Model-Based Fault Diagnosis for Dynamic Processes Using ...silviosimani.it/DPS2011_simani_presentation.pdf · 23/09/2011 Silvio Simani Model-Based Fault Diagnosis for Dynamic Processes

ModelModel--Based Fault Based Fault Diagnosis for Dynamic Diagnosis for Dynamic

Processes Using Processes Using Identification TechniquesIdentification Techniques

Silvio SimaniSilvio SimaniDepartment of EngineeringDepartment of Engineering

University of FerraraUniversity of FerraraVia Saragat, 1E Via Saragat, 1E -- 44100 Ferrara (FE) 44100 Ferrara (FE)

ITALYITALYPh: +39 0532 97 4844 Ph: +39 0532 97 4844 Fax: +39 0532 97 4870Fax: +39 0532 97 4870

URL: URL: www.ing.unife.it/simaniwww.ing.unife.it/simaniEmail: Email: [email protected]@unife.it

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Silvio SimaniSilvio Simani ModelModel--Based Fault Diagnosis for Dynamic Processes Using IdentificationBased Fault Diagnosis for Dynamic Processes Using Identification TechniquesTechniques

DPS'11, 19DPS'11, 19--21 September 2011, Zamosc, Poland21 September 2011, Zamosc, Poland 22

Projects & Research TopicsProjects & Research Topics

Turbocharged Diesel Engine Modelling for Nonlinear Turbocharged Diesel Engine Modelling for Nonlinear Controller DesignController Design (2007(2007--2009)2009)Computerised Decision Support SystemsComputerised Decision Support Systems for Oral for Oral Anticoagulant Treatment (OAT) Dose Management (2005Anticoagulant Treatment (OAT) Dose Management (2005--2007)2007)Development of Development of Fault Tolerant NGC (Navigation, Guidance & Fault Tolerant NGC (Navigation, Guidance & Control)Control) Algorithms for CUAV (Civil Unmanned Aerial Algorithms for CUAV (Civil Unmanned Aerial Vehicle) Patrolling & Rescue Missions in Harsh Environment Vehicle) Patrolling & Rescue Missions in Harsh Environment ((20042004--2008, 2008, 20092009--2020111)1)Wind turbine FDI and FTC (2010Wind turbine FDI and FTC (2010--2012)2012)

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Fault Diagnosis IssuesFault Diagnosis Issues

IIn practical situations, the straightforward n practical situations, the straightforward application ofapplication of modelmodel--based FDI techniques can based FDI techniques can be difficult, due to thebe difficult, due to the dynamic model dynamic model complexitycomplexityViable procedure for the practical application Viable procedure for the practical application of FDI techniques is really necessaryof FDI techniques is really necessaryPossible solutions...Possible solutions...

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Main PointsMain Points

Dynamic model identificationDynamic model identification for FDI for FDI is is successfully usedsuccessfully used

the requirement for physical modelthe requirement for physical modelling is obviatedling is obviated

Linear and nonlinear dynamic prototypesLinear and nonlinear dynamic prototypesLinear identified modelsLinear identified models

oo Monitoring of the operation and performance of the system Monitoring of the operation and performance of the system w.r.t. an expected working conditionw.r.t. an expected working condition

Nonlinear identified modelsNonlinear identified modelsoo Different working conditions Different working conditions

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Main Points (ContMain Points (Cont’’d)d)

The main challenges are to provide a technology for The main challenges are to provide a technology for signalling the onset of faults before expensive failure occurs signalling the onset of faults before expensive failure occurs Methodology considered along with maintenance schedules Methodology considered along with maintenance schedules with an aim to cut down maintenance cost, while steadily with an aim to cut down maintenance cost, while steadily improving the reliability of the systemimproving the reliability of the systemImportant implication on the use of onImportant implication on the use of on--line FDI and line FDI and diagnostic tools once the diagnostic tools once the dynamic processdynamic process is under is under customer operationcustomer operationStructural simplicity when compared with different schemesStructural simplicity when compared with different schemes

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Industrial Example: Related Industrial Example: Related Project (2007Project (2007--2009)2009)Control scheme calibration and tuning for Control scheme calibration and tuning for commercial diesel engines (boats, ships, commercial diesel engines (boats, ships, farm tractors, ...)farm tractors, ...)

