Mojdeh Shakeri

Sequential testing algorithms for multiple fault diagnosis

We consider the problem of constructing optimal and near-optimal test sequences for multiple fault diagnosis. The computational complexity of solving the optimal multiple-fault isolation problem is super exponential, that is, it is much more difficult than the single-fault isolation problem, which, by itself, is NP-hard. By employing concepts from information theory and AND/OR graph search and by exploiting the single fault testing strategies of Pattipati et al. (1990), we present several test sequencing algorithms for the multiple fault isolation problem. These algorithms provide a trade-off between the degree of suboptimality and computational complexity. Furthermore, we present novel diagnostic strategies that generate a diagnostic directed graph, instead of a traditional diagnostic tree, for multiple fault diagnosis. Using this approach, the storage complexity of the overall diagnostic strategy reduces substantially. The algorithms developed herein have been successfully applied to several real-world systems.

Optimal and near-optimal algorithms for multiple fault diagnosis with unreliable tests

We consider the problem of constructing optimal and near-optimal multiple fault diagnosis (MFD) in bipartite systems with unreliable (imperfect) tests. It is known that exact computation of conditional probabilities for MFD is NP hard. The novel feature of our diagnostic algorithms is the use of Lagrangian relaxation and subgradient optimization methods to provide: 1) near optimal solutions for the MFD problem and 2) upper bounds for an optimal branch and bound algorithm. The proposed method is illustrated using several examples. Computational results indicate the following: 1) our algorithm has superior computational performance to the existing algorithms (approximately three orders of magnitude improvement over the algorithm by Z. Binglin et al. (1993)); 2) near optimal algorithm generates the most likely candidates with a very high accuracy; 3) our algorithm can find the most likely candidates in systems with as many as 1000 faults.