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Technical paper on multi-mode diagnostics algorithms for complex systems, relevant to AI safety through fault detection and system reliability in multi-mode autonomous systems.
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Abstract
Multi-mode systems can operate in different modes, leading to large numbers of different dynamics. Consequently, applying traditional structural diagnostics to such systems is often untractable. To address this challenge, we present a multi-mode diagnostics algorithm that relies on a multi-mode extension of the Dulmage-Mendelsohn decomposition. We introduce two methodologies for modeling faults, either as signals or as Boolean variables, and apply them to a modular switched battery system in order to demonstrate their effectiveness and discuss their respective advantages.
Summary
This paper addresses the challenge of diagnosing faults in multi-mode systems, which operate across different dynamic configurations and are difficult to analyze using traditional structural diagnostics. The authors propose a multi-mode diagnostics algorithm based on a multi-mode extension of the Dulmage-Mendelsohn decomposition and introduce two fault modeling approaches: signal-based and Boolean variable-based representations. The methodologies are demonstrated on a modular switched battery system, with discussion of their respective strengths and limitations.
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| Page | Type | Quality |
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| AI Governance Coordination Technologies | Approach | 91.0 |
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# Fault Diagnosability Analysis of Multi-Mode Systems
Fatemeh Hashemniya
Benoît Caillaud
Erik Frisk
Mattias Krysander
Mathias Malandain
Department of Electrical Engineering
Linköping University, SE 581-83, Linköping, Sweden
e-mail: {fatemeh.hashemniya, erik.frisk, mattias.krysander}@ liu.se
National Institute for Research in Digital Science and Technology (Inria),
Inria centre at Rennes University, Rennes, France.
e-mail: {benoit.caillaud, mathias.malandain}@inria.fr
###### Abstract
Multi-mode systems can operate in different modes, leading to large numbers of different dynamics. Consequently, applying traditional structural diagnostics to such systems is often untractable. To address this challenge, we present a multi-mode diagnostics algorithm that relies on a multi-mode extension of the Dulmage-Mendelsohn decomposition. We introduce two methodologies for modeling faults, either as signals or as Boolean variables, and apply them to a modular switched battery system in order to demonstrate their effectiveness and discuss their respective advantages.
###### keywords:
Multi-mode systems, Diagnostics, Dulmage-Mendelsohn decomposition.
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## 1 Introduction
Fault detection and diagnosis are important for the health monitoring of physical systems.
Model-based approaches for single-mode, smooth, systems is a well-established field, supported by a large body of literature covering various approaches like structural methods Blanke et al. ( [2006](https://ar5iv.labs.arxiv.org/html/2312.14030#bib.bib4 "")), parity space techniques, and observer-based methods Isermann ( [2006](https://ar5iv.labs.arxiv.org/html/2312.14030#bib.bib11 "")).
While single-mode systems are often described using differential algebraic equations (DAEs), the modeling of non-smooth physical systems yields switched DAEs, also known as multi-mode DAEs (mmDAEs), which combine continuous behaviors, defined as solutions of a set of DAE systems,
with discrete mode changes Trenn ( [2012](https://ar5iv.labs.arxiv.org/html/2312.14030#bib.bib14 "")); Benveniste et al. ( [2020](https://ar5iv.labs.arxiv.org/html/2312.14030#bib.bib2 "")). Direct application of
traditional fault diagnosis methods to all possible configurations of multi-mode systems quickly
becomes intractable, as the number of modes tends to be exponential in the size of the system.
The method proposed by Khorasgani and Biswas ( [2017](https://ar5iv.labs.arxiv.org/html/2312.14030#bib.bib12 "")) works around this issue by coupling a mode estimation algorithm with a single-mode diagnosis methodology, akin to just-in-time compilation in computer science. This approach unfortunately puts the burden on solving mode estimation problems, which often turn out to be intractable for the same reason.
Structural fault detectability and isolability is a graph-based method to evaluate diagnosability properties on
DAEs Frisk et al. ( [2012](https://ar5iv.labs.arxiv.org/html/2312.14030#bib.bib8 "")). It is based on the Dulmag
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