2026-09-28T11:48:19Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27815 2026-09-28T06:35:12Z ddc:004 open_access

A Realization-Theoretic Foundation for Fault Diagnosis, with Diagnosability Equivalence Predictions Provan, Gregory Model-based Diagnosis Diagnosability System Realization Theory Fault diagnosis encompasses a wide range of paradigms, including observer-based fault detection and isolation, consistency-based diagnosis, Bayesian diagnosis, geometric diagnosis, and structured machine-learning approaches. Despite their shared objective, these paradigms are formulated in different mathematical languages and are rarely analyzed within a common framework. This paper introduces a realization-theoretic foundation for diagnosis based on the Diagnostic System Specification (DSS), a representation that separates behavioural models, realizations, measurement fields, and inference procedures. We define diagnostic invariants as symmetry-preserving quantities of realized system structures and show that detectability is fundamentally an orbit separation property in the realization’s symmetry space. Building on this observation, we develop a theory of realizations in which diagnostic models appear as objects equipped with invariant families and nominal symmetry groups. We show that diagnostic paradigms differ not in their underlying architecture but in the realizations they induce and the invariants they expose. Our main result addresses the question: is there a single mathematical condition of which diagnosis approaches are equivalent in terms of diagnosability? We show that using orbit separation on a paradigm-appropriate realization shows the following: faults are distinguishable iff they lie in different orbits of the realization’s nominal symmetry group. We accomplish this by constructing a minimal sufficient realization associated with a measurement field and characterize it by a universal property. This yields a structural notion of diagnostic equivalence and provides a principled basis for comparing methods across traditionally separate paradigms. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Gregory Provan 2026 Is Part Of OASIcs, Volume 148, 37th International Conference on Principles of Diagnosis and Resilient Systems (DX 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/OASIcs.DX.2026.1 urn:nbn:de:0030-drops-278156 https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.DX.2026.1 eng https://creativecommons.org/licenses/by/4.0/legalcode