5th DAMADICS Workshop in Łagów Diagnosability and Sensor Placement. Application to DAMADICS...
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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