P.M. Frank

Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy—a survey and some new results

Abstract The paper reviews the state of the art of fault detection and isolation in automatic processes using analytical redundancy, and presents some new results. It outlines the principles and most important techniques of model-based residual generation using parameter identification and state estimation methods with emphasis upon the latest attempts to achieve robustness with respect to modelling errors. A solution to the fundamental problem of robust fault detection, providing the maximum achievable robustness by decoupling the effects of faults from each other and from the effects of modelling errors, is given. This approach not only completes the theory but is also of great importance for practical applications. For the case where the prerequisites for complete decoupling are not given, two approximate solutions—one in the time domain and one in the frequency domain—are presented, and the crossconnections to earlier approaches are evidenced. The resulting observer schemes for robust instrument fault detection, component fault detection, and actuator fault detection are briefly discussed. Finally, the basic scheme of fault diagnosis using a combination of analytical and knowledge-based redundancy is outlined.

Issues of Fault Diagnosis for Dynamic Systems

There is an increasing demand for dynamic systems to become safer, more reliable and more economical in operation. This requirement extends beyond the normally accepted safety-critical systems e.g., nuclear reactors, aircraft and many chemical processes, to systems such as autonomous vehicles and some process control systems where the system availability is vital. The field of fault diagnosis for dynamic systems (including fault detection and isolation) has become an important topic of research. Many applications of qualitative and quantitative modelling, statistical processing and neural networks are now being planned and developed in complex engineering systems. Issues of Fault Diagnosis for Dynamic Systems has been prepared by experts in fault detection and isolation (FDI) and fault diagnosis with wide ranging experience.Subjects featured include: - Real plant application studies; - Non-linear observer methods; - Robust approaches to FDI; - The use of parity equations; - Statistical process monitoring; - Qualitative modelling for diagnosis; - Parameter estimation approaches to FDI; - Fault diagnosis for descriptor systems; - FDI in inertial navigation; - Stuctured approaches to FDI; - Change detection methods; - Bio-medical studies. Researchers and industrial experts will appreciate the combination of practical issues and mathematical theory with many examples. Control engineers will profit from the application studies.

Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach

Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller.

Analytical and Qualitative Model-based Fault Diagnosis – A Survey and Some New Results

In this paper the state of the art of model-based fault diagnosis in plants of automatic control systems is reviewed and some new results of the authors research group are outlined. Attention is focused upon both the analytical approach that makes use of quantitative mathematical models and the knowledge-based approach using qualitative models along with qualitative and heuristic reasoning. In the latter case priority is given to the use of fuzzy models for residual generation and fuzzy reasoning for residual evaluation. By the suggestion of a knowledge-based observer-like concept for residual generation, the basic idea of a novel type of diagnostic observer, the so-called knowledge observer (of symptom observer), is introduced. The neural network approach is briefly outlined for both residual generation and evaluation. Moreover, different strategies of practical implementation are discussed. These include a novel human operator supported technique of fuzzy residual evaluation which allows one to make direct use of the human natural intelligence, common sense and experience. The advantages and disadvantages of the different approaches are pointed out and some perspectives for future research are given.

Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models☆

Abstract This paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear Takagi–Sugeno (TS) fuzzy model approach. First, the TS fuzzy models with time-delay are present and the stability conditions are derived using Lyapunov–Razumikhin functional approach. Then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer-based controller is proposed. It shows that the analysis results provide an efficient technique for the design of fuzzy controllers. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time-delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities.

Deterministic nonlinear observer-based approaches to fault diagnosis: A survey

Abstract This paper gives a review of the principal observer-based fault diagnosis approaches for nonlinear systems. Some schemes extending the well-known diagnosis methods for linear systems to the nonlinear case are considered. The robustness of these schemes in presence of unknown inputs is discussed. Similarities between the approaches considered are pointed out also. The survey is concluded with a description of some open problems.

ENHANCEMENT OF ROBUSTNESS IN OBSERVER-BASED FAULT DETECTION

A prerequisite for the feasibility of the technique of observer-based fault detection and isolation (FDI) in dynamic systems is a satisfactory robustness with respect to modelling uncertainties. This paper surveys the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation. Among these methods are the generalized observer scheme, the robust parity space check, the unknown input and H ∞ observer scheme, the decorrelation filter, and the concept of adaptive threshold selection. It is pointed out that the unknown input observer concept, which provides perfect decoupling from the modelling errors or its optimal approximation with the aid of H ∞ techniques, constitutes a general framework of robust residual generation that generalizes and unifies numerous other approaches, among them the parity space and detection filter approach. It is further shown that this FDI method can even be applied to a certain class of nonlinear systems.

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.

A unified approach to the optimization of fault detection systems

In this paper, problems of optimizing observer-based fault detection (FD) systems in the sense of increasing the robustness to the unknown inputs and simultaneously enhancing the sensitivity to the faults are studied. The core of the study is the development of an approach that simultaneously solves four optimization problems. Different algorithms are derived for the application of this approach to the optimal selection of post-filters as well as optimization of fault detection filters, and to the systems with and without structure constraints. The achieved results also reveal some interesting relationships among the optimization problems considered. Copyright

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.