Active Fault Diagnosis for Stochastic Systems Within Neyman–Pearson Framework

This article investigates the active fault diagnosis (AFD) problem for a class of multiple-input multiple-output (MIMO) stochastic systems. A novel AFD framework is proposed based on the Neyman-Pearson framework, within which the input is designed to improve diagnosis performance by maximizing the fault detection rate (FDR) under a given false alarm rate (FAR). The analytical relationship between the FDR and the FAR is deduced to construct a new input design criterion for AFD, whose maximization is proven to result in the minimum of the misdiagnosis probability and the maximum of the FDR under a given FAR. The constructed design criterion allows the input design optimization problem to be solved to global optimums. By injecting the globally optimal input into the system, the AFD decision is made based on a newly established test statistic and the corresponding decision rule according to the real-time measurement output. The AFD decision rule within the Neyman-Pearson framework is proven to be equivalent to that within the Bayesian decision framework with given loss factors. Numerical experiment results demonstrate the effectiveness and superiority of the proposed AFD approach, moreover, the diagnosis performance can be adjusted between the FDR and the FAR according to practical requirements by changing the detection threshold.