Diesel engine modellingDiesel engine modelling and identificationand identificationgreygrey--boxbox: analytical approach: analytical approach and identification (and identification (~~1 1 year)year)

blackblack--boxbox: fuzzy modelling: fuzzy modelling and identification (and identification (~~1 week!)1 week!)

BOSCHBOSCH Electronic Control Unit (ECU)Electronic Control Unit (ECU)

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Physical ModellingPhysical Modelling

State parametersState parametersP, T, P, T, ρρ, c, W, ..., c, W, ...N (speed)N (speed)X (chemical X (chemical composition)composition)......

VariablesVariables......

EquationsEquationsMass conservationMass conservationEnergy conservationEnergy conservationMomentum conservationMomentum conservationMotion quantity Motion quantity conservationconservationState equationsState equationsTransformation Transformation equations equations

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FDI Application ReviewFDI Application Review

About 250 documents (Springer, Blackwell,About 250 documents (Springer, Blackwell, ElsevierElsevier conference conference proceedings, and journals) proceedings, and journals) –– years: 1995 years: 1995 –– 2009 + IEEE/IEE 2009 + IEEE/IEE (journals, transactions, letters, magazines, conference (journals, transactions, letters, magazines, conference proceedings, and standards) proceedings, and standards) –– years: 1969 years: 1969 –– 20092009

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FDI Application Review FDI Application Review (Cont(Cont’’d)d)

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Forthcoming EventForthcoming Event

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This Talk: IntroductionThis Talk: Introduction

Simulation modelsSimulation modelsIndustrial gas turbine: Industrial gas turbine: Example 1Example 1 -- LinearLinear approachapproachWind turbine: Wind turbine: Example 2Example 2 –– Nonlinear Nonlinear schemescheme

Dynamic system identification Dynamic system identification && residual residual generator designgenerator designActuator Actuator && sensor FDIsensor FDISimulation resultsSimulation resultsReliability Reliability & robustness & robustness analysisanalysisComparisons with different FDI schemesComparisons with different FDI schemes

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Gas Turbine Scheme Gas Turbine Scheme (Example 1)(Example 1)

Main components of Main components of the gas turbine simulatorthe gas turbine simulator

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Gas Turbine Simulation ModelGas Turbine Simulation ModelApplication Example 1Application Example 1

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I--------------------------------------------------------------------------------I

m9

t4

m9.

t1

p1

ff

p7

t7n.

Case1 Case2

av

t7

p8

p7.

ambientair

fuelflow

m10

m8_

Nt

Simulated fault condtions

one = Compressor contamination two = Thermcouple sensor fault three = HP turbine seal damage four = Fuel actuator friction wear

HTDU modelR B P 17/9/97

mods by AJLO 4/1/99

NOTE:

To run the with a fault condition. Set the required initial conditions (init 1, 2 or 3) then double click the required fault condition(s) before running the simulation. To reset to a no fault condition, simply reset the inital condtions.

valveangle

t

Tinlet

t1

Pinlet

p1_

p8

av

t7 p7 m9

c5

Pinlet

amb P

Pressurisingvalve

HTDUturbine

Governor

Clock1

fourthreetwo

Init 3

one

Init 2

Print ss

Init1

Plot

Gas Turbine Simulink SimulatorGas Turbine Simulink Simulator

Application Example 1Application Example 1

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Model ValidationModel Validation

Fuel flow rate MFuel flow rate Mff and electrical power Pand electrical power Pee

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I/O Measurement AccuracyI/O Measurement Accuracy

Output Output measurementmeasurement

accuracyaccuracy

Control input Control input signal accuracysignal accuracy

FMEAFMEAanalysysanalysys

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Tools and TechniquesTools and Techniques

