This chapter gives an overview of main traditional fault diagnosis techniques, including hardware redundancy based technique, signal processing based fault diagnosis and plausibility test, and their classification. The model-based fault diagnosis is then introduced in relationship with these traditional fault diagnosis techniques. It is followed by a review of the historical development of the model-based fault diagnosis technique and the major tasks in designing a model-based fault diagnosis system. Chapter 2 serves as an outline of the major issues to be addressed in this book.
In the framework of the model-based fault diagnosis technique, whose core consists of residual generation, evaluation and threshold computation, unknown input decoupling, robustness in residual generation, residual evaluation and threshold computation, FDI fault detection and isolation system design and synthesis are the major topics which are briefly reviewed in this chapter.
Also in this chapter, the major mathematical and control theoretical methods to be used as tools for solving FDI problems are briefly introduced. Numerous system representation forms are first presented in this chapter, which allow us to model nominal dynamic systems both in the time and frequency domains.
These types of models are then extended to address disturbances unknown inputs and to model different types of faults. Also model uncertainties are dealt with in this chapter. As a major tool for the subsequent studies in this book, the so-called coprime factorization technique is introduced. The second part of this chapter is dedicated to the application case examples and their mathematical models.
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They are: Speed control system of a DC motor, inverted pendulum control system, three-tank system, vehicle lateral dynamic system, and continuous stirred tank heater. Fault detectability, isolability and identifiability describe structural properties of a dynamic system, which are of fundamental importance in dealing with the analysis and synthesis of model-based FDI systems.
This chapter gives the definitions and existence conditions of fault detectability, isolability and identifiability, and together with them, some examples. Beginning with this chapter, residual generation issues are addressed in the next four chapters. The main objective of this chapter is to introduce the basic ideas of residual generation on the one hand and to present most popular residual generation schemes, including fault detection filters FDF , diagnostic observers DO , parity space PA schemes, on the other hand.
In order to investigate the interconnections among these residual generation schemes and to study optimum and robustness issues in the sequel, remarkable attention is also paid to the parameterization of all LTI linear time-invariant residual generators, which can be expressed in terms of an FDF and a dynamic post-filter.
In Chap. It is followed by a comprehensive study on designing unknown input residual generators. For the design purpose, different control theoretical and mathematical methods are applied, including eigenstructure assignment approach, geometric approach, unknown input observer theory, matrix pencil approach. The investigation in this chapter is a logic consequence of the study in the previous chapter, where it is demonstrated that a perfect unknown input decoupling can only be achieved under the strict conditions that are often too hard for a real application.
Alternatively, the well-established robust control theory can be applied to the development of residual generators being robust against unknown inputs. To this end, the needed mathematical and control theoretical preliminaries are first introduced in this chapter with a focus on the co-inner—outer factorization technique and LMI linear matrix inequality optimization technique. The first scheme presented in Chap.
In the framework of PA based residual generation, the robust residual generation is addressed in the context of a trade-off between the robustness against unknown inputs and the sensitivity for the faults, which is then formulated as optimization problems with different performance indices.
Model-Based Fault Diagnosis Techniques | caltitentrapu.tk
Numerous algorithms for the solutions of these optimization problems are derived, which lead to the design of parity vector or matrix. Analog to this study, optimal design of FDFs is also dealt with in the trade-off context. The last FDF scheme proposed in this chapter is the unified solution, which is developed on the basis of the co-inner—outer factorization. The detailed study on the unified solution gives a deep insight into the model-based residual generation, which will also play an important role in the integrated design of FD systems to be addressed in the subsequent chapters.
Chapter 8 is dedicated to the most challenging topic on the mode-based residual generation, that is, residual generation based on a model with uncertainties.
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To this end, preliminary knowledge of advanced LMI technique and stability of systems with stochastic uncertainties is first introduced. The core of this chapter is the reference model based residual generation strategy, in which the unified solution presented in Chap. The residual generator design is then realized on the basis of a minimization of the difference between the reference and real residual signals. This strategy is applied to the FDF design for systems with norm-bounded uncertainties, polytopic uncertainties, and stochastic uncertainties.
In the norm-based residual evaluation framework, signal norms are used for the evaluation of residual signals delivered by a residual generator, in order to make a right decision on the existence of a fault. In this chapter, basic concepts and standard evaluation functions widely used in practice are first briefly reviewed.
Associated with them, definitions of different types of thresholds are introduced. A fault indicator, based on a deviation between measurements and model-equation-based computations. Determination of the kind, location and time of detection of a fault. Follows fault detection.
Determination of the kind, size, location and time of detection of a fault. A continuous real-time task of determining the conditions of a physical system, by recording information, recognising and indication anomalies in the behaviour. Monitoring a physical and taking appropriate actions to maintain the operation in the case of fault. Use of static and dynamic relations among system variables and parameters in order to describe a system's behaviour in quantitative mathematical terms. Use of more not necessarily identical ways to determine a variable, where one way uses a mathematical process model in analytical form.
Ability of a system to perform a required function under stated conditions, within a given scope, during a given period of time. Ability of a system not to cause danger to persons or equipment or the environment. In uences a variable by an addition of the fault itself.
They may represent, e. Are represented by the product of a variable with the fault itself. They can appear as parameter changes within a process. Typically, a voting technique is applied to the hardware redundant system to decide if a fault has occurred and its location among all the redundant system components.
In view of the con ict between reliability and the cost of adding more hardware, it is possible to use the dissimilar measured values together to. This is the meaning of analytical or functional redundancy. It exploits redundant analytical relationships among various measured variables of the monitored process [Patton et al. This property of the residual is used to determine whether or not faults have occurred [Patton et al.
Consistency checking in analytical redundancy is normally achieved through a comparison between a measured signal with estimated values. The estimation is generated by a mathematical model of the considered plant. Figure 1. Redundant sensors Input. In practice, the most frequently used diagnosis method is to monitor the level or trend of the residual and take action when the signal reaches a given threshold. This method of geometrical analysis, whilst simple to implement, has a few drawbacks. The most serious is that, in the presence of noise, input variations and change of operating point of the monitored process, false alarms are possible.
The major advantage of the model-based approach is that no additional hardware components are required in order to realize a Fault Detection and Isolation FDI algorithm. In many cases, the measurements necessary to control the process are also sucient for the FDI algorithm so that no additional sensors have to be installed [Patton et al.
Faults Input u t. Parity equations; 3.
An important aspect of these methods is the kind of fault to be detected. As noted above, one can distinguish between additive faults which in uence the variables of the process by a summation and multiplicative faults which are products of the process variables. Spectral analysis FFT ; 3. Maximum-entropy estimation. The characteristic quantities or features from fault detection methods show stochastic behaviour with mean values and variances.