5th DAMADICS Workshop in Łagów

Diagnosability and Sensor Placement. Application to DAMADICS Benchmark

Diagnosability and Sensor Placement. Application to DAMADICS Benchmark

Ph. D. Student: Stefan Spanache

Director: Dr. Teresa Escobet i Canal

Co-Director: Dr. Louise Travé-Massuyès

Departament d’Enginyeria de Sistemes, Automàtica i Informatica Industrial

Universitat Politècnica de Catalunya

5th DAMADICS Workshop in Łagów

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INDEX

0. Introduction

1. The objectives

2. Hypothetical Fault Signature Matrix

3. Minimal Additional Sensor Sets

4. Application example: DAMADICS Benchmark

5. Conclusions and future work

5th DAMADICS Workshop in Łagów

0. Introduction

INTRODUCTION 4

Model-based fault diagnosis methods

KNOWN INPUTS

PROCESS MODEL

DETECTION

ISOLATION

UNKNOWN INPUTS FAULTS

MEASURED STATE

ESTIMATED STATE

FAULT INDICATION

ISOLATED FAULT

INTRODUCTION 5

Analytical Redundancy Relations (ARRs)

5th DAMADICS Workshop in Łagów

1. The objectives

DIAGNOSABILITY AND SENSOR PLACEMENT

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The objectives

Main: design of an algorithm for

- set of additional sensors that can provide a maximum level of diagnosability

- cost optimisation method for these additional sensors

Main steps- automatic ARR generation

- ARR-based fault diagnosability assessment

- diagnosability improvement; Minimal Additional Sensor Sets

5th DAMADICS Workshop in Łagów

2. Hypothetical Fault Signature Matrix

HYPOTHETICAL FAULT SIGNATURE MATRIX

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Analytical Redundancy

E = set of equations

X = set of variables

Xe = exogenous variables

U = unknown variables

O = known variables

RR = redundant relations

E = set of equations

X = set of variables

Xe = exogenous variables

U = unknown variables

O = known variables

RR = redundant relations

E = {PR1,..., PRn} are Primary Relations describing the behaviour of system's physical components

E = {PR1,..., PRn} are Primary Relations describing the behaviour of system's physical components

HYPOTHETICAL FAULT SIGNATURE MATRIX

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ARR derivation example

PR1: z = x + y A

PR2: y = -z I

PR1: z = x + y A

PR2: y = -z I

EE

X = {x, y, z} = U OX = {x, y, z} = U O

O = {x, y, z} U = O = {x, y, z} U = O = {x, z} U = {y}O = {x, z} U = {y}

ARR3: x = 2zARR3: x = 2z{A, S(x)}, I, {S(y), S(z)}{A, S(x)}, I, {S(y), S(z)}

Discriminability level D = 1Discriminability level D = 1 Discriminability level D = 3Discriminability level D = 3

HYPOTHETICAL FAULT SIGNATURE MATRIX

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ARR derivation; general case

HYPOTHETICAL FAULT SIGNATURE MATRIX

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HFS Matrix example

Hypothesis: all variables are measuredHypothesis: all variables are measured all Hypothetical ARRs (H-ARRs)all Hypothetical ARRs (H-ARRs)

5th DAMADICS Workshop in Łagów

3. Minimal Additional Sensor Sets

MINIMAL ADDITIONAL SENSOR SETS

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Diagnosability degree

Given a system with a set of sensors S and a set of faults F = {F1, F2, ..., Fn}

- full diagnosability: {F1}, {F2}, ...,{Fn};

- partial diagnosability: {F1,..., Fi},..., {Fp,..., Fn}.

D-class = a subset of faults that cannot be discriminated between one another

DS = the number of D-classes given by the set of sensors S

Then the set S is characterised by its diagnosability degree ds = DS/CARD(F)

Fully diagnosable system: ds = 1Non-sensored system: ds = 0

Given a system with a set of sensors S and a set of faults F = {F1, F2, ..., Fn}

- full diagnosability: {F1}, {F2}, ...,{Fn};

- partial diagnosability: {F1,..., Fi},..., {Fp,..., Fn}.

D-class = a subset of faults that cannot be discriminated between one another

DS = the number of D-classes given by the set of sensors S

Then the set S is characterised by its diagnosability degree ds = DS/CARD(F)

Fully diagnosable system: ds = 1Non-sensored system: ds = 0

MINIMAL ADDITIONAL SENSOR SETS

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Minimal Additional Sensor Sets

Given ( ,S,F) partially diagnosable, S is an Additional Sensor Set iff ( ,SS,F) is fully diagnosable.

Note: S is a set of hypothetical sensors.

S is a Minimal Additional Sensor Set (MASS) iff S' S, S' is not an Additional Sensor Set.

There are cases when this problem has no solution.

If S* is the set of all hypothetical sensors, then the fault signature matrix of

( ,SS*,F) is HFS.

