Distributed Active Fault Diagnosis for Large-Scale Stochastic Systems

This paper investigates the active fault diagnosis (AFD) problem for a class of large-scale stochastic systems (LSSSs) composed of several input-coupled stochastic subsystems (SSs). A novel distributed AFD approach is developed to improve diagnosis performance by injecting the input designed for diagnosis purposes into the system under the input coupling between SSs. In the centralized AFD, the input is designed to minimize the misdiagnosis probability of the LSSS, whereas in the distributed AFD, the input design goal is to minimize the sum of the misdiagnosis probabilities of all SSs. As there is no closed-form expression for the misdiagnosis probability, the Holder-quarter divergence is defined to construct a novel input design criterion, whose maximization is proven to minimize an upper bound on the misdiagnosis probability. This input design criterion allows the input design problems for the centralized AFD and for each SS in each iteration of the distributed AFD to be solved to global optimality. The input design problem for the distributed AFD is solved to sub-optimality by a new distributed iterative optimization algorithm, and its global optimums are proven to be equivalent to those of the input design problem for the centralized AFD. The optimal input is injected into the system, and the AFD decision is made based on real-time measurement outputs according to the minimum probability of misdiagnosis decision rule. The distributed AFD decision is proven to be equivalent to the centralized AFD decision, and the distributed AFD decision-making has a lower computational complexity. A numerical example is presented to demonstrate the effectiveness of the proposed distributed AFD approach.