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

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 5th DAMADICS Workshop in Łagów

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

Analytical Redundancy Relations (ARRs) INTRODUCTION

1. The objectives 5th DAMADICS Workshop in Łagów

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 DIAGNOSABILITY AND SENSOR PLACEMENT

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

Analytical Redundancy 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 HYPOTHETICAL FAULT SIGNATURE MATRIX

ARR derivation example PR1: z = x + y A PR2: y = -z I E  X = {x, y, z} = UO O = {x, y, z} U =  O = {x, z} U = {y} ARR3: x = 2z {A, S(x)}, I, {S(y), S(z)} Discriminability level D = 3 Discriminability level D = 1 HYPOTHETICAL FAULT SIGNATURE MATRIX

ARR derivation; general case HYPOTHETICAL FAULT SIGNATURE MATRIX

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

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

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 degreeds = DS/CARD(F) Fully diagnosable system:ds = 1 Non-sensored system:ds = 0 MINIMAL ADDITIONAL SENSOR SETS

Minimal Additional Sensor Sets • Given ( ,S,F) partially diagnosable, S is an Additional Sensor Set iff ( ,SS,F) is fully diagnosable. • Note: Sis 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) dSS = dSS*and ii)  S'  S, dSS = dSS* MINIMAL ADDITIONAL SENSOR SETS

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

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

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) Additional external components: PT - pressure transmitters FT - volume flow rate transmitter TT - temperature transmitter V1, V2 - cut-off valves V3 - bypass valve Application example: DAMADICS Benchmark

DAMADICS Benchmark (II) The primary relations: 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) Application example: DAMADICS Benchmark

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 Application example: DAMADICS Benchmark

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 Application example: DAMADICS Benchmark

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 Application example: DAMADICS Benchmark

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 5th DAMADICS Workshop in Łagów

Diagnosability and Sensor Placement. Application to DAMADICS Benchmark