Fault diagnosis in nonlinear systems through an adaptive filter under a convex set representation

Abstract

In this paper, the main goal is to design an approach that performs fault detection, isolation and estimation for a large class of nonlinear systems. Fault diagnosis is established by regarding system as a convex combination of linear time invariant (LTI) stochastic models and not as a single global model. The nonlinear representation is based on a bank of decoupled Kalman filters. This paper consists in generating a robust model selection of the "best" representative linear model. Under fault isolation conditions, the main contribution is to design an adaptive filter which makes possible multiple faults detection which appear simultaneously or in a sequential way, isolation and estimation over the whole operating range of nonlinear system. The stability conditions of the adaptive filter are developed. These conditions result in convex linear matrix inequalities (LMIs) that can be solved efficiently with optimization techniques. Performances of the method are tested on an academic example. Copyright@2003 EJC.

Design of a Robust Polytopic Unknown Input Observer for FDI: Application for Systems described by a Multi-Model Representation

“…and these functions are directly generated via works of [15] and [12], which permit to generate insensitive residual to faults. Under the assumptions that these weighting functions ρ i k are considered as scheduling variables which are not affected by faults or modeling errors as proposed by [15] and [12], the nonlinear system (1) can be described by the following state space representation:…”

“…, N ]. If conditions (15) hold true, the estimation error e k and the residual r k are described as:…”

“…However, it is essential to examine faulty distribution matrices F i with modeling error matrix E * which have to generate different spaces. Indeed, de-coupling can reject perturbations through the term T E * in equation (15), whereas fault are represented by the term T F (ρ). If it is very important in FDI scheme to cancel perturbation on a system, it is widely important to be able to detect and isolate fault through estimation error e k and r k .…”

“…15 . The model has four states: concentration of A (C A ) with an initial concentration C A0 , concentration of B (C B ), temperature v with a fixed value for the feed temperature v 0 and cooling jacket temperature v k .…”

“…we suppose only local identification as in some industrial systems around specific operating point. Compared to methods that could detect both operating conditions evolution and detect, isolate and estimate faults in nonlinear system as proposed by [12] and [15], this paper considers time varying modeling errors. Thus, the main contribution of this paper consists in the synthesis of a residual generator based on a Polytopic Unknown Input Observer (PUIO) which generates robust residual against error modeling under fault occurrence.…”