Abstract
We present an approach dealing with repeated fault events in the framework of model-based monitoring of discrete-event systems (DES). Various notions of diagnosability reported in the literature deal with uniformly bounded finite detection of counting delays over all faulty behaviors (uniform delays for brevity). The situation where the diagnosability notion of interest fails to hold under a given observation configuration leads typically to the deployment of more observational devices (e.g., sensors), which may be costly or infeasible. As an alternative to the additional deployment of observational devices, one might want to relax the uniformity of delays, while delays remain finite. To this end, we introduce a notion of diagnosability characterized with nonuniformly bounded finite counting delays (nonuniform counting delays for brevity), where finite delay bounds can vary on faulty behaviors. To evaluate the introduced notion of diagnosability with nonuniform counting delays, a polynomial-time verification algorithm is developed. Notably, the developed verification technique can readily be modified to construct a computationally superior verification algorithm for diagnosability under uniformly bounded finite counting delays (uniform counting delays for brevity) as compared to an algorithm previously reported in the literature. We also develop a novel on-line event counting algorithm that improves the time and space complexities of the currently available algorithms for the counting of special events.
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Notes
An application of the [1, ∞ ]-diagnosability concept includes diagnosis of repeated routing violations in material handling systems (Garcia and Yoo 2005). In this case, the assessment of monitoring capability associated with repeated routing violations is accomplished by evaluating uniform [1, ∞ ]-diagnosability. Using the new verification algorithm, various observational configuration results were obtained successfully, as reported in Garcia and Yoo (2005).
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Acknowledgements
The research reported in this paper was supported in part by the U.S. Department of Energy under contracts W-31-109-Eng-38 and DE-AC07-05ID14517. We are grateful to the reviewers for their comments and suggestions.
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Yoo, TS., Garcia, H.E. Event Counting of Partially-Observed Discrete-Event Systems with Uniformly and Nonuniformly Bounded Diagnosis Delays. Discrete Event Dyn Syst 19, 167–187 (2009). https://doi.org/10.1007/s10626-008-0056-1
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DOI: https://doi.org/10.1007/s10626-008-0056-1