LinearLinear dynamic statedynamic state--space modelspace modelPrediction Error Method (PEM)Prediction Error Method (PEM)

ARX models ARX models –– Output observersOutput observers

Subspace technique (N4SID)Subspace technique (N4SID)SS models SS models –– Kalman filtersKalman filters

Practical ToolsPractical ToolsMatlabMatlab®® System Identification ToolboxSystem Identification Toolbox™™SimulinkSimulink®® for predictor implementationfor predictor implementation

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FDI TechniquesFDI Techniques

Residual generationDynamic observersKalman filtersUsed as output predictors

Residual evaluationGeometrical analysisStatistical tests (e.g. standard deviation, mean value, correlation analysis, whiteness, χ2-test)

⎩⎨⎧

+=++=+

kkk

kkkkexy

euxxˆˆ

ˆˆ 1C

HBA

( )( )⎩

⎨⎧

>−≤

casefaulty,casefreefault,

εε

k

krJrJ

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Considered Fault Conditions Considered Fault Conditions (Ex. 1)(Ex. 1)

Fault Fault ‘‘‘‘case 1case 1’’’’: malfunctioning of a thermocouple in the : malfunctioning of a thermocouple in the turbine gas path: thermocouple fault, i.e. turbine gas path: thermocouple fault, i.e. output sensor faultoutput sensor fault. . The fault development rate is set to 5% error in the The fault development rate is set to 5% error in the measured actual temperature per hourmeasured actual temperature per hour

Fault Fault ‘‘‘‘case 2case 2’’’’: malfunctioning of the actuator of the : malfunctioning of the actuator of the turbine, turbine, i.e. i.e. the the actuator faultactuator fault. It leads to the loss of . It leads to the loss of performance due to the wear of the fuel valve actuator, thus performance due to the wear of the fuel valve actuator, thus causing a slower response to flow rate demands. Modelled causing a slower response to flow rate demands. Modelled as a simple first order lag on the resulting fuel flow. The as a simple first order lag on the resulting fuel flow. The actuator response time constant increases linearly with the actuator response time constant increases linearly with the time in order to represent a progressive damage to the time in order to represent a progressive damage to the actuatoractuator

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Simulated Results Simulated Results (Ex. 1)(Ex. 1)

Fault free residualFault free residual FaultFault--free & free & faultyfaulty

residualsresiduals

Dynamic observer example: Dynamic observer example: abrupt faultabrupt faultOneOne--step ahead predictorsstep ahead predictors

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Simulated Results (ContSimulated Results (Cont’’d)d)

0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

6

7

x 10-4

Kalman filterKalman filterresiduals:residuals:

termocouple termocouple sensorsensor

incipientincipientfaultfault

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DetectionDetectiondelaydelay withwith

positive andpositive andnegativenegative

thresholdsthresholds

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Kalman Kalman filterfilter

residuals: residuals: whiteness whiteness

test test (example)(example)

FaultFault--freefree&&

faultyfaultyresidualsresiduals

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Monte Carlo analysisMonte Carlo analysisFalse alarm rateFalse alarm rateMissed fault rateMissed fault rateTrue detection/isolation rateTrue detection/isolation rateMean detection/isolation delay timeMean detection/isolation delay time

Simulated turbineSimulated turbineuncertaintiesuncertainties

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Comparison with:Comparison with:Unknown Input Kalman Filters (UIKF)Unknown Input Kalman Filters (UIKF)Neural Networks (NN)Neural Networks (NN)

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Application Application Example 2Example 2

Detection and isolation of sensor faults Detection and isolation of sensor faults for for a wind turbine benchmarka wind turbine benchmarkWind turbine simulatorWind turbine simulator

Measurement noise & realistic fault casesMeasurement noise & realistic fault casesNonlinear modellingNonlinear modelling

Aerodynamic torque, control strategyAerodynamic torque, control strategyUncertain measurements (Uncertain measurements (e.g. e.g. wind speed)wind speed)

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StateState--ofof--thethe--ArtArt

