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Input design for detecting changes in dynamic systems

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Feza Kerestecioglu
added 3 research items
This paper analyzes the sequential decision problem related to failure detection and diagnosis in dynamical systems when an input to the data generating mechanism is available to the decision-maker. The sequential decision rules are augmented by an input design rule. It is shown that some important properties of the decision rules related to the classical case (where no input is available) still hold: The terminal decision rule is a collection of fixed sample size Bayes rules and the problem when the sample size is not restricted can be approximated asymptotically.
This work is concerned with the detection and diagnosis of abrupt changes in the dynamics of single input single output stochastic systems and the design of auxiliary inputs for this purpose. First, the problem is put in a decision theoretic framework and the concepts of classical decision theory (where no input is available to the decision maker) are augmented to accommodate the input design as well as the decision rules for change detection. It is shown that some important properties of the decision rules related to the classical case still hold. The sequential probability ratio test (SPRT) which arises as a suboptimal test within this framework is investigated in detail. The Fundamental Identity of sequential analysis and the performance measures of the test are derived for the case of autoregressive models. The application of SPRT to the change detection problem is discussed and the properties of an associated cumulative sum (CUSUM) test are analyzed. In designing inputs to improve the performance of the CUSUM test the design objectives are taken as not only to minimize the average detection delay but also to ensure a specified false alarm rate. Both o²ine and online generated signals are considered. The detection mechanism as well as the input design techniques are extended to the multihypothesis case.
—This paper analyzes the sequential decision problem related to failure detection and diagnosis in dynamical systems when an input to the data generating mechanism is available to the decision-maker. The sequential decision rules are augmented by an input design rule. It is shown that some important properties of the decision rules related to the classical case (where no input is available) still hold: The terminal decision rule is a collection of fixed sample size Bayes rules and the problem when the sample size is not restricted can be approximated asymptotically.
Feza Kerestecioglu
added a research item
The problem of detecting abrupt changes in dynamical systems has gained importance recently as the demand for fault tolerant and reliable engineering systems has increased. The detection of malfunctions and performance degradations in complex automatic systems is crucial to assure safe and low cost operation. This aspect of change detection is referred to as fault detection and diagnosis or instrument fault detection by many authors. The theory and many applications has been covered in books by Himmelblau (1978), Pau (1981), Patton et al. (1989) and Basseville & Nikiforov (1993) and also in survey papers by Willsky (1976), Mironovski (1981), Isermann (1984), Gertler (1988); Frank (1990a) and Patton (1997).