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Monolithic diagnosability analysis
The diagnosability property needs to be analyzed at the design stage of the DES. The online diagnosis is executed if and only if the diagnosability of the DES is verified. However, there is no guaranty that the diagnosability property of system is initially fulfilled. The aim of this study is to propose some methods of engineering that allow iterating the diagnosability analysis. When a DES is determined to be non-diagnosable, the model of DES must be modified and the diagnosability needs to be reanalyzed until the DES is diagnosable.
Most of the approaches in literature (in Section 3.1) build the whole state space a priori and then analyze the diagnosability using the entirely constructed state space. The process of these approaches in shown in Figure 2.1. For most of approaches, the diagnosability analysis of a given LPN model is transferred to the study of its reachability graph (RG) or some kinds of modified RG (e.g. MBRG in [Cab+14]). Therefore, the whole RG is necessarily built. Then, a diagnoser is built based on the RG for the diagnosability analysis. If the LPN model is non-diagnosable, the model is modified and then the RG and the diagnoser of the modified model are built once again. The previous process is iterated until the modified LPN is diagnosable. These approaches are not favorable for industrial use, because the state space of the monolithic model is rebuilt each time when the system is modified. For a large-scale LPN, these approaches are not efficient for iterating the diagnosability analysis and there exists combinatorial explosion problem.
Modular diagnosability analysis
For some large-scale systems which are more complex, the monolithic diagnosis is not feasible because the monolithic diagnoser is required i.e., it is impossible to build a monolithic diagnoser of the system because of the computational complexity and the combinatorial explosion problem. Many approaches such as decentralized diagnosis, modular diagnosis and distributed diagnosis are proposed to achieve the same diagnosis performance of the monolithic diagnosis without building the monolithic diagnoser. In literature, the approaches of modular diagnosability are based on the automata models. For a modularly designed system (it is assumed that the communication between modules is via common events), if automata are used to model the system, it is not easy to give directly the monolithic model. Usually, the model of each module is generated, then the monolithic model can be obtained by building the parallel composition of the modules. However, for a modularly designed system, it is not favorable to build the monolithic model and analyze the monolithic diagnosability because of the combinatorial explosion problem. In this case, if the modular diagnosability of the system is fulfilled, the on-line diagnosis can be implemented by using only the local diagnoser of each module. However, if the modularly designed system is modeled by Petri net (PN), the monolithic model may be directly given due to the advantage of PN (the concurrent processes are well represented by using PN). The monolithic diagnosability remains infeasible. In this thesis, we focus on system that is modeled by a collection of PN modules or by a monolithic model that can be decomposed under certain conditions into a collection of PN modules. A new modular diagnosability verification is proposed based on the PN model by removing some assumptions of the approaches in the literature. The aim of this approach is to reduce the computational complexity and combinatorial explosion problem.
PN-based approaches
More recently, Petri nets (PNs) are used for diagnosability analysis and on-line fault diagnosis, which provide an expressive and compact representation of DES models. Researchers use PNs in order to tackle the combinatorial explosion. The classic assumptions for diagnosability analysis using LPN are as following:
1. The LPN does not deadlock after firing any fault transition;
2. No cycle of unobservable transitions exists;
3. Faults are permanent, i.e., when a fault occurs the system remains infinitely faulty;
4. The same observable label may be associated with different transitions;
5. The structure of LPN and the initial marking M0 are well known.
It is worth noticing that the assumptions are varied for different approaches. Precisely, for the approaches mentioned in the following sections:
– The approach in [Wen+05] assumes that the LPN model is safe and live;
– The approach in [Cab+14; Liu+14] assumes that the LPN model does not deadlock after firing any fault transition and LPN model is bounded;
– The approach in [Cab+12] assumes that the LPN model does not deadlock after firing any fault transition and LPN model can be bounded or unbounded;
Table of contents :
Contents
List of Figures
List of Tables
1 Introduction
1.1 Background
1.2 Contributions
1.3 Manuscript’s structure
2 Problem statement and positioning of the works
2.1 Problem statement
2.2 Positioning of the works
2.2.1 Monolithic diagnosability analysis
2.2.2 Modular diagnosability analysis
2.3 Basic notions
2.3.1 Automata
2.3.2 Petri Nets (PNs)
3 Monolithic diagnosability analysis using LPN
3.1 Literature review
3.1.1 Automata-based approaches
3.1.1.1 Diagnoser approach
3.1.1.2 Twin-plant approach
3.1.1.3 Verifier approach
3.1.1.4 Other automata-based approaches
3.1.2 PN-based approaches
3.1.2.1 Diagosability analysis by checking T-invariants
3.1.2.2 Diagosability analysis using Minimal explanations
3.1.2.3 On-the-fly diagnosability analysis
3.1.2.4 Verifier Net (VN) approach
3.1.2.5 Other PN-based approaches
3.2 Contributions on monolithic diagnosability analysis
3.2.1 Diagnosis and diagnosability analysis using reduction rules
3.2.1.1 Reduction rules for regular unobservable transitions
3.2.1.2 Reduction rules for observable transitions
3.2.1.3 Impact of the reduction rules on the on-line diagnosis
3.2.2 Sufficient condition of diagnosability for safe and live LPN
3.2.3 On-the-fly diagnosability analysis using minimal explanations
3.2.4 On-the-fly diagnosability analysis using T-invariants
3.2.5 On-the-fly diagnosability analysis using VN
3.3 Synthesis of the contributions (on monolithic diagnosability analysis)
4 Modular diagnosability analysis using LPN
4.1 Literature review of decentralized fault diagnosis, modular fault diagnosis and distributed fault diagnosis
4.1.1 Decentralized diagnosis
4.1.2 Modular diagnosis
4.1.3 Distributed diagnosis
4.1.4 Synthesis of literature review
4.2 Modular diagnosability analysis using LPN model
4.2.1 Definition of LPN module, sound decomposition and modular diagnosability using LPN
4.2.2 Reduction rules for modular diagnosability
4.2.3 Local diagnosability analysis
4.2.4 Incremental modular diagnosability analysis
4.2.5 #reduction technique to combat combinatorial explosion for modular diagnosability analysis
4.2.6 Complexity analysis
4.3 Synthesis of the contributions (on modular diagnosability analysis)
5 Case study
5.1 Manufacturing benchmark
5.1.1 Monolithic diagnosability analysis of the manufacturing benchmark
5.1.1.1 Case 1
5.1.1.2 Case 2
5.1.1.3 Case 3
5.1.2 Modular diagnosability analysis of the manufacturing benchmark
5.1.2.1 Case 1
5.1.2.2 Case 2
5.2 Multi-track level crossing benchmark
5.2.1 Monolithic diagnosability analysis of the LC benchmark
5.2.2 Modular diagnosability analysis of the LC benchmark
5.3 Synthesis of the two case studies
6 Conclusions and perspectives
6.1 Conclusions
6.2 Perspectives
Bibliography
