diagnosability and sensor placement. application to damadics benchmark

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


2

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


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)


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


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


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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


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ARR derivation; general case


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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)


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


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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*


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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


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


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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)


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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)



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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)


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



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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)


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



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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

diagnosability and sensor placement. application to damadics benchmark

Documents

set of sensors s

andii s s

set of hypothetical

mass iff s s

sets s

sensor placement2

set of variablesxe

set of equationsx