Fault Isolation of Linear Stochastic Time-Varying Systems With Strong Noise

In this article, the problem of fault isolation is studied for linear stochastic time-varying systems. Different from the existing results about fault isolation, the system in this article suffers from strong noise, which increases the difficulty of distinguishing different fault components since the difference in measurement distributions caused by different fault components is small. To handle this problem, a novel fault isolation scheme comprising a set of residuals, a set of evaluation functions, and a decision logic is proposed. First, based on the hypothesis testing method, two performance indices reflecting the probability of two classes of false isolation induced by noise are introduced to quantitatively evaluate the influence of strong noise on residuals. Under a given threshold, the existence of the optimal residual with two minimal performance indices is proved in this article, which minimizes the effect of noise on residuals. Subsequently, a suboptimal recursive residual whose parameter gradually tends to the parameter of the optimal residual is designed. Following this, by employing the $\chi ^{2}$ test and the predesigned decision logic, fault isolation can be realized. Finally, two illustrative examples are provided to show the effectiveness of the proposed method.