TEE for ML (Chen et al.)

[2312.14030] Fault Diagnosability Analysis of Multi-Mode Systems 
 
 
 
 
 
 
 
 
 
 
 

 
 

 
 
 
 
 
 
 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 ) , parity space techniques, and observer-based methods  Isermann ( 2006 ) .

 
 
 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 ); Benveniste et al. ( 2020 ) . 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 ) 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 ) . It is based on the Dulmage-Mendelsohn decomposition (DM), a building block of the
structural analysis of equation systems. In this study, we show how its extension to multi-mode
systems, introduced in  B

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