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.

[1]  Krishna R. Pattipati,et al.  Application of heuristic search and information theory to sequential fault diagnosis , 1990, IEEE Trans. Syst. Man Cybern..

[2]  J. Beasley.  A lagrangian heuristic for set‐covering problems , 1990 .

[3]  J. K. Lenstra,et al.  Local Search in Combinatorial Optimisation. , 1997 .

[4]  Yun Peng,et al.  A Probabilistic Causal Model for Diagnostic Problem Solving Part II: Diagnostic Strategy , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Michael I. Jordan,et al.  Factorial Hidden Markov Models , 1995, Machine Learning.

[6]  G. Nemhauser,et al.  Integer Programming , 2020 .

[7]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[8]  Krishna R. Pattipati,et al.  Computationally efficient algorithms for multiple fault diagnosis in large graph-based systems , 2003, IEEE Trans. Syst. Man Cybern. Part A.

[9]  Thiagalingam Kirubarajan,et al.  Real-time system diagnosis with sensors of uncertain quality , 2003, SPIE Defense + Commercial Sensing.

[10]  K.R. Pattipati,et al.  Optimal and near-optimal algorithms for multiple fault diagnosis with unreliable tests , 1996, Conference Record. AUTOTESTCON '96.

[11]  Zoubin Ghahramani,et al.  Learning Dynamic Bayesian Networks , 1997, Summer School on Neural Networks.

[12]  J. Brandon,et al.  A genetic algorithm for diagnosis problem solving , 1993, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[13]  David G. Stork,et al.  Pattern Classification , 1973 .

[14]  Krishna R. Pattipati,et al.  Multiple disease (fault) diagnosis with applications to the QMR-DT problem , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[15]  Krishna R. Pattipati,et al.  A hidden Markov model-based algorithm for fault diagnosis with partial and imperfect tests , 2000, IEEE Trans. Syst. Man Cybern. Part C.

[16]  Krishna R. Pattipati,et al.  Test sequencing algorithms with unreliable tests , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[17]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[18]  M. Fisher,et al.  Optimal solution of set covering/partitioning problems using dual heuristics , 1990 .

[19]  Nevin Lianwen Zhang,et al.  Exploiting Causal Independence in Bayesian Network Inference , 1996, J. Artif. Intell. Res..

[20]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[21]  Krishna R. Pattipati,et al.  On a multimode test sequencing problem , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[22]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[23]  Jr. G. Forney,et al.  The viterbi algorithm , 1973 .

[24]  Krishna R. Pattipati,et al.  Optimal and near-optimal algorithms for multiple fault diagnosis with unreliable tests , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[25]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..