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Residual Generation for Fault Diagnosis: Nominal and Robust Design

Diagnosis is the task to deduce, from observed variables of a system, if any component is faulty and if so, locate the faulty component. In a technical application, diagnosis is performed by filtering measurements and control signals to generate signals, called residuals, that carries fault information. The filters, in a model based diagnosis system, are based on a model of the process being supervised. The residuals are inputs to a residual evaluator, where it is inferred if and which fault that is present.

The topic of this thesis is to develop design methods for residual generators, to fit in a scheme for fault isolation, i.e. location of any faulty components. The main goal is that the design methods handle the main problems in fault diagnosis, namely unknown signals that influence process dynamics and uncertain models.

A design method based on a minimal polynomial basis approach using nominal process models is developed where focus is on two main issues: \emph{completeness} of solution, i.e. the method is able to generate all residual generators using numerically efficient algorithms, and \emph{minimality}, i.e. the residual generators of minimal order is trivially extracted from the algorithm output. In addition, the method provide the designer with a design tool with few design variables with clear interpretations.

When synthesizing residual generators based on uncertain models, focus is on handling model uncertainty rather than minimality issues, and the main goal is to attenuate influence from worst case uncertainty while keeping sensitivity to the faults. A theory for robust residual generator design is developed with two key elements. One is the use of a reference model that represents desired performance of the synthesized residual generator, i.e. time or frequency-domain specifications on fault response in the residuals. A second element is an optimization criterion used to synthesize the robust residual generator. It is shown that a poor choice of reference model leads to unnecessary poor robustness properties of the diagnosis system. Therefore, a methodology for selecting the reference model is developed.

In conclusion, similar problems are addressed in both the nominal and the robust case. The goal, and main property, of both the nominal and robust design algorithms are that they provide the diagnosis system designer with an intuitive and numerically reliable tool when designing residual generators that fit in a structured residual isolation scheme.

Erik Frisk


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Senast uppdaterad: 2021-11-10