Linear or linearized model techniquesLinear or linearized model techniquesFault detection observerFault detection observerKalman filtering/EKFKalman filtering/EKFUnknown Input ObserverUnknown Input Observer

Fault isolationFault isolationNonlinearity disturbance deNonlinearity disturbance de--couplingcoupling

Adaptive filtersAdaptive filters

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DataData--Driven ModelDriven Model--Based FDIBased FDI

InputInput--output measurements from the fault free output measurements from the fault free systemsystemData partitioningData partitioningIdentification of a piecewise affine prototypeIdentification of a piecewise affine prototype

HybridHybrid or or switchingswitching modelsmodels

Residual generation with process simulatorResidual generation with process simulatorFixed threshold residual evaluationFixed threshold residual evaluation

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Nonlinear PWA ModellingNonlinear PWA ModellingPiecewisePiecewiseaffine affine prototypeprototype

Data matricesData matricesandandcovariancecovariancematricesmatrices

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Parameter EstimationParameter EstimationSequence of matricesSequence of matricesin each region in each region

Singularity condition for Singularity condition for k = nk = nand parameter estimation and parameter estimation ((ideal caseideal case with white noisewith white noise))

ErrorsErrors--InIn--Variables (EIV)Variables (EIV)framework: equivalent framework: equivalent additive additive ((““whitewhite””) ) noise noise affecting inputaffecting input--output output measurementsmeasurements

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““RealReal”” Case EstimationCase EstimationData sequences are modified Data sequences are modified according to the EIV descriptionaccording to the EIV description

““NoiseNoise”” covariance covariance matrix representing the matrix representing the modelmodel--process mismatchprocess mismatch

Singularity curves Singularity curves ΓΓkk

(i)(i)

in the in the

noisy space: in the ideal case, noisy space: in the ideal case, they share a common point, they share a common point, corresponding to the noise corresponding to the noise affecting the dataaffecting the data

It holds for white noise!It holds for white noise!

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Optimization ProblemOptimization ProblemBest solution Best solution consistent with the consistent with the ideal case: single ideal case: single point condition and point condition and continuity of the continuity of the modelmodel

Singularity Singularity curves in curves in the ideal the ideal and real and real casescases

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Tools and TechniquesTools and TechniquesNonlinear modellingNonlinear modelling

Hybrid prototypes Hybrid prototypes PiecePiece--Wise Affine modelsWise Affine models

Data clustering/partitioningData clustering/partitioningEIV local affine model identification (EIV)EIV local affine model identification (EIV)

Practical ToolsPractical ToolsMatlabMatlab®® Fuzzy Modelling and Identification Fuzzy Modelling and Identification ToolboxToolbox™™ (FMID)(FMID)SimulinkSimulink®® for predictor implementationfor predictor implementation

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Models for FDI: Models for FDI: Input FaultsInput FaultsAdditive noiseAdditive noise, , according to the EIV according to the EIV frameworkframework

u(t)

y(t)

Output Measurementsand noise

+

+

+ +

y*(t)MonitoredSystem

Input Measurementsand noise

Input SensorFaults

y(t)~

u(t)~f (t)

u

u*(t)

+)(f)(*)( ttutu u+=

⎩⎨⎧

+=+=

)(~)(*)()(~)(*)(tytytytututu

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Input Fault Input Fault FDI SchemeFDI Scheme

y(t)

+

+

+_

r(t)Σ

Residuals

y(t)^

Wind Turbine

Input measurements

Hybrid model

Full simulator

y(t)^

u*(t)

f (t)u

u(t)

Input sensor additive faultsInput sensor additive faults

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Models for FDI: Models for FDI: Output FaultsOutput FaultsAdditive noiseAdditive noise, , according to the EIV according to the EIV frameworkframework⎩

⎨⎧

+=+=

)(~)(*)()(~)(*)(tytytytututu

u(t)

y(t)

Output Measurementsand noise

+ +

u*(t)

