Dynamic multiple fault diagnosis (DMFD) is a challenging and difficult problem due to coupling effects of the states of components and imperfect test outcomes that manifest themselves as missed detections and false alarms. The objective of the DMFD problem is to determine the most likely temporal evolution of fault states, the one that best explains the observed test outcomes over time.Here, we discuss four formulations of the DMFD problem. These include the deterministic situation corresponding to a perfectlyobserved coupled Markov decision processes, to several partiallyobserved 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 (coordination) level, we update the Lagrange multipliers (coordination variables, dual variables) using the subgradient method. The top level facilitates coordination among each of the subproblems, and can thus reside in a vehicle-level diagnostic control unit. At the bottom level, we use a dynamic programming technique (specifically, the Viterbi decoding or Max-sum algorithm) to solve each of the subproblems. The key advantage of our approach is that it provides an approximate duality gap, which is a measure of suboptimality of the DMFD solution. Interestingly, the perfectly-observed DMFD problem leads to a dynamic set covering problem, which can be approximately solved via Lagrangian relaxation and Viterbi decoding. Computational results on real-world problems are presented.
Abstract-Imperfect test outcomes, due to factors such as unreliable sensors, electromagnetic interference, and environmental conditions, manifest themselves as missed detections and false alarms. The main objective of our research on on-board diagnostic inference is to develop near-optimal algorithms for dynamic multiple fault diagnosis (DMFD) problems in the presence of imperfect test outcomes. Our problem is to determine the most likely evolution of fault states, the one that best explains the observed test outcomes. Here, we develop a primal-dual algorithm for solving the DMFD problem by combining Lagrangian relaxation and the Viterbi decoding algorithm in an iterative way. A novel feature of our approach is that the approximate duality gap provides a measure of suboptimality of the DMFD solution.
In this paper, we investigate four key issues associated with data-driven approaches for fault classification using the Pratt and Whitney commercial dual-spool turbofan engine data as a test case. The four issues considered here include the following. (1) Can we characterize, a priori, the difficulty of fault classification via self-organizing maps? (2) Do data reduction techniques improve fault classification performance and enable the implementation of data-driven classification techniques in memory-constrained digital electronic control units (DECUs)? (3) When does adaptive boosting, an incremental fusion method that successively combines moderately inaccurate classifiers into accurate ones, help improve classification performance? (4) How to synthesize classifier fusion architectures to improve the overall diagnostic accuracy? The classifiers studied in this paper are the support vector machine, probabilistic neural network, k-nearest neighbor, principal component analysis, Gaussian mixture models, and a physics-based single fault isolator. As these algorithms operate on large volumes of data and are generally computationally expensive, we reduce the data set using the multiway partial least squares method. This has the added benefits of improved diagnostic accuracy and smaller memory requirements. The performance of the moderately inaccurate classifiers is improved using adaptive boosting. These results are compared to the results of the classifiers alone, as well as different fusion architectures. We show that fusion reduces the variability in diagnostic accuracy, and is most useful when combining moderately inaccurate classifiers.
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