Fault Detection and Isolation for an Uncertain Takagi-Sugeno Fuzzy System using the Interval Approach

1. Introduction

State еstimаtiоn plays an important role in a context of systеm diаgnosis. It.is an.analytical source of rеdundаncy used to generate system fаilure symptoms by making a.comparison between the real behavior signals of the system and the estimated signals. A not desired variation between these signals indicates the possible presence of fаults affecting the systеm operation.

An accurate representation of the system model is the challenge faced by the scientific community. Several methods have been proposed to model the systems behavior in order to ensure proper supervision. Indeed, in many industrial fields, which must give product with good precision or which are dangerous, such as nuclear power plants or aerospace, all faults must be detected to ensure the materials and human security and the product precision (Bedoui et al, 2013). Hardware redundancy is often considered to detect and locate faults solution, or any material is ideal. Each instrument has an uncertainty which is often indicated by the manufacturer. Hardware redundancy consists in using several sensors to measure one output. This technique allows being sure of the output measure. The disadvantage of this technique is the installation blocking and considerable additional cost.

The diagnosis is an important field that allows detecting and locating the origin of faults or failure and permits to locate and track their evolution. It is based on the principle of residuals generation. The principle of residual generation is to compare the evolution of the system state to the state estimated. Computing the state estimation error leads to conclude if the system is faulty or no. If the residual is null, the system has a good behavior and no faults are affecting the system. In the opposite case it is possible to detect a fault affecting the system. These residuals are only functions of the measurement of noise and faults, and are determined, in this work, in the case of sensor faults.

In this work, a method for diagnosis of nonlinear systems with measurement uncertainties (sensors) based on the interval analysis as tools for state estimation is proposed. This method is used to make the fault detection and location.

In general, faults can be detected by developing performing checks to verify the adequacy of the information provided by the model and the sensors. An inconsistency appears when the residual is out of the vicinity of zero (for filter-based methods (Kalman, 1960), observers (Luenberger, 1964) or space parity (Chow & Willsky, 1984)) or when the parameters derived abnormally in the methods of parametric estimations (Isermann, 1984).

The interval analysis is to define an envelope in which the fault is considered non-existent and any measurement deviation inside this envelope is considered normal. Otherwise, the system is declared faulty. This approach has been explored by Adrot (Adrot et al, 2002; 2000) and recently by Bedoui (Bedoui et al, 2014) and applied to a mechatronic system by Letellier (Letellier, 2012).

Recently, Takagi-Sugeno Fuzzy systems are the subject of many researches by virtue of their approximation capabilities (Witczak et al, 2008 ; Khedher & Othman, 2010). They can represent exactly a nonlinear model (Tanaka et al, 1998; Witczak et al., 2008; Khedher & Othman, 2010). They are constructed by a set of linear models blended together with nonlinear functions holding the convex-sum property. In the case of Takagi-Sugeno Fuzzy systems, state estimation is based on the design of nonlinear observers (multiple observers) using the same nonlinear weighting functions as the Takagi-Sugeno models (Akhenak et al, 2009; 2003; Ichalal et al, 2009a; Khedher et al, 2008; 2009).