Coupled Factorial Hidden Markov Models (CFHMM) for Diagnosing Multiple and Coupled Faults

In this paper, we formulate a coupled factorial hidden Markov model-based (CFHMM) framework to diagnose dependent faults occurring over time (dynamic case). In our previous research, the problem of diagnosing multiple faults over time (dynamic multiple fault diagnosis (DMFD)) is solved based on a sequence of test outcomes by assuming that the faults and their time evolution are independent. This problem is NP-hard, and, consequently, we developed a polynomial approximation algorithm using Lagrangian relaxation within a FHMM framework. Here, we extend this formulation to a mixed memory Markov coupling model, termed dynamic coupled fault diagnosis (DCFD) problem, to determine the most likely sequence of (dependent) fault states, the one that best explains the observed test outcomes over time. An iterative Gauss-Seidel coordinate ascent optimization method is proposed for solving the DCFD problem. A soft Viterbi algorithm is also implemented within the framework for decoding-dependent fault states over time. We demonstrate the algorithm on simulated systems with coupled faults and the results show that this approach improves the correct isolation rate (CI) as compared to the formulation where independent fault states (DMFD) are assumed. As a by-product, we show empirically that, while diagnosing for independent faults, the DMFD algorithm based on block coordinate ascent method, although it does not provide a measure of suboptimality, provides better primal cost and higher CI than the Lagrangian relaxation method for independent fault case. Two real-world examples (a hybrid electric vehicle, and a mobile autonomous robot) with coupled faults are also used to evaluate the proposed framework.