Volltext-Downloads (blau) und Frontdoor-Views (grau)

Fault indicators and unique mode-dependent state equations from a fixed-causality diagnostic bond graph of linear models with ideal switches

  • Analytical redundancy relations are fundamental in model-based fault detection and isolation. Their numerical evaluation yields a residual that may serve as a fault indicator. Considering switching linear time-invariant system models that use ideal switches, it is shown that analytical redundancy relations can be systematically deduced from a diagnostic bond graph with fixed causalities that hold for all modes of operation. Moreover, as to a faultless system, the presented bond graph–based approach enables to deduce a unique implicit state equation with coefficients that are functions of the discrete switch states. Devices or phenomena with fast state transitions, for example, electronic diodes and transistors, clutches, or hard mechanical stops are often represented by ideal switches which give rise to variable causalities. However, in the presented approach, fixed causalities are assigned only once to a diagnostic bond graph. That is, causal strokes at switch ports in the diagnostic bond graph reflect only the switch-state configuration in a specific system mode. The actual discrete switch states are implicitly taken into account by the discrete values of the switch moduli. The presented approach starts from a diagnostic bond graph with fixed causalities and from a partitioning of the bond graph junction structure and systematically deduces a set of equations that determines the wanted residuals. Elimination steps result in analytical redundancy relations in which the states of the storage elements and the outputs of the ideal switches are unknowns. For the later two unknowns, the approach produces an implicit differential algebraic equations system. For illustration of the general matrix-based approach, an electromechanical system and two small electronic circuits are considered. Their equations are directly derived from a diagnostic bond graph by following causal paths and are reformulated so that they conform with the matrix equations obtained by the formal approach based on a partitioning of the bond graph junction structure. For one of the three mode-switching examples, a fault scenario has been simulated.

Download full text files

Export metadata

Additional Services

Search Google Scholar Check availability


Show usage statistics
Document Type:Article
Author:Wolfgang Borutzky
Parent Title (English):Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering
First Page:695
Last Page:708
Publisher:SAGE Publications
Publishing Institution:Hochschule Bonn-Rhein-Sieg
Date of first publication:2018/02/15
Embargo Date:2019/02/15
Copyright:© IMechE 2018. This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
This article is the result of a complete revision and asubstantial extension of a paper entitled ‘Generation of Mode-dependent ARRs from a Bond Graph of a Mode Switching LTI Model’ presented at the 4th International Conference on Control, Decision andInformation Technologies (CoDIT 2017), 5–7 April, 2017, Universitat Politecnica de Catalunya, Barcelona, Spain, USB Conference Proceedings.
Keyword:Fault detection and isolation; diagnostic bond graphs; fixed causalities generation of analytical redundancy relations; ideal switches; mode-dependent implicit state space model; mode-switching linear time-invariant models
Departments, institutes and facilities:Fachbereich Informatik
Dewey Decimal Classification (DDC):6 Technik, Medizin, angewandte Wissenschaften / 62 Ingenieurwissenschaften / 620 Ingenieurwissenschaften und zugeordnete Tätigkeiten
Open access funding:Deutsche Forschungsgemeinschaft / Allianz- und Nationallizenzen: Diese Beiträge sind mit Zustimmung der Rechteinhaber aufgrund einer DFG-geförderten National- bzw. Allianzlizenz frei zugänglich.
Entry in this database:2018/02/22
Licence (Multiple languages):License LogoIn Copyright (Urheberrechtsschutz)