Abstract
Knowledge compilation is no novelty in model-based diagnosis of discrete-event systems. The system is preprocessed in order to generate a data structure that allows for the efficient explanation of any symptom online, while the system is being operated. Unfortunately, this technique requires the diagnosability of the system. Even worse, it comes with a prohibitive cost in terms of computational complexity, owing to the explosion of the state space even for systems of moderate size, which makes the whole approach impractical for real applications. To overcome these two obstacles, a novel technique based on scenarios is proposed. Scenarios are compiled into a flexible data structure called an open dictionary, which allows for the efficient explanation of symptoms. The dictionary is open inasmuch as it can be expanded by new scenarios and symptoms.
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Notes
- 1.
A combination of these two categories of modeling is represented by hybrid systems [17].
- 2.
In the worst case, the size of the behavior space is exponential with the number of components. For example, for 30 components with 5 states each, we have \(5^{30} \approx 10^{20}\) possible states.
- 3.
According to the Subset Construction determinization algorithm [5], each state of the DFA is identified by a subset of the states of the NFA. To shrink the DFA, each state of the DFA includes only the significant states of the NFA. A state is significant when it is either final or it is exited by a transition marked with t, where t is observable.
- 4.
A regular expression is defined inductively on the alphabet \(\varSigma \). The empty symbol \(\varepsilon \) is a regular expression. If \(a \in \varSigma \), then a is a regular expression. If x and y are regular expressions, then the followings are regular expressions: \(x {\; | \;}y\) (alternative), \(x\,y\) (concatenation), x? (optionality), \(x^*\) (repetition zero or more times), and \(x^+\) (repetition one or more times).
- 5.
Each state of the DFA includes only the significant states of the NFA (cf. footnote 3).
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Acknowledgements
This work was supported by Regione Lombardia (Smart4CPPS, Linea Accordi per Ricerca, Sviluppo e Innovazione, POR-FESR 2014-2020 Asse I).
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Bertoglio, N., Lamperti, G., Zanella, M. (2020). Intelligent Diagnosis of Discrete-Event Systems with Preprocessing of Critical Scenarios. In: Czarnowski, I., Howlett, R., Jain, L. (eds) Intelligent Decision Technologies 2019. Smart Innovation, Systems and Technologies, vol 142. Springer, Singapore. https://doi.org/10.1007/978-981-13-8311-3_10
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