Fault Diagnosability Evaluation for Markov Jump Systems With Multiple Time Delays

Abstract

Fault diagnosability evaluation is important for monitoring and control system design. The evaluation results provide knowledge of the achievable performance of concerned systems from the fault diagnosis perspective. In this article, the diagnosability analysis of Markov jump systems with multiple time delays is addressed by using statistics. Specifically, cases with both completely and partially known transition probabilities are considered. First, the characteristics of the multiple time delays and the Markov process are extracted based on a constructed system dynamic. This step is followed by defining the fault detectability and isolability of the considered system. On this basis, Kullback–Leibler divergence-based fault diagnosability measures for different fault cases are given, and the relations between these measures are investigated. For cases with completely known transition probabilities, due to random variation in the structure, a quantitative fault diagnosability method is proposed by simultaneously considering the fault diagnosis performance and the importance of different system structures. For cases with partially known or even completely unknown transition probabilities, instead of a scalar measure, an interval measure and the corresponding evaluation method are developed to take advantage of as much available information as possible. Finally, the effectiveness of the developed measures is verified via simulation.