+ +

f (t)y

y*(t)Monitored

System

Input Measurementsand noise y(t)~

u(t)~)(f)(*)( y ttyty +=

FaultFaultmodelmodel

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Output Fault Output Fault FDI SchemeFDI Scheme

Model used as Model used as ““full simulatorfull simulator””

u(t)

y(t)

+

+

+_

r(t)Σ

Sensors

Residuals

y(t)^

f (t)y

y*(t)Wind Turbine

Fuzzy Model

Input measurements

Full simulator

(One-step-ahead predictor)

Hybrid Model

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Residual EvaluationResidual Evaluation

Fixed threshold selectionFixed threshold selection:: νν

settled in order to minimise settled in order to minimise false alarm & missed fault rates, while maximising fault false alarm & missed fault rates, while maximising fault detection ratedetection rate

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Wind Turbine DescriptionWind Turbine Description

Three blade Three blade horizontal axis horizontal axis turbineturbineRotor shaft moved Rotor shaft moved by wind. A gear by wind. A gear box is usedbox is usedThe rotational speed & the generated power The rotational speed & the generated power regulated with 2 control strategiesregulated with 2 control strategies

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Turbine Turbine Control Control DescriptionDescription

2 control strategies:2 control strategies:Converter torque & pitch angle of the turbine bladesConverter torque & pitch angle of the turbine bladesPower generation optimisation Power generation optimisation

Partial load regionPartial load region: a specific ratio between the : a specific ratio between the blade tip speed and wind speed is maintainedblade tip speed and wind speed is maintained

Rotational speed and converter torque are controlledRotational speed and converter torque are controlledFull power regionFull power region: converter torque kept : converter torque kept constantconstant

rotational speed is adjusted by controlling the pitch rotational speed is adjusted by controlling the pitch angle of the bladesangle of the blades

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Wind Turbine AerodynamicsWind Turbine Aerodynamics

Aerodynamic Aerodynamic torque and tiptorque and tip--

speed ratiospeed ratioWind speed is not unknown,Wind speed is not unknown,but measured but highly noisybut measured but highly noisy

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Wind Turbine Wind Turbine SubSub--ModelModelss

DriveDrive--traintrainmodelmodel

Hydraulic Hydraulic pitch systempitch system

GeneratorGenerator &&converter converter

modelsmodels

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Measurement sensors modelled by adding the actual Measurement sensors modelled by adding the actual variable values with stochasticvariable values with stochastic GaussianGaussian noise noise processes. Mean and standard deviation values depend processes. Mean and standard deviation values depend on the considered measurementson the considered measurements

WT Control StrategyWT Control Strategy2 main working conditions: 2 main working conditions: switching between switching between (i)(i)power optimisationpower optimisation & & (ii)(ii) constant power productionconstant power production

ββrr

= 0= 0

(ii) PI controller (ii) PI controller

(ii)(ii)

(i)(i)

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Wind Turbine BenchmarkWind Turbine Benchmark

Wind turbine schemeWind turbine scheme&&

considered fault casesconsidered fault cases

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Fault Models Fault Models (WT Benchmark)(WT Benchmark)

FaultFault11 or Faultor Fault33: fixed values on pitch 1 or 3 : fixed values on pitch 1 or 3 position sensors #1position sensors #1

ffuu((tt) ) affecting theaffecting the ββ11((tt) ) oror ββ33((tt) ) sensors; their sensors; their measurements stuck tomeasurements stuck to 55oo or or 1010oo forfor 100100 ss. . 2000 s. < t < 2100 s.2000 s. < t < 2100 s. oror 2600 s. < t < 2700 s2600 s. < t < 2700 s..

FaultFault2 2 : : ββ22((tt) ) sensor gain change #2sensor gain change #2from from 11 to to 1.21.2active betweenactive between 2300 s. < t < 2400 s2300 s. < t < 2400 s. .

