A coupled factorial hidden Markov model (CFHMM) for diagnosing coupled faults

In this paper, we formulate a coupled factorial hidden Markov model-based framework to diagnose dependent faults occurring over time. In our previous research, the problem of diagnosing dynamic multiple faults (DMFD) is solved by assuming that the faults are independent. Here, we extend this formulation to determine the most likely evolution of dependent fault states (NP-hard problem), the one that best explains the observed test outcomes over time. An iterative Gauss-Seidel coordinate ascent optimization method along with the coupling assumptions (mixed memory Markov model) is proposed for solving the dynamic coupled fault diagnosis (DCFD) problem. A soft Viterbi algorithm is also implemented within the framework for decoding dependent fault states over time. We demonstrate the algorithm on small-scale and real-world systems and the simulation results show that this approach improves the correct isolation rate as compared to the formulation with independent fault states (DMFD).