Structural diagnosis for distributed systems

Abstract

The recent development of technological systems implies a high complexity of behaviors for today’s systems. An answer to the increased systems’ complexity is to look at them as a multitude of heterogeneous subsystems and develop distributed techniques to control and manage them. This raises a number of problems. Firstly, as the size and number of components increase, so does the number of fault occurrences that may drive the system to undergo critical failures. Fault detection and isolation (FDI), maintenance and repair are an increasing part of the operational every day’s tasks and they impact drastically the total cost of final products. This thesis focuses on fault detection and isolation. Among the different methods to generate diagnosis tests by taking advantage of analytical redundancy, this thesis adopts the so-called parity space approach based on analytical redundancy relations (ARRs). Given a model of the system in the form of a set of differential equations, ARRs are relations that are obtained from the model by eliminating non measured variables. This can be performed in an analytical framework using elimination theory but another way of doing this is to use structural analysis. Structural analysis is based on a structural abstraction of the model that only retains a representation of which variables are involved in which equations. Despite the rusticity of the abstract model, structural analysis provides a set of powerful tools, relying on graph theory, to analyze and infer information about the system. Interestingly, it applies indifferently to linear or nonlinear systems. The goal of this thesis is to develop effective techniques based on structural analysis for diagnosis of distributed continuous systems. In this framework, the system is decomposed into a set of subsystems according to functional, geographical or privacy constraints. The thesis is organized in two parts, highlighting the redundancies that are built into the global structural model and that can be used to generate diagnosis tests starting from the redundancies existing in the subsystem’s models and formulating and solving the optimization problem linked to the choice of a subset of diagnosis tests at the subsystems level that can lead to a set of diagnosis tests achieving maximum diagnosability for the global system. The first part takes benefit of the concept of Fault-Driven Minimal Structurally Overdetermined Set (FMSO set) that is introduced in the thesis. An FMSO set determines a subset of equations of the model with minimal redundancy from which an ARR sensitive to a set of faults can be obtained. Two solutions for generating FMSOs for the global system are presented, in a decentralized framework with supervisors at each level of a hierarchy and in a totally distributed framework. These are based on the properties of the FMSO sets for the subsystems in relation to those of the global system derived in the thesis. The second part formulates the optimization problem in a heuristic search framework and proposes three solutions based on iterating an A* algorithm combined with a function able to assess whether a global FMSO set can be achieved from the selected local FMSO sets. The concepts introduced in the thesis and the results are applied to the case study of a Reverse Osmosis Desalination Plant and a Spacecraft Attitude Determination and Control System of a Low Earth-Orbit Satellite.