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Modelling & FDI StrategyModelling & FDI Strategy3 3 identified hybrid modelsidentified hybrid models

1)1)

uu((tt) = [) = [ττrefref

((tt)),,

vvhubhub

((tt)),,

ββii

((tt)])]TT, , yy((tt) =) =

ωωrr

((tt)), i = 1 , i = 1 (Fault(Fault11 ))

2)2)


((tt)),,

vvhubhub

((tt)),,

ββii

((tt)])]TT, , yy((tt) =) =

ωωrr

((tt)), i = 2 , i = 2 (Fault(Fault22 ))

3)3)


((tt)),,

vvhubhub

((tt)),,

ββii

((tt)])]TT, , yy((tt) =) =

ωωrr

((tt)), i = 3 , i = 3 (Fault(Fault33 ))

440 440 ×× 101033 samples & samples & 100100 Hz sampling rateHz sampling rate

Clustering algorithm Clustering algorithm withwith1)1) M = M = 33 clustersclusters & & n = n = 33 forfor {{ττrefref

((tt)),,

vvhubhub

((tt)),,

ββii

((tt)), , ωωrr

((tt))}}

Identification and validation dataIdentification and validation dataVAF (Variance Accounted For)VAF (Variance Accounted For) > > 90%90%

Optimisation of the loss function (hybrid model prediction errorOptimisation of the loss function (hybrid model prediction error))

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Hybrid Modelling ResultsHybrid Modelling Results

0 500 1000 1500 2000 2500 3000 3500 4000 45000

1

2

3Hybrid model

Time (s.)

0 500 1000 1500 2000 2500 3000 3500 4000 4500-2

0

2

4Measured output

Time (s.)

Each colour corresponds to a Each colour corresponds to a local identified affine modellocal identified affine model

^

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Results for FaultResults for Fault11

ββ11

((tt))

sensor fault residualssensor fault residuals rr((tt), ), and the faultand the fault indicator functionindicator function

0 500 1000 1500 2000 2500 3000 3500 4000 4500

-0.5

0

0.5

Time (s.)

Residuals

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

Time (s.)

Fault indicator (boolean)

Thresholds fixed for Thresholds fixed for minimising false minimising false alarm ratealarm rate

FFaultault detected if its residual detected if its residual exceeds the thresholds by exceeds the thresholds by more than 50 consecutive more than 50 consecutive samplessamples

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ββ22

((tt))

sensor fault residualssensor fault residuals rr((tt), ), and the faultand the fault indicator functionindicator function

0 500 1000 1500 2000 2500 3000 3500 4000 4500-0.6-0.4-0.2

00.2

Time (s.)

Residuals

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

Time (s.)

Fault indicator

Minimal detectable fault Minimal detectable fault = 6 for pitch sensor #2 = 6 for pitch sensor #2 (WT benchmark = 1.2)(WT benchmark = 1.2)

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ββ33 ((tt) ) sensor fault residualssensor fault residuals rr((tt), ), and the faultand the fault indicator functionindicator function

0 500 1000 1500 2000 2500 3000 3500 4000 4500-1.5

-1

-0.5

0

Time (s.)

Residuals

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

Time (s.)


Minimal detectable fault Minimal detectable fault = 18= 18°° for pitch sensor #3 for pitch sensor #3 (WT benchmark = 10(WT benchmark = 10°°))

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Comparisons with Linear KFsComparisons with Linear KFs

0 500 1000 1500 2000 2500 3000 3500 4000 4500-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time (s.)

Kalman filter residuals for Fault2

0 500 1000 1500 2000 2500 3000 3500 4000 4500-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time (s.)


Kalman filter residualsKalman filter residuals……

…… do not allow fault detection!do not allow fault detection!

Residuals for FaultResiduals for Fault11


0 500 1000 1500 2000 2500 3000 3500 4000 4500-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time (s.)



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Wind Turbine BenchmarkWind Turbine Benchmark

Wind turbine schemeWind turbine scheme&&

considered fault casesconsidered fault cases

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Fault ModelsFault Models

WT BenchmarkWT Benchmark

FaultFault44: fixed value on rotor : fixed value on rotor speed sensor 1speed sensor 1ffyy(t)(t) affecting theaffecting the ωωrr(t)(t) sensor; its measurement stuck sensor; its measurement stuck to to 1.41.4 radrad/s/s1500 s. < t < 16001500 s. < t < 1600 ss..

