness of thesystem The last section contains the conclusions of thiswork

2 Fault-Tolerant Online Tuning Structure

Health degradation and sensor fault are both capable of caus-ing a mismatch between the OBEM and the actual engineIf health degradation and sensor fault coexist an analysis ofthemismatch and the correspondingmethod tominimize themismatch must be provided During the traditional onlinetuning process the information used for the tuning processcontains measurement noise sensor bias and any attendantmodeling error however the effect of the senor fault is nottypically considered [26] If the mismatch is caused onlyby sensor fault the tuning process should not be initiatedbecause this kind of mismatch cannot be solved by updatinghealth information During the onlineOBEM tuning processthe influence of a faulty sensor should be considered becausethe mismatch caused by the faulty signal will also be consid-ered during the tuning process If the online tuning systemis able to remove the corresponding faulty signal the tuningresults will be accurate and themismatch between the OBEMand actual engine will be minimized

Engine

FTOTS

IFDI

OBEM

Measuredoutputs

Computedoutputs

Fault information

Health information

Switchingmodule

Switching informationu

z

Figure 1 A general fault-tolerant OBEM tuning structure

The FTOTS is used to analyze the mismatch cause andto minimize the mismatch caused by health degradationThefunctions of this system include sensor fault diagnostics andfault-tolerant online OBEM tuning There are three maincomponents of this system including the IFDI the FTOTSand the channel switching module The IFDI is used in theestimation process to locate the faulty sensor and the FTOTSis used in the tuning process to minimize the mismatchThe two systems work on different channels and are switchtriggered by the signal The general structure is shown inFigure 1

The IFDI is developed based on FDI The IFDI has twotasks sensor fault diagnostics and online tuning operationdecisionThe IFDI is used to locate the faulty sensor andmakethe channel switching decision Compared with conventionalFDI IFDI has the extra function of providing switchinginformation to the channel switching module

The FTOTS combines the OBEM tuning system (OTS)with fault-tolerant function FTOTS is used to remove faultyinput signals based on the fault information of the IFDI andminimize the mismatch caused by health degradation In thissystem the number of measured outputs is greater than thatof health parameters so the absence of single signal will notaffect the estimation of the Kalman filter

The channel switching module is used to perform thefunction of channel switching between the estimation pro-cesses and tuning process During the estimation processof the IFDI the health information provided to the OBEMretains its original values ℎref [14] however during the tuningprocess the health parameters are tuned by the FTOTS Dif-ferent working conditionsmean that the IFDI and the FTOTSwill not work in parallel otherwise there interruption occursbetween the two systems The channel switching module isable to resolve the conflict between the IFDI and the FTOTSThe channel switching process between the IFDI and theFTOTS of the system is shown in Figure 2

21 IFDI Structure In this paper the IFDI and the FTOTSare both established based on a nonlinear component-levelengine model [27] The model is a two-spool high-bypassturbofan engine Linearization computation is completedbased on the two-step perturbation method [27] The linearmodel in state-space form is

Δ (119905) = 119860Δ119909 (119905) + 119861Δ119906 (119905) + 119871Δℎ (119905) + 119866Δ119911 (119905) Δ119910 (119905) = 119862Δ119909 (119905) + 119863Δ119906 (119905) + 119872Δℎ (119905) + 119867Δ119911 (119905) (1)

International Journal of Aerospace Engineering 3

IFDIStart

Switchingmodule

Removingfault signal

Fault information

Tuningstarting

Yes

IFDI continueworkingNo

FTOTS

Tuning completed

IFDI starting

Yes

Tuning continuingNo

Figure 2 The channel switching process of a fault-tolerant OBEMtuning structure

where 119909 represents the state variables of the engine such as119909 = [119873119867 119873119871]119879 119906 represents the control input of the enginesuch as the fuel input and ℎ represents the health parameterThe health parameters are the efficiency and flow capacityof the engine compressors and turbines As they deviatefrom the nominal baseline the performance delivered byeach component degrades [2] 119911 presents the environmentalinputs such as altitude and Mach number 119910 represents themeasured outputs of the engine and 119860 119861 119862 119863 119871 119872 119866119867 are the corresponding matrices of the model The enginehealth parameters are listed as follows

Fan efficiency (119864fan) and fan flow capacity (119865fan)LPC efficiency (119864LPC) and LPC flow capacity (119865LPC)HPC efficiency (119864HPC) andHPCflow capacity (119865HPC)HPT efficiency (119864HPT) and HPT flow capacity (119865HPT)LPT efficiency (119864LPT) and LPT flow capacity (119865LPT)

And the engine measured outputs are listed as follows

High pressure rotor speed (119873119867) and low pressurerotor speed (119873119871)Outlet pressure of fan (OPfan) and outlet temperatureof fan (OTfan)Outlet pressure of LPC (OPLPC) and outlet tempera-ture of LPC (OTLPC)Outlet pressure of HPC (OPHPC) and outlet tempera-ture of HPC (OTHPC)Outlet pressure of HPT (OPHPT) and outlet tempera-ture of HPT (OTHPT)Engine exhaust pressure (EGP) and engine exhausttemperature (EGT)

HKF is a hybrid structure consisting of a Kalman filterand OBEM and the OBEM receives offline ℎref as referenceto minimize the deviation of the measured outputs betweenthe OBEM and the actual engine The establishment of theHKF is completed based on the literature [16 17] with a formof

Δkal = 119860kal (119909kal minus 119909OBEM) + 119870kal (119910 minus ) = 119862kal (119909kal minus 119909OBEM) + 119910OBEM (2)

where 119909kal = [ 119909ℎ ] 119860kal = [ 119860 1198710 0 ] 119861kal = [ 1198610 ] and 119862kal =[119862 119872]119870kal is the gain matrix of the HKF 119910 is the measuredoutput and is the estimated measured output of HKF Thegain matrix119870kal is calculated based on the literature [28]

The IFDI consists of a bank of HKFs For sensor faultdetection 119899HKFs are designed where 119899 is the number of sen-sors EachHKF estimates the corresponding state variables ofthe engine based on a unique set of 119899 minus 1 sensors The sensorthat is not used by a particular HKF is the hypothetical faultyone monitored by that HKF

The functions of the IFDI are performed based on aweighted sum of squared residuals (WSSR) [16] EachHKF inthe IFDI computes the correspondingWSSR Comparedwithconventional FDI there are two kinds ofWSSR in IFDI one isWSSRHKF which represents the deviation of outputs betweenHKF and the actual engine and the other is WSSROBEMwhich represents the deviation of outputs between theOBEMand the actual engine The function of faulty sensor locationis achieved based on WSSRHKF and the function of onlinetuning decision is achieved based on WSSROBEM The formof WSSR corresponding to the 119894th HKF is

WSSR119894HKF = 119882119894119903 (119890119894HKF)119879 119890119894HKFWSSR119894OBEM = 119882119894119903 (119890119894OBEM)119879 119890119894OBEM

(3)

where 119890119894HKF = 119910119894 minus 119894 119890119894OBEM = 119910119894 minus 119910119894OBEM and 119910119894 are theoutputs from 119899 minus 1 sensors that the 119894th Kalman filter uses119910119894OBEM are the corresponding outputs from the OBEM usedas the baseline outputs of the 119894th Kalman filter and 119894 arethe corresponding estimated outputs of the 119894th Kalman filter119882119894119903 represents the corresponding weighting factor of the 119894thKalman filter 119882119894119903 = (119910119894OBEM)minus2 The computation of WSSR isshown in Figure 3