Objective: finding all sets S with the properties:

i) dSS = dSS* and

ii) S' S, dSS = dSS*

Given ( ,S,F) partially diagnosable, S is an Additional Sensor Set iff ( ,SS,F) is fully diagnosable.

Note: S is a set of hypothetical sensors.

S is a Minimal Additional Sensor Set (MASS) iff S' S, S' is not an Additional Sensor Set.

There are cases when this problem has no solution.

If S* is the set of all hypothetical sensors, then the fault signature matrix of

( ,SS*,F) is HFS.

Objective: finding all sets S with the properties:

i) dSS = dSS* and

ii) S' S, dSS = dSS*

MINIMAL ADDITIONAL SENSOR SETS

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The procedure

HFS matrixHFS matrix

AFS matrixesAFS matrixes

Objective: finding all AFS matrixes with the rank equal to rank(HFS) and with minimal number of sensorsObjective: finding all AFS matrixes with the rank equal to rank(HFS) and with minimal number of sensors

5th DAMADICS Workshop in Łagów

4. Application example: DAMADICS Benchmark

Application example: DAMADICS Benchmark

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DAMADICS Benchmark (I)

The actuator consists in three main components:

control valve or hydraulic (H)

pneumatic servo-motor or mechanics (M)

positioner, which can also be decoupled in three components:

position controller (PC)

electro/pneumatic transducer (E/P)

displacement transducer (DT)

The actuator consists in three main components:

control valve or hydraulic (H)

pneumatic servo-motor or mechanics (M)

positioner, which can also be decoupled in three components:

position controller (PC)

electro/pneumatic transducer (E/P)

displacement transducer (DT)

Additional external components:Additional external components:

V1, V2 - cut-off valves

V3 - bypass valve

V1, V2 - cut-off valves

V3 - bypass valve

PT - pressure transmitters

FT - volume flow rate transmitter

TT - temperature transmitter

PT - pressure transmitters

FT - volume flow rate transmitter

TT - temperature transmitter

Application example: DAMADICS Benchmark

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DAMADICS Benchmark (II)

The primary relations:The primary relations:

X - servomotor’s rod displacement

PV - process variable

Fv - flow rate on valve outlet

Ps - pressure in servomotor’s chamber

X - servomotor’s rod displacement

PV - process variable

Fv - flow rate on valve outlet

Ps - pressure in servomotor’s chamber

Pz - the supply pressure (600 Mpa)

SP - the set point

CVI - the control current

P - pressure difference across the valve (P1-P2)

Pz - the supply pressure (600 Mpa)

SP - the set point

CVI - the control current

P - pressure difference across the valve (P1-P2)

Component Equation

Pneumatic servomotor X= r1(Ps, P)

Control valve Fv = r2(X, P)

Position controller CVI = r3(SP, PV)

E/P transducer + pressuresupplier

Ps = r4(X, CVI, Pz)

Positioner feedback PV = r5(X)

Application example: DAMADICS Benchmark

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DAMADICS Benchmark (III)

The components that can be faulty: {M, P, H, DT, S(Ps), S(Fv), S(PV), S(dP), S(Pz)}

Considering only Sa = {S(Fv), S(PV), S(dP), S(Pz)}

The FS matrix:

The components that can be discriminated: {M,P,S(Pz)}, {H,S(Fv)}, DT, S(dP) and S(PV)

Discriminability level D = 5

The components that can be discriminated: {M,P,S(Pz)}, {H,S(Fv)}, DT, S(dP) and S(PV)

Discriminability level D = 5

Application example: DAMADICS Benchmark

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DAMADICS Benchmark (IV)

The HFS matrix after adding a sensor for PsThe HFS matrix after adding a sensor for Ps

The components that can be discriminated: M, {P,S(Pz)}, {H,S(Fv)}, DT, S(Ps), S(PV), S(PV)

Discriminability level D = 7

The components that can be discriminated: M, {P,S(Pz)}, {H,S(Fv)}, DT, S(Ps), S(PV), S(PV)

Discriminability level D = 7

Application example: DAMADICS Benchmark

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DAMADICS Benchmark (V)

The HFS matrix after adding a sensor for XThe HFS matrix after adding a sensor for X

The components that can be discriminated: {M, P,S(Pz)}, {H,S(Fv)}, DT, S(X), S(PV), S(dP)

Discriminability level D = 6

The components that can be discriminated: {M, P,S(Pz)}, {H,S(Fv)}, DT, S(X), S(PV), S(dP)

Discriminability level D = 6

5th DAMADICS Workshop in Łagów

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Conclusions and future work

Sensor availability provides a diagnosed system with Analytical Redundancy which, in turn, increases the Discriminability between the system components Given a required discriminability level Optimal

(discriminability/cost) instrumentation system can be found

Exhaustive search for best dS Optimisation of ds using Genetic Algorithms

Closed loops effects in fault discrimination