X. Ding

Frequency domain approach to optimally robust residual generation and evaluation for model-based fault diagnosis

Methods of residual generation and evaluation for model-based fault diagnosis in uncertain linear dynamic systems are investigated with the aid of frequency domain approaches and H∞-optimization techniques. Based on the factorization technique, the construction of residual generators in terms of a parametrization concept is proposed. With its help the fault detection and isolation problem with perfect model uncertainty decoupling is studied and, moreover, by its optimal approximation the problem of optimally robust residual generation is treated. The optimization problem is solved by H∞-techniques. To increase the robustness of residual evaluation a frequency domain residual evaluation index is introduced, and optimal input adaptive fault thresholds are derived with respect to the frequency domain evaluation index. The results are illustrated in terms of an inverted pendulum example.

Fault detection via factorization approach

Abstract Problems of designing fault detection and identification filters in the frequency domain are formulated and solved. Using the factorization approach a characterization of all fault detection filters is derived. This enables the derivation of necessary and sufficient conditions for the existence of fault identification as well as detection and isolation filters. It is shown that these conditions are a generalization of existing results. The formulas of constructing the filters are also derived. In comparison with the algorithms given in previous work they are computationally straightforward and simple. Finally, the proposed method for designing fault identification filters is extended so that more practical cases can be handled.

A frequency domain approach to fault detection of uncertain dynamic systems

Problems related to fault detection of uncertain dynamical systems are studied. The purpose of this study is to solve residual generation and evaluation problems. With the aid of frequency domain fault detection approaches, a relationship between residual generators, residual evaluation function and the minimum size of detectable faults is established. This enables the authors to formulate the tasks as optimization problems that are solvable using frequency domain optimization techniques. An expression for achievable minimum size of detectable faults by using linear residual generators is finally derived.<<ETX>>

Nonlinear observer design via an extended observer canonical form

Based on the theory of designing unknown input observers, an extended nonlinear observer canonical form is introduced. Observers can easily be constructed for those systems which can be transformed into this canonical form. Necessary and sufficient conditions for the existence of such transformation are derived and furthermore an algorithm for calculating this transformation in given.

An Adaptive Observer-Based Fault Detection Scheme for Nonlinear Dynamic Systems

Abstract An adaptive observer-based fault detection scheme is presented. This scheme is applicable not. only for detecting abrupt faults in a nonlinear dynamic system but also for estimating unknown parameters which may represent faults with slow time constants, some kinds of nonlinearities or time-varying system parameters.

Robust observer design via factorization approach

Problems of designing robust observers in the frequency domain are formulated and solved. Using the factorization approach, a characterization of all observers is derived. This enables the description of all achievable transfer functions of estimate errors in terms of a RH/sub infinity /-parameter matrix. It is shown that the problem of designing optimally robust observers can therefore be transformed into the well-known model matching problem that can be solved with H/sub infinity /-optimization techniques. It is shown that the proposed methods can be used to solve the problem of finding exact unknown input observers.<<ETX>>

Structure analysis via orthogonal functions

The use of orthogonal functions to analyse the structure of a system is investigated. Applying the definitions of observability and controllability to a system that is approximated with the help of orthogonal functions, it is shown that the concepts of the state space and the space of orthogonal functions are equivalent, provided that two weak conditions are met. This result ensures that the observability and controllability properties remain invariant under the transformation introduced by the approximation. Furthermore, new criteria to test observability and controllability are given in terms of the coefficient matrix of the orthogonal expansion. Because this test does not require the knowledge of the system matrices A, B and C, the results derived may be used for the identification of systems. It is demonstrated that all the results obtained remain true, even for an approximation with low accuracy. These properties allow the application of orthogonal functions for the analysis of systems

Fault Diagnosis Using Adaptive Observers

This paper presents an adaptive observer based fault detection scheme. With the aid of nonlinear adaptive observer theory, an approach of constructing adaptive residual generators is developed. Using such kind of residual generators, we are able not only to detect abrupt faults but also to estimate unknown parameters in the system observed which may represent faults with slow time constants, some kinds of nonlinearities or varying system parameters. This may enhance the robustness of residual generators with respect to model uncertainties and provide a new *ay t o solve fault detection problem for nonlinear systems. The proposed scheme is illustrated in terms of an application example.

An Approach to Residual Generator and Evaluator Design and Synthesis

Abstract Problems related to fault detection for uncertain dynamic systems are studied. The objective of this study is to develop an approach to residual generator and evaluator design and synthesis. The basic idea of the new approach is to design residual generators and establish thresholds in such a way that the requirements on the size of detectable faults and the rate of false alarm prescribed are met.

An approach to robust residual generation and evaluation

Problems of robust residual generation and evaluation are investigated with the aid of frequency-domain approaches and H/sub infinity /-optimization techniques. Based on the parameterization of achievable residual dynamics the robust residual generation is defined as an optimization problem that can be solved by H/sub infinity /-techniques. To increase the robustness of residual evaluation, a frequency-domain residual measure is introduced, under which fault thresholds are derived.<<ETX>>