The sensor fault detection and online tuning decisionlogic is designed as shown in Figure 4 If there is no sensorfault all WSSRHKFs are lower than the corresponding thresh-old and the sensor fault diagnostics results of the IFDI are 0If the 119894th sensor is faulty all HKFs will use corrupted infor-mation except for the 119894th one It is able to accommodate thefaulty sensor and is thus able to estimate health informationmore accurately because the estimated results are not affectedby the faulty signalTheWSSR119894HKF corresponding to the faultysensor should be lower than the corresponding threshold andthe remaining 119899 minus 1 WSSRHKFs are higher than thresholdstherefore the faulty sensor can be located Meanwhile theWSSR119894OBEM of the 119894th HKF is used to show the mismatchbetween the OBEM and the actual engine because it is notaffected by the faulty signalWhen the value of theWSSR119894OBEMexceeds the threshold 120578119894 the online tuning system should beinitiated this step comprises the additional function providedby the IFDI

The threshold values 120582119894 and 120578119894 are determined usingdiagnostics logic Setting the threshold 120582119894 to a low valueincreases the chance of detecting faults but also increasesthe chance of generating false alarms and vice versa Thethreshold 120578119894 is set to ensure that the online tuning process


Sensor sortingith sensor is

removed from y to

computationOutput sorting

ith output isremoved from

y

y－

y1

y2

yn

y1－

y2－

yi－

yn－

HKF 1

HKF 2

HKF i

HKF n

e1（＋

e1－

e2（＋

e2－

ei（＋

ei－

en（＋

en－

create yi vector

yi

y－ to createyi－ vector

WSSR

WSSR1HKF

WSSR2HKF

WSSRiHKF

WSSRnHKF

WSSR1OBEM

WSSR2OBEM

WSSRiOBEM

WSSRnOBEM

Figure 3 Computation of WSSR

Bank ofHKF

Choosing theminimumvalue of

lt i

lt i

ith sensor is faulty

ith sensoris normal

Yes

Yes

No

No Online tuning is needed

Online tuning is not needed

y

y－

WSSRiOBEM

WSSRiHKFWSSR

WSSRHKF

Figure 4 Sensor fault detection and online tuning decision logic

is not falsely triggered by process and measurement noiseinterference It would be reasonable to use different thresholdvalues at different power settings to achieve effective faultdetection performance [16] The sensors have measurementdeviations and mismatch caused by sensor deviation isunavoidable so the standard deviations of the sensors shouldbe considered in the selection of thresholds in order to avoidfalse alarms In this paper the WSSRs were computed withdimensionless treatment and thus the thresholds of differentHKFs should be set at the same order of magnitude at thecorresponding power setting

22 Development of FTOTS FTOTS refers to an improvedOTS with a fault-tolerant function An OTS is developedusing an HKF to perform the function of online OBEMtuning and it consists of a closed-loop structure consistingof a Kalman filter and an OBEM In an OTS a Kalman filer

is used as the ldquocontrollerrdquo to produce the outputs from theOBEM used to track the outputs of the actual engine TheOBEM receives health information from the Kalman filterto compute tuned measured outputs The OTS is a type ofnonlinear estimator because the estimation of the measuredoutputs is completed by a nonlinear OBEM The OTS takesadvantage of the high degree of matching between the OBEMand the actual engine to improve the accuracy of estimationand to reduce the estimation error caused by discrepanciesbetween the state-space formulation of the filter and theactual engine The general structure of an OTS is shown inFigure 5

An OBEM in an OTS is represented by

OBEM = 119891 (119909OBEM 119906 ℎ 119911) 119910OBEM = 119892 (119909OBEM 119906 ℎ 119911) (4)


Engine Kalman filter OBEM

u

z

Measuredoutputs

Estimated healthinformation

Computed outputs

Figure 5 General structure of an OTS

where the OBEM receives health information from theKalman filter in real-time and the outputs of the Kalmanfilter are estimated health information ℎ = ℎref + Δℎ Thestructure of the Kalman filter is simplified because it doesnot need to compute measured outputs The structure of theKalman filter is converted into

Δkal = 119860kalΔ119909kal + 119870kal (119910 minus 119910OBEM) Δℎ = 119862kalΔ119909kal

(5)

where 119862kal = [ 0 00 IM ] 119870kal = [ 11989611198962

] 1198961 is related to the rotorspeed 1198962 is related to the health parameter and IM is theidentity matrix

119909kal of the filter consists of two parts 119909kal = [ 119909ℎ ] where119909 represents the rotor speed and ℎ represents the healthparameter According to 119860kal = [ 119860 1198710 0 ] the variation in 119909will not affect the variation in ℎ and there is no couplingrelationship between the two parts As variation in the rotorspeed is not computed in an OTS the elements of matricesassociated with rotor speed can be removed from the Kalmanfilter such that 1199091015840kal = ℎ 1198601015840kal = [0 0] and1198701015840kal = 1198962

The simplified structure of the Kalman filter in an OTS isshown in (6) 119862kal becomes IM 1198601015840kal and1198701015840kal are part of 119860kaland 119870kal and the elements of 119860kal and 119870kal related to rotorspeed are removed to establish 1198601015840kal and1198701015840kal

Δ1015840kal = 1198601015840kalΔ1199091015840kal + 1198701015840kal (119910 minus 119910OBEM) Δℎ = IMΔ1199091015840kal

(6)

1198601015840kal becomes a zero matrix because the values of theelements that are related to health parameters equal 0 thusthe structure of the Kalman filter becomes

Δ1015840kal = 1198701015840kal (119910 minus 119910OBEM) Δℎ = IMΔ1199091015840kal

(7)

The structure of the OTS can be described by

Δ1015840kal = 1198701015840kal (119910 minus ) = 119910OBEM (8)

The OTS is similar to a closed-loop control system Toachieve a quick and smooth tuning process and maintain

stability of system gain matrix 1198701015840kal is computed based onthe linear quadratic regulator theory [29 30] The linearquadratic computations are completed based on the completeform of the Kalman filter in the OTS because the statevariables of the Kalman filter in the OTS do not contain rotorspeeds and the estimated measured outputs are removedFurthermore 1198701015840kal is extracted from 119870kal and the Kalmanfilter in the OTS is transformed into the complete form

Δkal = 119860kalΔ119909kal + 119870kal (minusΔ) Δ = 119862kalΔ119909kal (9)

where 119870kalΔ = 119862kal(119870kalΔ119909kal) and input parameter Δ119906lq =minus119870kalΔ119909kalThe quadratic performance index is

119869kal = intinfin0

(Δ119909kal119879QMΔ119909kal + Δ119906lq119879RMΔ119906lq) 119889119905 (10)

where QM and RM are state deviation weighting and controldeviation weighting matrices QM = QM119879 ge 0 RM =RM119879 ge 0 the Riccati equation is introduced to compute theoptimal gain matrix and the positive definite and symmetricmatrix 119875 can be computed by

119860kal otimes 119875 + 119875 otimes 119860kal119879 minus 119875 otimes 119862kal

119879 otimes RMminus1 otimes 119862kal otimes 119875+QM = 0 (11)

Δ119906lq isΔ119906lq = minusRMminus1119862kal

119879119875Δ119909kal (12)

119870kal is

119870kal = RMminus1119862kal119879119875 (13)

The elements related to speed rotors in 119870kal are removedto compute1198701015840kal

To adapt to different situations a linear parameter-varying (LPV) structure is introduced into the Kalman filterin theOTSTheLPV structure of theOTS is established basedon the literature [31] The nonlinear engine is viewed as acollection of linear models corresponding to the measuredoutputs and environmental inputs [32] The LPV model is


