1. 5th DAMADICS Workshop in Łagów 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. 5th DAMADICS Workshop in Łagów2 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

3. 5th DAMADICS Workshop in Łagów 0. Introduction

4. INTRODUCTION4 Model-based fault diagnosis methods KNOWN INPUTS PROCESS MODEL DETECTION ISOLATION UNKNOWN INPUTS FAULTS MEASURED STATE ESTIMATED STATE FAULT INDICATION ISOLATED FAULT

5. INTRODUCTION5 Analytical Redundancy Relations (ARRs)

6. 5th DAMADICS Workshop in Łagów 1. The objectives

7. DIAGNOSABILITY AND SENSOR PLACEMENT7 The objectives n 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 n Main steps - automatic ARR generation - ARR-based fault diagnosability assessment - diagnosability improvement; Minimal Additional Sensor Sets

8. 5th DAMADICS Workshop in Łagów 2. Hypothetical Fault Signature Matrix

9. HYPOTHETICAL FAULT SIGNATURE MATRIX9 Analytical Redundancy E = set of equations X = set of variables X e = exogenous variables U = unknown variables O = known variables RR = redundant relations E = set of equations X = set of variables X e = exogenous variables U = unknown variables O = known variables RR = redundant relations E = {PR 1,..., PR n } are Primary Relations describing the behaviour of system's physical components

10. HYPOTHETICAL FAULT SIGNATURE MATRIX10 ARR derivation example PR 1 : z = x + yA PR 2 : y = -zI PR 1 : z = x + yA PR 2 : y = -zI   E E X = {x, y, z} = U  O O = {x, y, z}U =  O = {x, z}U = {y} ARR 3 : x = 2z {A, S(x)}, I, {S(y), S(z)} Discriminability level D = 1 Discriminability level D = 3

11. HYPOTHETICAL FAULT SIGNATURE MATRIX11 ARR derivation; general case

12. HYPOTHETICAL FAULT SIGNATURE MATRIX12 HFS Matrix example Hypothesis: all variables are measured all Hypothetical ARRs (H-ARRs)

13. 5th DAMADICS Workshop in Łagów 3. Minimal Additional Sensor Sets

14. MINIMAL ADDITIONAL SENSOR SETS14 Diagnosability degree Given a system  with a set of sensors S and a set of faults F = {F 1, F 2,..., F n } - full diagnosability: {F 1 }, {F 2 },...,{F n }; - partial diagnosability: {F 1,..., F i },..., {F p,..., F n }. D-class = a subset of faults that cannot be discriminated between one another D S = the number of D-classes given by the set of sensors S Then the set S is characterised by its diagnosability degree d s = D S /CARD(F) Fully diagnosable system: d s = 1 Non-sensored system:d s = 0 Given a system  with a set of sensors S and a set of faults F = {F 1, F 2,..., F n } - full diagnosability: {F 1 }, {F 2 },...,{F n }; - partial diagnosability: {F 1,..., F i },..., {F p,..., F n }. D-class = a subset of faults that cannot be discriminated between one another D S = the number of D-classes given by the set of sensors S Then the set S is characterised by its diagnosability degree d s = D S /CARD(F) Fully diagnosable system: d s = 1 Non-sensored system:d s = 0

15. MINIMAL ADDITIONAL SENSOR SETS15 Minimal Additional Sensor Sets Given ( ,S,F) partially diagnosable, S is an Additional Sensor Set iff ( ,S  S,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 ( ,S  S *,F) is HFS. Objective: finding all sets S with the properties: i) d S  S = d S  S* and ii)  S'  S, d S  S = d S  S* Given ( ,S,F) partially diagnosable, S is an Additional Sensor Set iff ( ,S  S,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 ( ,S  S *,F) is HFS. Objective: finding all sets S with the properties: i) d S  S = d S  S* and ii)  S'  S, d S  S = d S  S*

16. MINIMAL ADDITIONAL SENSOR SETS16 The procedure HFS matrix AFS matrixes Objective: finding all AFS matrixes with the rank equal to rank(HFS) and with minimal number of sensors

17. 5th DAMADICS Workshop in Łagów 4. Application example: DAMADICS Benchmark

18. Application example: DAMADICS Benchmark18 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: 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

19. Application example: DAMADICS Benchmark19 DAMADICS Benchmark (II) The primary relations: X - servomotor’s rod displacement PV - process variable F v - flow rate on valve outlet P s - pressure in servomotor’s chamber X - servomotor’s rod displacement PV - process variable F v - flow rate on valve outlet P s - pressure in servomotor’s chamber P z - the supply pressure (600 Mpa) SP - the set point CVI - the control current  P - pressure difference across the valve (P 1 -P 2 ) P z - the supply pressure (600 Mpa) SP - the set point CVI - the control current  P - pressure difference across the valve (P 1 -P 2 )

20. Application example: DAMADICS Benchmark20 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 S a = {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

21. Application example: DAMADICS Benchmark21 DAMADICS Benchmark (IV) The 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

22. Application example: DAMADICS Benchmark22 DAMADICS Benchmark (V) The 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

23. 5th DAMADICS Workshop in Łagów23 Conclusions and future work n Sensor availability provides a diagnosed system with n Analytical Redundancy which, in turn, increases the n Discriminability between the system components n Given a required discriminability level Optimal (discriminability/cost) instrumentation system can be found n Exhaustive search for best d S Optimisation of d s using Genetic Algorithms n Closed loops effects in fault discrimination