Weighted Fuzzy Observer-Based Fault Detection Approach for Discrete-Time Nonlinear Systems via Piecewise-Fuzzy Lyapunov Functions

The main focus of this paper is on the analysis and integrated design of $\mathcal {L}_2$ observer-based fault detection (FD) systems for discrete-time nonlinear industrial processes. To gain a deeper insight into this FD framework, the existence condition is introduced first. Then, an integrated design of $\mathcal {L}_2$ observer-based FD approach is realized by solving the proposed existence condition with the aid of Takagi-Sugeno fuzzy dynamic modeling technique and piecewise-fuzzy Lyapunov functions. Most importantly, a weighted piecewise-fuzzy observer-based residual generator is proposed, aiming at achieving an optimal integration of residual evaluation and threshold computation into FD systems. The core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors. In comparison with the standard norm-based fuzzy observer-based FD methods, the proposed scheme may lead to a significant improvement of the FD performance. In the end, the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant.

I. Introduction

Over the past decades, observer-based fault detection and isolation (FDI) techniques for linear systems have received considerable attention and made tremendous progress in both model-based [1]–[3] and data-driven frameworks [4]–[6]. Most recently, much effort has been dedicated to the integrated design of observer-based fault detection (FD) systems, which are composed of an observer-based residual generator, a residual evaluator, and a decision-making unit with an embedded threshold [3]. It has been reported that integrating all the available information into the decision process can improve the FD performance. Noting that nonlinearity exists in many practical systems, intensive attention has been paid to observer-based FD approaches for nonlinear processes [7]. However, solutions for nonlinear FDI problems have often been dedicated to some special kinds of nonlinear systems, such as affine nonlinear systems [8], Lipschitz nonlinear systems [9], networked control systems (NCSs) [10], and switched systems [11]. Moreover, to our best knowledge, there have been very few results available in the literature on the integrated design of FD systems for a general type of discrete-time nonlinear processes, which motivates us for this work.