OBEM

OTS

Aerongine

LPV model

IM

u

z

y

yOBEM

h

Δh

+

++

minus

1sΔx

kaldΔxkal

href

Kkal

Figure 6 Structure of the OTS

established based on a family of linear models at multipleoperation points The functions between the elements of thelinear model and the scheduling parameters are establishedand the scheduling parameters are chosen from themeasuredoutputs of the OBEM and environmental inputs In an LPVstructure the elements of the matrices will be associated inparallel with the scheduling parameters In this paper 119873119867 ischosen as the scheduling parameter 120575 in the LPV structure ofthe OTS There are functions between the family of 119873119867 andcorresponding elements of matrices in the OTS at differentsteady-state points The elements of the OTS will be tuned inparallel with the variation in119873119867 Equation (14) and Figure 6show the structure

Δ1015840kal = 1198701015840kal (120575) (119910 minus ) = 119910OBEM (14)

The FTOTS is established based on the OTSThe FTOTShas an input selection function (ISF) to remove faulty signalThe form of the FTOTS is

Δ1015840kal = 1198701015840kal (120575) ISF (FSsensor) (119910 minus ) = 119910OBEM (15)

When there is no sensor fault information FSsensor equals0 and ISF is the identity matrix Once fault information isprovided the corresponding element of ISF becomes zeroand the faulty signal will not affect the tuning process of theFTOTS

When the tuning process is completed the channelswitching module should switch to the estimation processso that the FTOTS provides switching information to theswitching module The end points of the tuning includetwo parts one is the variation rate of the estimated healthparameters and the other is the WSSR119894OBEM correspondingto the faulty sensor When the variation rate of the estimatedhealth parameter approaches zero and the WSSROBEM of the

ISF

OBEM

FTOTS

Aerongine

LPV model

u

z

y

yOBEM

h

Δh

+

++

FSsensor

1s IMΔx

kaldΔxkal

href

Kkal

minus

Figure 7 Structure of the FTOTS

faulty sensor is lower than the corresponding threshold 120578119894 thetuning process is completed The structure of the FTOTS isshown in Figure 7

Note that there are multiple operation points in the LPVstructure of the OTS Considering that the length of paper islimited an operation point of the engine is chosen from thecollection of operation points in the LPV structure to showthe computation process of gain matrix1198701015840kal in the OTS

The operation point of the engine model is usedin this paper with the data 119909 = [119873119867 119873119871]119879 119910 =[119873119867 119873119871 OTfan OPfan OTHPC OPHPC]119879 and ℎ =[119864fan 119864HPC 119864HPT 119864LPT]119879

To show the variation in health parameters directly thedegradation coefficients (DCs) of the health parameters areused to represent the ratio of the degraded health parameterto the nominal health parameter In themodel theDCs of thehealth parameters are defined as

DC119864fan = 119864fandeg radation

119864fannoimal

DC119864HPC= 119864HPCdeg radation

119864HPCnoimal

DC119864HPT= 119864HPTdeg radation

119864HPTnoimal

DC119864LPT = 119864LPTdeg radation

119864LPTnoimal

(16)

The state variables of the Kalman filter in the FTOTS are1199091015840kal = [DC119864fan DC119864HPCDC119864HPT

DC119864LPT]119879The operation point of the engine is 119909 = [6920 3682]119879

and the corresponding matrices are


119860kal =

[[[[[[[[[[[[

minus59555119890 minus 1 minus32675119890 minus 1 721901198901 minus668331198903 minus846141198903 minus16744119890134872119890 minus 1 minus10403 minus202461198903 353061198902 355481198902 minus217501198903

0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

119862kal =

[[[[[[[[[[[[

1 0 0 0 0 00 1 0 0 0 0

minus19975119890 minus 4 79158119890 minus 3 172811198901 10851119890 minus 1 11191119890 minus 1 minus99153119890 minus 3minus27605119890 minus 1 96362 517111198902 156311198902 164521198902 minus5799833112119890 minus 2 22213119890 minus 2 249881198901 293361198902 28507119890 minus 1 49636119890 minus 4125451198902 144531198902 minus381591198904 520691198904 minus818841198904 minus546561198902

]]]]]]]]]]]]

(17)

The values of QM and RM are set to QM = 1119890minus2otimes IM6times6and RM = 11198905 otimes IM6times6 and according to (11) the value ofmatrix 119875 is

119875 =[[[[[[[[[[[[

276871198904 minus372381198903 160661198901 minus220221198901 140891198901 minus79049119890 minus 1minus372381198903 366621198903 minus100281198901 minus32553 33513 46983166061198901 minus10028119890 minus 4 26593119890 minus 5 minus17107119890 minus 4 17806119890 minus 4 minus49549119890 minus 5minus220222 minus325529 46174119890 minus 2 44899119890 minus 2 minus31945119890 minus 2 minus43312119890 minus 2140891198901 33513 minus36636119890 minus 2 minus31945119890 minus 2 24349119890 minus 2 32363119890 minus 2minus70949 46983 minus13572119890 minus 1 minus43313119890 minus 2 32363119890 minus 2 12449119890 minus 1

]]]]]]]]]]]]

(18)

Furthermore the computation result of gain matrix 119870kalbased on (13) is

119870kal =

[[[[[[[[[[[[

27688119890 minus 1 minus37238119890 minus 2 24189119890 minus 3 minus36301119890 minus 1 minus52211119890 minus 2 25885119890 minus 1minus37238119890 minus 2 minus36662119890 minus 2 14355119890 minus 3 3118611989001 minus12464119890 minus 2 minus11413119890 minus 216606119890 minus 4 minus10028119890 minus 4 26593119890 minus 5 minus17107119890 minus 4 17806119890 minus 4 minus49549119890 minus 5minus22022119890 minus 4 minus32553119890 minus 5 77828119890 minus 6 60134119890 minus 6 13515119890 minus 4 minus17911119890 minus 414089119890 minus 4 33513119890 minus 5 minus61045119890 minus 6 82847119890 minus 5 minus97390119890 minus 5 minus25028119890 minus 4minus70949119890 minus 5 46983119890 minus 5 minus23091119890 minus 5 minus25119119890 minus 4 minus16219119890 minus 4 minus53121119890 minus 5

]]]]]]]]]]]]

(19)

and the corresponding gain matrix1198701015840kal in OTS is

1198701015840kal =[[[[[[

16606119890 minus 4 minus10028119890 minus 4 26593119890 minus 5 minus17107119890 minus 4 17806119890 minus 4 minus49549119890 minus 5minus22022119890 minus 4 minus32553119890 minus 5 77828119890 minus 6 60134119890 minus 6 13515119890 minus 4 minus17911119890 minus 414089119890 minus 4 33513119890 minus 5 minus61045119890 minus 6 82847119890 minus 5 minus97390119890 minus 5 minus25028119890 minus 4minus70949119890 minus 5 46983119890 minus 5 minus23091119890 minus 5 minus25119119890 minus 4 minus16219119890 minus 4 minus53121119890 minus 5