FaultFault88: offset in : offset in converter torqueconverter torque ττgengen((tt)) controlcontrolffyy(t)(t), converter fault active for , converter fault active for 100 s.100 s.3800 s. < t < 3900 s.3800 s. < t < 3900 s.

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Nonlinear ModellingNonlinear Modelling2 2 identified identified hybridhybrid modelsmodels

1)1)

uu((tt) = ) = [[ττrefref

((tt),),

ττaeroaero

((tt)], )], yy((tt) =) =

ωωrr

((tt))2)2)

uu((tt) = ) = [[ττrefref

((tt),),

ττaeroaero

((tt)],)],

y(t) =y(t) =

ττgengen

((tt))

440 440 ×× 101033 samples & samples & 100100 Hz sampling rateHz sampling rateDataData clustering algorithm withclustering algorithm with

1)1) M = M = 44 clustersclusters & & n = 2n = 2 for for z=z={{ττrefref (t),(t), ττaeroaero (t),(t), ωωrr (t)}(t)}2)2) M = M = 22 clustersclusters & & n = n = 22 forfor z=z={{ττrefref (t),(t), ττaeroaero (t),(t), ττgengen (t)}(t)}

Identification and validation dataIdentification and validation dataVAF (Variance Accounted For)VAF (Variance Accounted For) > > 90%90%Loss function minimisation for different Loss function minimisation for different MM and and nn

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Nonlinear Modelling ResultsNonlinear Modelling Results

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

1.5

2

2.5Individual local models

Time (s.)

ωωrr

(t)(t)

output and local output and local models with models with M = 4M = 4,, n = 2n = 2

ττgengen

(t)(t)

output and local output and local models withmodels with M = 2M = 2,, n = 2n = 2

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

1.5

2

2.5

3

3.5x 104 Individual local models

Time (s)

EachEach colour corresponds to the colour corresponds to the output of output of the the ii--thth local affine modellocal affine model

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0 500 1000 1500 2000 2500 3000 3500 4000 4500

-0.5

0

0.5

Time (s.)

Residuals

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

Time (s.)


ωωrr

((tt) ) sensor fault residualssensor fault residuals rr((tt), ), and the faultand the fault indicator functionindicator function

ωωrr

((tt) ) sensor fault residualssensor fault residuals

Thresholds fixed Thresholds fixed for minimising false for minimising false alarm ratealarm rate

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0 500 1000 1500 2000 2500 3000 3500 4000 4500-50

0

50

100

Time (s.)

Residuals

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

Time (s.)


Note: fault detected if its residual Note: fault detected if its residual exceeds the thresholds by more exceeds the thresholds by more than 50 consecutive samplesthan 50 consecutive samples

ττgengen

((tt) ) converter fault residualsconverter fault residuals rr((tt))

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Comparison with Linear KFComparison with Linear KF

0 500 1000 1500 2000 2500 3000 3500 4000 4500-1

-0.5

0

0.5

1

1.5

Time (s.)


ωωrr

((tt) ) sensor fault sensor fault residuals from KF: residuals from KF: output prediction output prediction errors errors

0 500 1000 1500 2000 2500 3000 3500 4000 4500-1200

-1000

-800

-600

-400

-200

0

200

400

Time (s.)


ττgengen

((tt) ) converter fault converter fault residualresiduals from KF: s from KF: output prediction output prediction errorerrorss

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Concluding RemarksConcluding Remarks

Practical results in actuator and sensor FDIPractical results in actuator and sensor FDIIdentified modelIdentified model--based FDI approachbased FDI approach

Simplicity of the FDI structureSimplicity of the FDI structureAlgorithmic simplicity is seen as a very important Algorithmic simplicity is seen as a very important aspect when considering the need for verification aspect when considering the need for verification and validation of a demonstrable scheme for and validation of a demonstrable scheme for industrial certification and practical process FDI industrial certification and practical process FDI The more complex the computations required to The more complex the computations required to implement the scheme, the higher the cost and implement the scheme, the higher the cost and complexity in terms of certificationcomplexity in terms of certification

