Active fault diagnosis for linear stochastic systems subject to chance constraints

Abstract

In this paper, the problem of active fault diagnosis (AFD) is investigated for a class of linear stochastic systems subject to chance constraints, where the input signals are specifically designed to enhance diagnosis performance by discriminating between multi-fault modes. As the misdiagnosis probability cannot be expressed in the closed form, a reachable upper bound on it is derived to construct a novel input design criterion for AFD based on the Cauchy–Schwarz divergence. A sufficient condition is provided to decompose the multivariate chance constraints into a set of univariate ones. A three-stage optimization approach is proposed to solve the input design problem incorporating chance constraints for AFD. In the upper stage, the best iteration parameter is determined for subsequent iterative optimization to obtain the least conservative risk allocation scheme. In the middle stage, the total risk of violating the multivariate constraints is optimally allocated to a set of univariate ones through iterative optimization, which can improve diagnosis performance. In the lower stage, a set of univariate chance constraints is equivalently converted into expectation constraints under the allocated risk, and then the input design problem under the constructed design criterion is solved to global optimality. The optimal input signals are injected, and the AFD decision is made based on real-time measurement information according to the minimum probability of misdiagnosis decision principle. Finally, simulation results on a four-tank system demonstrate the effectiveness and superiority of the proposed AFD method.