]]]]]] (20)


a b

Channelselectionmodule

IFDI

Switchingsignal

yOBEM

OBEMSensorfault

information h

Engine

FTOTS

y

Startinginformation

Switc

h

Figure 8 Switching channel between the FDI and the OTS

23 Channel Switching Module The outputs of the OBEMare used as baseline outputs of the HKF To maintain theeffectiveness of IFDI the outputs of the OBEM should betuned to minimize the mismatch between the OBEM and theactual engine caused by health degradation If the processof OBEM tuning operates parallel to the HKF estimationthen the HKF estimation loses its accuracy because duringthe working process the health parameters must remain at areference level [2] Without the fault information providedby the IFDI the online tuning process is affected by thefaulty signal The switching module is designed to avoid theinterference of the IFDI and the FTOTS

There are two process channels in the structure one isthe IFDI estimation process which is marked as ldquoardquo and theother is the FTOTS online tuning process which ismarked asldquobrdquo Both channels operate under the control of the switchingmodule

Firstly the estimation channel is chosen and the estima-tion process of the IFDI is initiated The IFDI is used todecide whether online tuning should be started so channelldquoardquo is originally chosen to make sure that the IFDI is able tocomplete the diagnostics process After the estimation workof the IFDI the channel selection module receives the corre-sponding information from the IFDI to initiate the channelswitching process If the IFDI provides the starting signal forthe OBEM online tuning then tuning channel ldquobrdquo will bechosen and the FTOTS will initiate online tuning When theFTOTS completes the tuning process the channel switchingmodule switches to channel ldquoardquo to restart the estimationprocess The switching structure is shown in Figure 8

3 Simulation Results

The first simulation shows how the IFDI locates the faultysensor based on the WSSRHKF and makes an online tuning

decision based on the WSSROBEM In the simulation theengine is working under static-state conditions and at 119905 = 1 sif the sensor of OTfan is faulty then different HKFs provide aseries of WSSRs The different WSSRHKFs and WSSROBEM ofthe faulty sensor are shown in Figure 9

Figure 9(a) shows WSSRHKFs of different sensors andFigure 9(b) shows how WSSROBEM of the faulty sensor120582OTfan

changes The final values of different WSSRHKFsare [293119890 minus 2 236119890 minus 2 321119890 minus 4 335119890 minus 2] correspond-ing to [119873119867 119873119871 OTfan OPfan] The value of WSSROBEMcorresponding to the fault sensor of OTfan is 839119890 minus 1 InFigure 9(a) there are four lines representing WSSRHKFsand one line representing the threshold 120582OTfan

WSSRHKF ofthe HKF corresponding to the faulty sensor OTfan is muchsmaller than the others because the faulty signal doesnot affect the estimation results of the other HKFs TheWSSRHKFOTfan

is lower than 120582OTfan and the other WSSRHKFs

are higher than it thus the faulty sensor is locatedIn Figure 9(b) 120578OTfan

is the threshold The value ofWSSROBEMOTfan

is higher than 120578OTfan which means the

mismatch between the OBEM and the actual engine isunacceptable The diagnostics logic referenced in this paperis proved by the simulation

The thresholds 120582OTfanand 120578OTfan

are selected based onthe standard deviation of the sensor In this paper thethresholds are set as the squared sum of the standarddeviations to avoid a false diagnostics result According tothe standard deviations of different sensors in the literature[10] the thresholds can be computed As the magnitudesof the different thresholds are of the same order the otherthresholds are not shown

The second simulation shows the effectiveness of theOTSIn the simulation the engine is working under static-stateconditions At 119905 = 1 s the efficiency of the fan and HPCdecreases by 5 simultaneously and the other health param-eters remain unchanged The remaining input parametersand health parameters remain at their origin values and theeffectiveness deterioration of fan andHPC causes variation inthe actual engine measured outputs such as119873119867 and119873119871 Theestimated health parameters and estimatedmeasured outputsare shown in Figure 10

Figures 10(a) and 10(b) show the health parametersestimated by the HKF and the OTS and Figures 10(c)and 10(d) show the estimated measured outputs of theHKF and the OTS During health degradation the valueof 119873119867 is reduced from 7963 rmin to 7285 rmin and thevalue of 119873119871 is reduced from 4341 rmin to 4052 rminThe estimation results of [119873119867 119873119871] of the OTS are[7285 rmin 4052 rmin] and the estimation results of[119873119867 119873119871] of the HKF are [7263 rmin 4034 rmin]

According to Figures 10(a) and 10(b) the OTS and theHKF are both able to estimate the variations of componentdeterioration in the situation of multiple component deterio-ration However the estimation accuracy of the HKF is lowerthan that of theOTS In Figures 10(c) and 10(d) the estimatedoutputs of the OTS are more accurate

In the HKF structure the estimated measured outputsare computed by a Kalman filter so the estimation accuracy


5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF

(a) WSSRHKFs of different HKFs

0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

(b) WSSROBEMs of faulty sensor OTfan

Figure 9 WSSRs of the IFDI

is affected by the linearization accuracy state-space formu-lation of the Kalman filter While in the OTS the estimatedmeasured outputs are computed by the nonlinear OBEM theestimation accuracy of the OTS can be guaranteed becauseof the high degree of matching between the OBEM and theactual engine

The third simulation shows the effectiveness of theFTOTS and the influence of a faulty signal during the tuningprocess In the simulation the engine is working under static-state conditions At 119905 = 1 s the effectiveness of the fan andtheHPCdecreases by 5 the other health parameters remainunchanged and the sensor of OTfan is faultyThe value of thesignal from the faulty sensor is 200K higher than the actualvalueThe estimated health parameters andmeasured outputsbetween the FTOTS with fault information and that withoutfault information are shown in Figure 11

Figures 11(a) and 11(b) show the estimated health param-eters of the FTOTS Figures 11(c) 11(d) and 11(e) show theestimated outputs of the FTOTS and Figure 11(f) showsthe difference between OTfan from the faulty sensor andthe actual output During the health degradation the valueof 119873119867 is reduced from 7963 rmin to 7285 rmin thevalue of 119873119871 is reduced from 4341 rmin to 4052 rminand the actual value of OTfan is reduced from 3098 Kto 3087 K If the correct fault information is received bythe FTOTS the estimation results of [119873119867 119873119871 OTfan] ofthe OTS are [7285 rmin 4052 rmin 3087K] otherwisethe estimation results of [119873119867 119873119871 OTfan] of the OTS are[7468 rmin 3917 rmin 3128K]

When the FTOTS receives the correct fault informationit is able to remove the faulty signal and complete the tuningprocess with the correct estimation results while the faultysignal causes incorrect tuning results of the FTOTS TheFTOTS is able tominimize themismatch between the OBEM

and the actual engine based on the correct fault informationwhen the sensor fault and health degradation coexist

In the final simulation the simulation results prove theeffectiveness of the fault-tolerant OBEM tuning structureIn the simulation the engine is working under static-stateconditions At 119905 = 1 s the effectiveness of the fan and HPCdecreases by 5 and the other health parameters remainunchangedThe sensor ofOTfan is faulty at the same time andthe value of the signal from the faulty sensor is 200K higherthan the actual value The corresponding simulation resultsare shown in Figure 12

Figure 12(a) shows the sensor fault location signal of theIFDI Figure 12(b) shows WSSRHKFs of different HKFs inthe IFDI and the threshold 120582OTfan

Figure 12(c) shows thechannel switching process of the system Figure 12(d) showsWSSROBEM of the faulty sensor and Figure 12(e) shows thevariation rate of health parameters Figures 12(f) 12(g) and12(h) show the computed measured outputs of the OBEMand Figures 12(i) and 12(j) show the health parametersestimated by the FTOTS

