Functional diagnosability and detectability of nonlinear models based on analytical redundancy relations

Abstract

International audienceThis paper introduces an original definition of diagnosability for nonlinear dynamical models called functional di-agnosability. Fault diagnosability characterizes the faults that can be discriminated using the available sensors in a system. The functional diagnosability definition proposed in this paper is based on analytical redundancy relations obtained from differential algebra tools. Contrary to classical definitions, the study of functional diagnosability highlights some of the analytical redundancy relations properties related to the fault acting on the system. Additionally, it gives a criterion for detecting the faults. Interestingly, the proposed diagnosability definition is closely linked to the notion of identifiability, which establishes an unambiguous mapping between the parameters and the output trajecto-ries of a model. This link allows us to provide a sufficient condition for testing functional diagnosability of a system. Numerical simulations attest the relevance of the suggested approach

Fault detection and identification via bounded-error parameter estimation using distribution theory

“…They had already been used to estimate parameters (or faults) when no initial guess of their values were known [6] and for doing fault detection [7]. According to [9], ARRs can take the following form:…”

Set-membership functional diagnosability: Definitions and analysis

“…Furthermore, the order of derivatives is so high that they are hardly suitable for fault detection. In [11], the authors propose to relax the constraints of [3] and to use ARRs involving one or more faults for studying diagnosability and detecting faults, the advantage being to easier the obtention of ARRs with derivatives of lower order. The obtention of such ARRs is based on the work of [4].…”

“…The obtention of such ARRs is based on the work of [4]. From these particular ARRs, the definition of functional diagnosability was proposed in [11]. The authors showed that if the model is identifiable with respect to the faults, then the residuals of these ARRs forming the functional signature have distinct trajectories.…”

“…In [11], the authors propose to use specific ARRs for defining functional diagnosability and achieving fault detection in algebraic dynamic systems. These ARRs are obtained from the Rosenfeld-Groebner algorithm implemented in Maple [1].…”

“…This problem is close to the one of parameter identifiability that ensures that two distinct parameters generate two distinct trajectories for a model. In this work, links between identifiability and diagnosability are recalled through the concept of functional diagnosability introduced in [11].…”