Dynamic Multiple Fault Diagnosis: Mathematical Formulations and Solution Techniques

Abstract — Imperfect test outcomes, due to factors such as unreliable sensors, electromagnetic interference, and environ-mental conditions, manifest themselves as missed detections and false alarms. This paper develops near-optimal algorithms for dynamic multiple fault diagnosis (DMFD) problems in the presence of imperfect test outcomes. The dynamic diagnostic inference problem is to determine the most likely evolution of component states, the one that best explains the observed test outcomes. Here, we discuss four formulations of the DMFD problem. These include the deterministic situation corresponding to a perfectly-observed coupled Markov decision processes, to several partially-observed factorial hidden Markov models ranging from the case where the imperfect test outcomes are functions of tests only to the case where the test outcomes are functions of faults and tests, as well as the case where the false alarms are associated with the nominal (fault-free) case only. All these formulations are intractable NP-hard combinatorial optimization problems. We solve each of the DMFD problems by decomposing them into separable subproblems, one for each component state sequence. Our solution scheme can be viewed as a two-level coordinated solution framework for the DMFD problem. At the top (coordi-nation) level, we update the Lagrange multipliers (coordination variables, dual variables) using the subgradient method. The to