In Figures 12(a) and 12(b) at 18 s the fault signal of theIFDI assumes a value of three to locate the faulty sensoraccording to the variation inWSSRHKFs and threshold 120582OTfanduring the estimation process and remains at a value of threeduring tuning process In Figures 12(c) 12(d) and 12(e) at18 s the channel switching signal assumes a value of minus1 whenWSSROBEMOTfan

is higher than the threshold 120578OTfan and the

tuning process is initiated When WSSROBEMOTfanis lower

than the threshold 120578OTfanand the variation rate of the health

parameter approaches zero the switching signal turns to avalue of one at 93 s to restart the estimation process InFigures 12(f) 12(g) and 12(h) during the original estimationprocess the outputs of the OBEM remain at their originalvalues to provide baseline outputs for the IFDI When the


Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102

(a) DC 119864fan comparison between two systems

Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101

(b) DC 119864HPC comparison between two systems

Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700

(c) 119873119867 comparison between two systems

Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350

(d) 119873119871 comparison between two systems

Figure 10 Comparisons of estimated results between the HKF and OTS

tuning process is started the outputs of the OBEM willtrack the outputs of the actual engine under the controlof the FTOTS During the tuning process the deviation ofthe measured outputs between the OBEM and the actualengine is minimized by the FTOTS and the faulty signaldoes not affect the tuning results In Figures 12(i) and 12(j)the estimated health parameters of the FTOTS are used toshow the health degradation of the engine and the FTOTSis able to update the OBEM online based on the estimatedhealth information According to the simulation results theeffectiveness of the fault-tolerant OBEM tuning structure isproven This system is able to successfully locate the faultysensor and make the online tuning decision during the

estimation process and complete the tuning process withoutthe influence of a faulty sensor

4 Conclusions

A fault-tolerant online OBEM tuning structure is developedto minimize the mismatch caused by health degradationand to protect the OBEM tuning process from the influenceof faulty signals when sensor fault and health degradationcoexist Moreover the estimation accuracy of the onlinetuning structure is improved In this structure the IFDI isdesigned to locate the faulty sensor and make tuning oper-ation decision the FTOTS is designed to complete the


Ref signalWith fault information

Without fault information

DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)

(a) DC119864fan of FTOTS



DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)

(b) DC119864HPC of FTOTS

Actual engineWith fault information


NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS

Output of actual engineWith fault information


308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)

(e) OTfan estimated by FTOTS

Output of actual engineSensor of OTfan

300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)

(f) OTfan from faulty sensor and actual output

Figure 11 Estimated results of the FTOTS


Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH

Sensor of NL Fault signalSensor of OTfan

Sensor of OPfan

(a) Fault signal of IFDI

0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF

(b) WSSRHKFs of IFDI

Estimation channelTuning channel

Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)

(c) Channel switching signal

0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM

(d) WSSROBEM corresponding toOTfan

minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC

(e) Variation rate of health parameters

Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1

(i) DC119864fan estimated by FTOTS

5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101

(j) DC119864HPC estimated by FTOTS

Figure 12 Simulation results of switching process of system

online tuning process with the help of the fault informationfrom the IFDI and a channel switching module is designedto separate the estimation process and tuning process toavoid interference between the IFDI and the FTOTS Theeffectiveness of the fault-tolerant tuning structure is provenin this paper by a series of simulations and the simulationresults show that fault-tolerantOBEM tuning structure is ableto separate health degradation and sensor fault in addition tobeing able to complete the online tuning process regardlessof the presence of a faulty sensor In future research thediagnostics system used to deal with the coexistence of healthdegradation and actuator fault or the coexistence of actuatorfault and sensor fault will be developed

Notations

Symbol

ℎ Performance degradation factor119906 Input parameterV White measurement noise119908 White process noise119909 State parameter119910 Output parameter119911 Environmental parameterDC Degradation coefficient119864 Effectiveness


EGT Engine exhaust temperature (K)EGP Engine exhaust pressure (Pa)119865 Flow capacityFS Fault signalQM State deviations weighting matrixRM Control deviations weighting matrixIM Identity matrixISF Input selection function119873 Rotor speedOT Outlet temperature (K)OP Outlet pressure (Pa)119876 State weighting matrix119877 Output weighting matrix119882 Mass flowWSSR Weighted sum of squared residuals120575 Scheduling parameter

Subscripts

kal Kalman filterref Referencelq Linear quadraticss Steady state119867 High pressureHPC High pressure compressorHPT High pressure turbine119871 Low pressureLPC Low pressure compressorLPT Low pressure turbine0 Initial value

Competing Interests

The authors declare that they have no competing interests

References

[1] J B Armstrong and D L Simon ldquoImplementation of an inte-grated on-board aircraft engine diagnostic architecturerdquo inProceedings of the 47th AIAAASMESAEASEE Joint PropulsionConference amp Exhibit AIAA-2011-5859 San Diego Calif USAAugust 2011

[2] T Kobayashi and D L Simon ldquoIntegration of on-line and off-line diagnostic algorithms for aircraft engine health manage-mentrdquo Journal of Engineering for Gas Turbines and Power vol129 no 4 pp 986ndash993 2007

[3] J A Turso and J S Litt ldquoA foreign object damage event detectordata fusion system for turbofan enginesrdquo Journal of AerospaceComputing Information and Communication vol 2 no 7 pp291ndash308 2005

[4] T J Grindle and F W Burcham Jr ldquoEngine damage to a NASADC-8-72 airplane from a high-altitude encounter with a diffusevolcanic ash cloudrdquo NASATM-2003-212030 2003

[5] C Hajiyev and F Caliskan ldquoSensoractuator fault diagnosisbased on statistical analysis of innovation sequence and RobustKalman Filteringrdquo Aerospace Science and Technology vol 4 no6 pp 415ndash422 2000

[6] F Caliskan and C M Hajiyev ldquoAircraft sensor fault diagnosisbased on Kalman filter innovation sequencerdquo in Proceedings of

the 37th IEEE Conference on Decision and Control vol 2 pp1313ndash1314 Tampa Fla USA December 1998

[7] T Kobayashi and D L Simon ldquoEvaluation of an enhancedbank of Kalman filters for in-flight aircraft engine sensor faultdiagnosticsrdquo Journal of Engineering for Gas Turbines and Powervol 127 no 3 pp 497ndash504 2005

[8] T Kobayashi andD L Simon ldquoApplication of a bank of Kalmanfilters for aircraft engine fault diagnosticsrdquo in Proceedings of theASME Turbo Expo 2003 Collocated with the 2003 InternationalJoint Power Generation Conference vol 1 pp 461ndash470 Amer-ican Society of Mechanical Engineers Atlanta Ga USA June2003

[9] W Xue Y-Q Guo and X-D Zhang ldquoA bank of Kalman filtersand a Robust Kalman filter applied in fault diagnosis of aircraftengine sensoractuatorrdquo in Proceedings of the 2nd InternationalConference on Innovative Computing Information and Control(ICICIC rsquo07) Kumamoto Japan September 2007

[10] K Salahshoor M Mosallaei and M Bayat ldquoCentralized anddecentralized process and sensor fault monitoring using datafusion based on adaptive extended Kalman filter algorithmrdquoMeasurement vol 41 no 10 pp 1059ndash1076 2008

[11] M Joerger and B Pervan ldquoKalman filter-based integrity mon-itoring against sensor faultsrdquo Journal of Guidance Control andDynamics vol 36 no 2 pp 349ndash361 2013

[12] B Pourbabaee N Meskin and K Khorasani ldquoRobust sensorfault detection and isolation of gas turbine engines subjectedto time-varying parameter uncertaintiesrdquo Mechanical Systemsamp Signal Processing vol 76-77 pp 136ndash156 2016

