Dynamic multiple fault diagnosis with imperfect tests

Fault diagnosis is the process of identifying the failure sources of a malfunctioning system by observing their effects at various test points. It has a number of applications in engineering and medicine. In this paper, we present a near-optimal algorithm for dynamic multiple fault diagnosis in complex systems. This problem involves on-board diagnosis of the most likely set of faults and their time-evolution based on blocks of unreliable test outcomes over time. The dynamic multiple fault diagnosis (dMFD) problem is an intractable NP-hard combinatorial optimization problem. Consequently, we decompose the dMFD problem into a series of decoupled sub-problems, and develop a successive Lagrangian relaxation algorithm (SLRA) with backtracking to obtain a near-optimal solution for the problem. SLRA solves the sub-problems at each sample point by a Lagrangian relaxation method, and shares Lagrange multipliers at successive time points to speed up convergence. In addition, we apply a backtracking technique to further maximize the likelihood of obtaining the most likely evolution of failure sources and to minimize the effects of imperfect tests.