OPTIMAL AND NEAR-OPTIMAL ALGORITHMS FOR MULTIPLE-FAULT DIAGNOSIS WITHUNRELIABLE TESTS

In this paper, we consider the problem of constructing optimal and nea r-optimal multiple fault diagnosis (MFD) in bipartite systems with unr eliable (imperfect) tests, It is known that exact computation of condi tional probabilities for MFD is NP-hard. The novel feature of our diag nostic 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. Computatio nal results indicate the following. 1) Our algorithm has superior comp utational performance to the existing algorithms (approximately three orders of magnitude improvement over the algorithm in [3]), 2) Near-op timal algorithm generates the most likely candidates with a very high accuracy. 3) Our algorithm can find the most likely candidates in syst ems,vith as many as 1000 faults.