[13] S Garg ldquoControls and health management technologies forintelligent aerospace propulsion systemsrdquo in Proceedings of the42nd AIAA Aerospace Sciences Meeting and Exhibit AIAA-2004-949 pp 11854ndash11876 Reno Nev USA January 2004

[14] J S Litt D L Simon S Garg et al ldquoA survey of intelligent con-trol and health management technologies for aircraft propul-sion systemsrdquo Journal of Aerospace Computing Information andCommunication vol 1 no 12 pp 543ndash563 2004

[15] A Behbahani S Adibhatla and C Rauche ldquoIntegrated model-based controls and PHM for improving turbine engine per-formance reliability and costrdquo in Proceedings of the 45thAIAAASMESAEASEE Joint Propulsion Conference amp ExhibitAIAA 2009-5534 Denver Colo USA August 2009

[16] T Kobayashi and D L Simon ldquoHybrid Kalman filter a newapproach for aircraft engine in-flight diagnosticsrdquo ARL-TR4001 2006

[17] T Kobayashi and D L Simon ldquoHybrid Kalman filter approachfor aircraft engine in-flight diagnostics sensor fault detectioncaserdquo Journal of Engineering for Gas Turbines and Power vol129 no 3 pp 746ndash754 2006

[18] S Garg ldquoPropulsion controls and diagnostics research at NASAGlennrdquo Tech Rep AIAA-2007-5713 2007

[19] D L Simon and S Garg ldquoA systematic approach for model-based aircraft engine performance estimationrdquo in Proceedings ofthe AIAA InfotechAerospace Conference InfotechAerospaceConferences AIAA-2009-1872 pp 2009ndash1872 Seattle WashUSA April 2009

[20] B Pourbabaee N Meskin and K Khorasani ldquoMultiple-modelbased sensor fault diagnosis using hybrid Kalman filterapproach for nonlinear gas turbine enginesrdquo in Proceedings ofthe 1st American Control Conference (ACC rsquo13) pp 4717ndash4723IEEE Washington DC USA June 2013


[21] B Pourbabaee N Meskin and K Khorasani ldquoSensor faultdetection isolation and identification using multiple-model-based hybrid Kalman filter for gas turbine enginesrdquo IEEETransactions on Control Systems Technology vol 24 no 4 pp1184ndash1200 2015

[22] J B Armstrong andD L Simon ldquoConstructing an efficient self-tuning aircraft engine model for control and health manage-ment applicationsrdquo in Proceedings of the 2012 Annual Confer-ence of the Prognostics and Health Management Society (PHMrsquo12) NASATM-2012-217806 pp 134ndash146 Minneapolis MinnUSA September 2012

[23] D L Simon and J B Armstrong ldquoAn integrated approach foraircraft engine performance estimation and fault diagnosticsrdquoJournal of Engineering for Gas Turbines and Power vol 135 no7 Article ID 071203 2013

[24] A W Rinehart and D L Simon ldquoAn integrated architecture foraircraft engine performance monitoring and fault diagnosticsengine test resultsrdquo in Proceedings of the 50th AIAAASMESAEASEE Joint Propulsion Conference Propulsion and EnergyForum Cleveland Ohio USA July 2014

[25] A Volponi ldquoEnhanced self tuning on-board real-time model(eSTORM) for aircraft engine performance health trackingrdquoTech Rep FR-26751 2008

[26] A Volponi T Brotherton and R Luppold ldquoEmpirical tuningof an on-board gas turbine engine model for real-time moduleperformance estimationrdquo Journal of Engineering for Gas Tur-bines and Power vol 130 no 2 Article ID 021604 pp 669ndash6782008

[27] L C Jaw and J D Mattingly Aircraft Engine ControlsmdashDesignSystem Analysis and Health Monitoring American Institute ofAeronautics and Astronautics Reston Va USA 2009

[28] D T Pham J Verron andM C Roubaud ldquoA singular evolutiveextended Kalman filter for data assimilation in oceanographyrdquoJournal of Marine Systems vol 16 no 3-4 pp 323ndash340 1998

[29] G A Dukeman ldquoProfile-following entry guidance using linearquadratic regulator theoryrdquo in Proceedings of the AIAA Guid-ance Navigation and Control Conference and Exhibit AIAA-2002-4457 Monterey Calif USA August 2002

[30] A Bemporad MMorari V Dua and E N Pistikopoulos ldquoTheexplicit linear quadratic regulator for constrained systemsrdquoAutomatica vol 38 no 1 pp 3ndash20 2002

[31] L Reberga D Henrion J Bernussou and F Vary ldquoLPVmodel-ing of a turbofan enginerdquo in Proceedings of the 16th IFACWorldCongress Prague Czech Republic July 2005

[32] R Toth ldquoModeling and identification of linear parameter-varying systemsrdquo Lecture Notes in Control and InformationSciences vol 403 pp 1ndash339 2010

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



diagnostics and engine control As advanced control systemshealth monitoring and diagnosis systems with OBEM weredeveloped to improve the performance and safety of aero-engines The NASA Glenn Research Center (GRC) proposedan intelligent engine control system that includes activecontrol health management and fault-tolerant control tech-nologies [13 14] The latest model-based control system usesOBEM to calculate unmeasured outputs such as aeroenginethrust compressor stall and surge [15] In 2006 the GRCintroduced OBEM into the structure of the linear Kalman fil-ter to establish the hybrid Kalman filter (HKF) [16 17] In thefollowing years the HKF was used for engine performanceestimation and sensor fault detection [18 19] Pourbabaee etal introduced the HKF into an FDI to achieve the functionsof sensor fault detection isolation and identification [20 21]

Recently a real-time self-tuning OBEM has been com-bined with a health management structure [22] Simon et alpresented a real-time self-tuning model used for engineperformance monitoring and fault diagnostics [22ndash24] Thismodel is a hybrid model including an OBEM and neuralnetworks Furthermore Volponi et al presented an onlinetuning engine model updated with a Kalman filter [25 26]This kind of an OBEM is able to minimize the mismatchbetween an OBEM and the actual engine and maintain theeffectiveness of the fault diagnostics system However duringthe tuning process the influence of a faulty signal is notconsidered so a tuning system with a fault-tolerant functionmust be developed because an online tuning system mayencounter coexisting health degradation and sensor fault

The following contents of this paper include three sec-tions Section 2 presents a general description of fault-tolerant tuning structures and the development of differentparts including the improved fault diagnostics and isolation(IFDI) fault-tolerantOBEM tuning system (FTOTS) and thechannel switching module Section 3 includes the simulationresults which were used to prove the effectiveness of thesystem The last section contains the conclusions of thiswork

2 Fault-Tolerant Online Tuning Structure

Health degradation and sensor fault are both capable of caus-ing a mismatch between the OBEM and the actual engineIf health degradation and sensor fault coexist an analysis ofthemismatch and the correspondingmethod tominimize themismatch must be provided During the traditional onlinetuning process the information used for the tuning processcontains measurement noise sensor bias and any attendantmodeling error however the effect of the senor fault is nottypically considered [26] If the mismatch is caused onlyby sensor fault the tuning process should not be initiatedbecause this kind of mismatch cannot be solved by updatinghealth information During the onlineOBEM tuning processthe influence of a faulty sensor should be considered becausethe mismatch caused by the faulty signal will also be consid-ered during the tuning process If the online tuning systemis able to remove the corresponding faulty signal the tuningresults will be accurate and themismatch between the OBEMand actual engine will be minimized