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Concluding Remarks (ContConcluding Remarks (Cont’’d)d)

Modelling uncertainty and measurement error Modelling uncertainty and measurement error seem to be well tackledseem to be well tackledThe achieved results highlight the potential of The achieved results highlight the potential of using such a method in real applicationsusing such a method in real applicationsExtensive simulations for estimating the reliability Extensive simulations for estimating the reliability of the developed FDI scheme and the final of the developed FDI scheme and the final performanceperformanceStudies have been carried out to evaluate the Studies have been carried out to evaluate the effectiveness of the approach when applied to effectiveness of the approach when applied to real datareal data

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ReferencesReferencesSimani, S.; Fantuzzi, C.; Rovatti, R.; Beghelli, S. Parameter idSimani, S.; Fantuzzi, C.; Rovatti, R.; Beghelli, S. Parameter identification for piecewiseentification for piecewise--affine affine fuzzy models in noisy environment. fuzzy models in noisy environment. International Journal of Approximate ReasoningInternational Journal of Approximate Reasoning Volume: Volume: 22, Issue: 122, Issue: 1--2, September 10, 1999, pp. 1492, September 10, 1999, pp. 149--167 167 Rovatti, R.; Fantuzzi, C.; Simani, S. HighRovatti, R.; Fantuzzi, C.; Simani, S. High--speed DSPspeed DSP--based implementation of piecewisebased implementation of piecewise--affine affine and piecewiseand piecewise--quadratic fuzzy systems. quadratic fuzzy systems. Signal ProcessingSignal Processing Volume: 80, Issue: 6, June, 2000, Volume: 80, Issue: 6, June, 2000, pp. 951pp. 951--963963Simani, S.; Fantuzzi, C.; Beghelli, S. Diagnosis techniques for Simani, S.; Fantuzzi, C.; Beghelli, S. Diagnosis techniques for sensor faults of industrial sensor faults of industrial processes. processes. IEEE Transactions on Control Systems TechnologyIEEE Transactions on Control Systems Technology. Volume: 8 , Issue: 5, 2000 , pp. . Volume: 8 , Issue: 5, 2000 , pp. 848 848 –– 855855Simani, S. Identification and fault diagnosis of a simulated modSimani, S. Identification and fault diagnosis of a simulated model of an industrial gas turbine. el of an industrial gas turbine. IEEE Transactions on Industrial InformaticsIEEE Transactions on Industrial Informatics, Volume: 1 , Issue: 3. 2005 , pp. 202 , Volume: 1 , Issue: 3. 2005 , pp. 202 -- 216216Simani, S. Simani, S. Fault diagnosis of a simulated industrial gas turbine via identiFault diagnosis of a simulated industrial gas turbine via identification approachfication approach. . International Journal of Adaptive Control and Signal ProcessingInternational Journal of Adaptive Control and Signal Processing Volume: 21, Issue: 4, May, Volume: 21, Issue: 4, May, 2007, pp. 3262007, pp. 326--353353SimaniSimani,, SilvioSilvio;; FantuzziFantuzzi, , CesareCesare.. Dynamic system identification and modelDynamic system identification and model--based fault based fault diagnosis of an industrial gas turbine prototypediagnosis of an industrial gas turbine prototype. . MechatronicsMechatronics Volume: 16, Issue: 6, July, 2006, Volume: 16, Issue: 6, July, 2006, pp. 341pp. 341--363363..SimaniSimani, S.; Patton, Ron J. Fault diagnosis of an industrial gas turbin, S.; Patton, Ron J. Fault diagnosis of an industrial gas turbine prototype using a system e prototype using a system identification approachidentification approach. . Control Engineering PracticeControl Engineering Practice Volume: 16, Issue: 7, July, 2008, pp. 769Volume: 16, Issue: 7, July, 2008, pp. 769--786786

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