Redundancy Relations for Fault Diagnosis in Nonlinear Uncertain Systems

Abstract

The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into a strict feedback form. Algebraic and geometric tools are used for this transformation. The features of the method are made particular for uncertain systems with a linear structure.

Algebraic approach for model decomposition: Application to fault detection and isolation in discrete-event systems

“…The algebraic structure used is known under the name of the algebra of functions. Recently, the algebra of functions was used in several topics of model-based monitoring for deterministic systems (Berdjag, 2006b;2006c), uncertain systems (Shumsky, 2007) and canonical decomposition (Zhirabok, 2006). An analysis of the algebra of functions was presented by Zhirabok and Shumsky (1993) and Berdjag et al (2006b).…”

Nonlinear actuator fault estimation observer: An inverse system approach via a T-S fuzzy model

“…The fuzzy inverse model or the T-S inverse model is used to control nonlinear systems (e.g., Babuska, 1998;Boukezzoula et al, 2003;2007), mainly for input and output data identification. Essentially, fuzzy inverse control is a data-driven control method primarily for SingleInput Single-Output (SISO) system.…”

“…For system reconfiguration, FDI algorithms should only detect and isolate the faults (Shumsky, 2007). The design and analysis of such algorithms have received considerable attention during the past two decades.…”

Integrated design of observer based fault detection for a class of uncertain nonlinear systems

“…This trade-off problem has been formulated in two ways: (1) given the FDR, minimize the FAR (Zhang and Ding, 2008), (2) given the FAR, maximize the FDR (Ding et al, 2000b). On the other hand, since nonlinear systems are more common in practice, observer based FD techniques for nonlinear systems have also been studied extensively (Frank, 1994;Hammouri et al, 1999;Ferrari et al, 2007;Narasimhan et al, 2007;Shumsky, 2007;Edelmayer et al, 2004). There are many works dealing with Lipschitz nonlinear systems (Pertew et al, 2007;Chen and Saif, 2007;Rajamani and Ganguli, 2004;Yaz and Azemi, 1998;de Souza et al, 1993;Xie et al, 1996;Abbaszadeh and Marquez, 2008), since, under some conditions, more general nonlinear systems can be transformed into Lipschitz nonlinear systems (Rajamani, 1998).…”