Engine

FTOTS

IFDI

OBEM

Measuredoutputs

Computedoutputs

Fault information

Health information

Switchingmodule

Switching informationu

z

Figure 1 A general fault-tolerant OBEM tuning structure

The FTOTS is used to analyze the mismatch cause andto minimize the mismatch caused by health degradationThefunctions of this system include sensor fault diagnostics andfault-tolerant online OBEM tuning There are three maincomponents of this system including the IFDI the FTOTSand the channel switching module The IFDI is used in theestimation process to locate the faulty sensor and the FTOTSis used in the tuning process to minimize the mismatchThe two systems work on different channels and are switchtriggered by the signal The general structure is shown inFigure 1

The IFDI is developed based on FDI The IFDI has twotasks sensor fault diagnostics and online tuning operationdecisionThe IFDI is used to locate the faulty sensor andmakethe channel switching decision Compared with conventionalFDI IFDI has the extra function of providing switchinginformation to the channel switching module

The FTOTS combines the OBEM tuning system (OTS)with fault-tolerant function FTOTS is used to remove faultyinput signals based on the fault information of the IFDI andminimize the mismatch caused by health degradation In thissystem the number of measured outputs is greater than thatof health parameters so the absence of single signal will notaffect the estimation of the Kalman filter

The channel switching module is used to perform thefunction of channel switching between the estimation pro-cesses and tuning process During the estimation processof the IFDI the health information provided to the OBEMretains its original values ℎref [14] however during the tuningprocess the health parameters are tuned by the FTOTS Dif-ferent working conditionsmean that the IFDI and the FTOTSwill not work in parallel otherwise there interruption occursbetween the two systems The channel switching module isable to resolve the conflict between the IFDI and the FTOTSThe channel switching process between the IFDI and theFTOTS of the system is shown in Figure 2

21 IFDI Structure In this paper the IFDI and the FTOTSare both established based on a nonlinear component-levelengine model [27] The model is a two-spool high-bypassturbofan engine Linearization computation is completedbased on the two-step perturbation method [27] The linearmodel in state-space form is

Δ (119905) = 119860Δ119909 (119905) + 119861Δ119906 (119905) + 119871Δℎ (119905) + 119866Δ119911 (119905) Δ119910 (119905) = 119862Δ119909 (119905) + 119863Δ119906 (119905) + 119872Δℎ (119905) + 119867Δ119911 (119905) (1)


IFDIStart

Switchingmodule


Fault information

Tuningstarting

Yes


FTOTS

Tuning completed

IFDI starting

Yes

Tuning continuingNo












(3)






removed from y to



y

y－

y1

y2

yn

y1－

y2－

yi－

yn－

HKF 1

HKF 2

HKF i

HKF n

e1（＋

e1－

e2（＋

e2－

ei（＋

ei－

en（＋

en－

create yi vector

yi


WSSR

WSSR1HKF

WSSR2HKF

WSSRiHKF

WSSRnHKF

WSSR1OBEM

WSSR2OBEM

WSSRiOBEM

WSSRnOBEM


Bank ofHKF


lt i

lt i


ith sensoris normal

Yes

Yes

No



y

y－

WSSRiOBEM

WSSRiHKFWSSR

WSSRHKF









u

z

Measuredoutputs


Computed outputs




(5)

where 119862kal = [ 0 00 IM ] 119870kal = [ 11989611198962





(6)



(7)













119879119875Δ119909kal (12)

119870kal is

119870kal = RMminus1119862kal119879119875 (13)




OBEM

OTS

Aerongine

LPV model

IM

u

z

y

yOBEM

h

Δh

+

++

minus

1sΔx

kaldΔxkal

href

Kkal








ISF

OBEM

FTOTS

Aerongine

LPV model

u

z

y

yOBEM

h

Δh

+

++

FSsensor

1s IMΔx

kaldΔxkal

href

Kkal

minus







119864fannoimal


119864HPCnoimal


119864HPTnoimal


119864LPTnoimal

(16)





119860kal =

[[[[[[[[[[[[


0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

119862kal =

[[[[[[[[[[[[

1 0 0 0 0 00 1 0 0 0 0


]]]]]]]]]]]]

(17)


119875 =[[[[[[[[[[[[


]]]]]]]]]]]]

(18)


119870kal =

[[[[[[[[[[[[


]]]]]]]]]]]]

(19)


1198701015840kal =[[[[[[


]]]]]] (20)


a b


IFDI

Switchingsignal

yOBEM

OBEMSensorfault

information h

Engine

FTOTS

y

Startinginformation

Switc

h























5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF


0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

















Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










IFDIStart

Switchingmodule


Fault information

Tuningstarting

Yes


FTOTS

Tuning completed

IFDI starting

Yes

Tuning continuingNo












(3)






removed from y to



y

y－

y1

y2

yn

y1－

y2－

yi－

yn－

HKF 1

HKF 2

HKF i

HKF n

e1（＋

e1－

e2（＋

e2－

ei（＋

ei－

en（＋

en－

create yi vector

yi


WSSR

WSSR1HKF

WSSR2HKF

WSSRiHKF

WSSRnHKF

WSSR1OBEM

WSSR2OBEM

WSSRiOBEM

WSSRnOBEM


Bank ofHKF


lt i

lt i


ith sensoris normal

Yes

Yes

No



y

y－

WSSRiOBEM

WSSRiHKFWSSR

WSSRHKF









u

z

Measuredoutputs


Computed outputs




(5)

where 119862kal = [ 0 00 IM ] 119870kal = [ 11989611198962





(6)



(7)













119879119875Δ119909kal (12)

119870kal is

119870kal = RMminus1119862kal119879119875 (13)




OBEM

OTS

Aerongine

LPV model

IM

u

z

y

yOBEM

h

Δh

+

++

minus

1sΔx

kaldΔxkal

href

Kkal








ISF

OBEM

FTOTS

Aerongine

LPV model

u

z

y

yOBEM

h

Δh

+

++

FSsensor

1s IMΔx

kaldΔxkal

href

Kkal

minus







119864fannoimal


119864HPCnoimal


119864HPTnoimal


119864LPTnoimal

(16)





119860kal =

[[[[[[[[[[[[


0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

119862kal =

[[[[[[[[[[[[

1 0 0 0 0 00 1 0 0 0 0


]]]]]]]]]]]]

(17)


119875 =[[[[[[[[[[[[


]]]]]]]]]]]]

(18)


119870kal =

[[[[[[[[[[[[


]]]]]]]]]]]]

(19)


1198701015840kal =[[[[[[


]]]]]] (20)


a b


IFDI

Switchingsignal

yOBEM

OBEMSensorfault

information h

Engine

FTOTS

y

Startinginformation

Switc

h























5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF


0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

















Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











removed from y to



y

y－

y1

y2

yn

y1－

y2－

yi－

yn－

HKF 1

HKF 2

HKF i

HKF n

e1（＋

e1－

e2（＋

e2－

ei（＋

ei－

en（＋

en－

create yi vector

yi


WSSR

WSSR1HKF

WSSR2HKF

WSSRiHKF

WSSRnHKF

WSSR1OBEM

WSSR2OBEM

WSSRiOBEM

WSSRnOBEM


Bank ofHKF


lt i

lt i


ith sensoris normal

Yes

Yes

No



y

y－

WSSRiOBEM

WSSRiHKFWSSR

WSSRHKF









u

z

Measuredoutputs


Computed outputs




(5)

where 119862kal = [ 0 00 IM ] 119870kal = [ 11989611198962





(6)



