Active Fault Analysis of Parametric Faults in Dynamic

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ACTIVE FAULT ANALYSIS OFPARAMETRIC FAULTS INDYNAMIC SYSTEMS

xxxxxxxxxxxxxxxxxxxxxPresented by xxxxxxxxxxxx

Roll xxxxxxRegd. No :- xxxxxxxxx

Branch :- Electrical &ElectronicsEngineering
http://../My%20Documents/Presentation3.ppt


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CONTENTS1. Importance of fault tolerance

2. Structure of fault tolerant control

system3. Fault Detection and Isolation(FDI)

4. Robust design ofFDI

5. Fault Diagnosis of Nonlinear DynamicSystem

6. System reconfiguration


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1. Importance of fault

tolerance The growing complexity of control system

increases the possibility of component and

system failure. System failure can cause mission abortion,

material damage and human fatality.

The improvement of system reliability can

not been totally dependent upon theimprovement of component reliability,because of the restriction of technologicallevel and cost consideration


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A fault tolerant system is designed with redundancycapacity. When its some components or subsystems fail,it can reconfigure its remaining components andinformation- processing capability to continue operation

properly. Hardware redundancy and Analytical (functional)

redundancy.

Example:Aircraft control system has several channels ofamplifiers. When one of them is failed, the systemcan switch to other channel and continueoperation ( e.g. landing) instead of disaster withhundreds of lives lost.


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Fault tolerance can greatly reduce the systemfault rate and it can use low reliablecomponents to achieve high reliable system.

Single channel system fault rateTriple channel redundant system

More researches need to be done.

Challenges to Control(A collective view), IEEE Trans. AC-32No.4, April 1987.

Aircraft Control SystemA projection to the year 2000, IEEEContr. Syst. Mag, pp11-13, Feb. 1985.

103

h

10 7 h


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2. Structure of fault

tolerant control systems

ActuatorsPlant

DynamicsSensors

ResidualGenerator

DecisionMaking

ReconfigurationAlgorithm

Controller

Output

reference input


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Residual Generation

Observer Approach

Kalman Filter Approach

Parity Space Approach

Decision Making

Fault Detection: Whether there is a fault or not?

Fault Isolation: Where has the fault happened?Fault Estimation: When did the fault happen?

How serious is the fault?


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Approaches to Decision Making

Statistical Hypotheses Test

Fuzzy Logic Inference

Neural Network Classifier

Fault Diagnosis Expert Systems


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3. Fault Detection and

Isolation(1) Observer scheme

System model with faults:

(1)

(2)

Actuator fault

Sensor faultd(t)Unknown Input (Modeling error

and/or disturbances)

( ) ( ) ( ) ( ) ( )x t Ax t Bu t R f t Ed t

1 1

y t Cx t Du t R f t( ) ( ) ( ) ( ) 2 2

f t1( )

f t2 ( )


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Observer equation(3)(4)

Weighted output residual(5)

Consider sensor faults ( )(6)

(7)

(8)(9)

( ) ( ) ( ) ( ) ( ) ( )x t A KC x t B KD u t Ky t ( ) ( ) ( )y t Cx t Du t

r t W y t y t ( ) ( ( ) ( ))

R I, f 02 1

r s H s f s H s d sf d( ) ( ) ( ) ( ) ( ) 2

H s W I sI A Kf c( ) [ ( ) ] 1

H s WC sI A Ed c( ) ( ) 1

A A KCc


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Fault detection rule(Assuming d(t)=0)no fault (10)

with fault (11)

thresholdUnknown Input d(t)will affect the correctness of faultdetection.

It is needed to seek for more robust methods.

Fault isolationWe use mobservers where the ith observer uses

i.e., all sensor outputs but the ith sensor output .

Therefore, the ith observer is free of

|| ( )||r t TD

|| ( )||r t TD

TD

y y y y yi i m1 2 1 1, , , , , ,

yi


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Binary hypotheses test

(14)

(15)According to Generalized Likelihood Ratio Test Theory, Weconstruct the following Decision function of Fault Detection(DFD)

(16)W(k): Covariance matrix ofr(k).

(17), where n(dimension ofr(k)) is the degree of

freedom of distribution

H E r k no fault0 0: [ ( )]

H E r k with fault1 0: [ ( )]

r k N W ( ) ~ ( , )0 ( ) ~ ( )k n2

2

( ) ( ) ( ) ( )k r k W k r k 1


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Innovation test

(20)

White noise: no fault

Zhang, H.G. and H. Y. Zhang, Fault tolerant scheme formultisensor navigation systems, Proc. of 18th Congress of theInternational of Aeronautical Sciences,Beijing, China, Sept. 1992.

r k y k H k x k k ( ) ( ) ( ) ( | ) 1


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(3). Parity space approach Static case

(21)

zero mean Gaussian noise vector,f-sensor fault vector

Ifm>n, we can find a matrix V

VH=0(22)

y Hx f

y Rm

x Rn

p Vy V Vf


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Decision function of Fault Detection(DFD)

(23)

(24)

Fault detection rule:no fault (25)

with fault (26)

p W p1

W E V V VE V [( )( ) ] [ ]

TD TD


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4. Robust design of FDI

It is difficult to distinguish between effects of

fault f(t)and modeling uncertainty d(t).

Eigenstructure assignment:

Design gain matrix Kand weight matrix Wto

makethen residual r(s)is decoupled from uncertainty

(unknown input) d(t)

H s WC sI A KC Ed ( ) [ ( )] 1

0


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5. Fault Diagnosis ofNonlinear Dynamic System

(1)Introduction

Linearized model method may not give

satisfactory result due to mismatch between

linear model and nonlinear behavior.

Analytical solution for FDI of general

nonlinear systems is difficult.Two ways to overcome the difficulties:


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> Restricting the class of nonlinear

systems

>Neuro-Fuzzy approach(2) Bilinear Systems:

)()()(

)()()()()(

2

11

tdEtCxty

tdEtxtuBtAxtxr

iii


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whererespectively the state,

output and unknowndisturbance of thesystem.

Observer:

exists if and only if

0

)(dim

0

0)(

00

2

1

2

1

2

12

2

12

E

EErankx

EC

EEAsIrank

E

EErankErank

E

ECCEErank

)()()(

)()()()()(1

tNytHtx

tytuLtGytFtr

iii

dyx ,,


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Fuzzy Logic Approach forFDI of Nonlinear System

()Takagi-Sugeno fuzzy model

The nonlinear system behavior is

described by

a fuzzy fusion of the outputs of all linear

models which are linearized at different

operating points of the nonlinear system.


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6. System reconfiguratio

(1) Sensor reconfiguration

l Hardware redundancy case:

Switch off faulty sensor(s) and switch on redundantsensor(s)

Analytical redundancy case:

Use observer to estimate the measurement of

faulty sensor(s)


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(2) Actuator reconfiguration

Switch off faulty actuator(s) and switch on

redundant actuator(s)

(3) Control signal reconfiguration

For modeled faults

Bhas changed to because of some faults of

control devices (e.g. surface damage of rudder,

elevator, flap etc).

( ) ( ) ( )x t Ax t Bu t

Bn


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