(7)













119879119875Δ119909kal (12)

119870kal is

119870kal = RMminus1119862kal119879119875 (13)




OBEM

OTS

Aerongine

LPV model

IM

u

z

y

yOBEM

h

Δh

+

++

minus

1sΔx

kaldΔxkal

href

Kkal








ISF

OBEM

FTOTS

Aerongine

LPV model

u

z

y

yOBEM

h

Δh

+

++

FSsensor

1s IMΔx

kaldΔxkal

href

Kkal

minus







119864fannoimal


119864HPCnoimal


119864HPTnoimal


119864LPTnoimal

(16)





119860kal =

[[[[[[[[[[[[


0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

119862kal =

[[[[[[[[[[[[

1 0 0 0 0 00 1 0 0 0 0


]]]]]]]]]]]]

(17)


119875 =[[[[[[[[[[[[


]]]]]]]]]]]]

(18)


119870kal =

[[[[[[[[[[[[


]]]]]]]]]]]]

(19)


1198701015840kal =[[[[[[


]]]]]] (20)


a b


IFDI

Switchingsignal

yOBEM

OBEMSensorfault

information h

Engine

FTOTS

y

Startinginformation

Switc

h























5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF


0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

















Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











u

z

Measuredoutputs


Computed outputs




(5)

where 119862kal = [ 0 00 IM ] 119870kal = [ 11989611198962





(6)



(7)













119879119875Δ119909kal (12)

119870kal is

119870kal = RMminus1119862kal119879119875 (13)




OBEM

OTS

Aerongine

LPV model

IM

u

z

y

yOBEM

h

Δh

+

++

minus

1sΔx

kaldΔxkal

href

Kkal








ISF

OBEM

FTOTS

Aerongine

LPV model

u

z

y

yOBEM

h

Δh

+

++

FSsensor

1s IMΔx

kaldΔxkal

href

Kkal

minus







119864fannoimal


119864HPCnoimal


119864HPTnoimal


119864LPTnoimal

(16)





119860kal =

[[[[[[[[[[[[


0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

119862kal =

[[[[[[[[[[[[

1 0 0 0 0 00 1 0 0 0 0


]]]]]]]]]]]]

(17)


119875 =[[[[[[[[[[[[


]]]]]]]]]]]]

(18)


119870kal =

[[[[[[[[[[[[


]]]]]]]]]]]]

(19)


1198701015840kal =[[[[[[


]]]]]] (20)


a b


IFDI

Switchingsignal

yOBEM

OBEMSensorfault

information h

Engine

FTOTS

y

Startinginformation

Switc

h























5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF


0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

















Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










OBEM

OTS

Aerongine

LPV model

IM

u

z

y

yOBEM

h

Δh

+

++

minus

1sΔx

kaldΔxkal

href

Kkal








ISF

OBEM

FTOTS

Aerongine

LPV model

u

z

y

yOBEM

h

Δh

+

++

FSsensor

1s IMΔx

kaldΔxkal

href

Kkal

minus







119864fannoimal


119864HPCnoimal


119864HPTnoimal


119864LPTnoimal

(16)





119860kal =

[[[[[[[[[[[[


0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

119862kal =

[[[[[[[[[[[[

1 0 0 0 0 00 1 0 0 0 0


]]]]]]]]]]]]

(17)


119875 =[[[[[[[[[[[[


]]]]]]]]]]]]

(18)


119870kal =

[[[[[[[[[[[[


]]]]]]]]]]]]

(19)


1198701015840kal =[[[[[[


]]]]]] (20)


a b


IFDI

Switchingsignal

yOBEM

OBEMSensorfault

information h

Engine

FTOTS

y

Startinginformation

Switc

h























5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF


0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

















Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119860kal =

[[[[[[[[[[[[


0 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

119862kal =

[[[[[[[[[[[[

1 0 0 0 0 00 1 0 0 0 0


]]]]]]]]]]]]

(17)


119875 =[[[[[[[[[[[[


]]]]]]]]]]]]

(18)


119870kal =

[[[[[[[[[[[[


]]]]]]]]]]]]

(19)


1198701015840kal =[[[[[[


]]]]]] (20)


a b


IFDI

Switchingsignal

yOBEM

OBEMSensorfault

information h

Engine

FTOTS

y

Startinginformation

Switc

h























5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF


0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

















Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










a b


IFDI

Switchingsignal

yOBEM

OBEMSensorfault

information h

Engine

FTOTS

y

Startinginformation

Switc

h























5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF


0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

















Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 10 15 200Time (s)

OTfan

0

005

01

015

02W

SSR H

KF

NWSSRHKF

NWSSRHKF

OTfanWSSRHKF

OPfanWSSRHKF


0

05

1

15

5 10 15 200Time (s)

OTfan

WSS

R OBE

M

OPfanWSSROBEM

















Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Ref signalHKFOTS

DC E

fan

10 20 30 400Time (s)

09

092

094

096

098

1

102


Ref signalHKFOTS

10 20 30 400Time (s)

DC E

HPC

094

095

096

097

098

099

1

101


Actual engineHKFOTS

10 20 30 400Time (s)

NH

(rm

in)

7200

7300

7400

7500

7600

7700


Actual engineHKFOTS

10 20 30 400Time (s)

NL

(rm

in)

4000

4050

4100

4150

4200

4250

4300

4350





4 Conclusions





DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












DC E

fan

06

07

08

09

1

11

5 10 15 200Time (s)




DC E

HPC

094

095

096

097

098

099

1

101

2010 1550Time (s)




NH

(rm

in)

7200

7300

7400

7500

7600

7700

7800

5 10 15 200Time (s)

(c) 119873119867 of FTOTS



NL

(rm

in)

3900

4000

4100

4200

4300

4400

5 10 15 200Time (s)

(d) 119873119871 of FTOTS



308

310

312

314

316

5 10 15 200Time (s)

OT f

an(K

)



300

350

400

450

500

550

600

5 10 15 200Time (s)

OT f

an(K

)




Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Faul

t sig

nal

0

1

2

3

4

5

5 10 15 200

Time (s)

Sensor of NH


Sensor of OPfan


0

005

01

015

5 10 15 200

Time (s)

OTfan

WSS

R HKF

NWSSRHKFN

WSSRHKFOTfan

WSSRHKF

OPfanWSSRHKF



Channel signal

Chan

nel s

igna

l

minus2

minus1

0

1

2

5 10 15 200

Time (s)


0

002

004

006

008

01

5 10 15 200

Time (s)

OTfan

WSS

R OBE

M

of OTfanWSSROBEM


minus02

minus01

0

01

02

03

Varia

tion

rate

of h

ealth

par

amet

ers

5 10 15 200

Time (s)

DCEfanDCEHPC


Actual engineOBEM

5 10 15 200

Time (s)

7200

7300

7400

7500

7600

7700

NH

(min

)

(f) 119873119867 of OBEM

Figure 12 Continued


Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Actual engineOBEM

5 10 15 200

Time (s)

4000

4050

4100

4150

4200

4250

4300

4350

NL

(rm

in)

(g) 119873119871 of OBEM

5 10 15 200

Time (s)

Actual engineOBEM

OT f

an

300

350

400

450

500

550

600

Sensor of OTfan

(h) OTfan of OBEM

Ref signalFTOTS

5 10 15 200Time (s)

DC E

fan

085

09

095

1


5 10 15 200Time (s)

Ref signalFTOTS

DC E

HPC

094

095

096

097

098

099

1

101




Notations

Symbol




Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Subscripts


Competing Interests


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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