Classification-based Online Adaption of a Fault Recognition Aproach for Nonlinear Systems

Dr.-Ing. Patrick Gerland

April 2007 - April 2011

State of Hesse

In this work, a new adaptive fault diagnosis system for Lipschitz nonlinear systems with dynamic uncertainties has been developed. Insights and methods from the field of Takagi-Sugeno (TS) fuzzy modeling and observer design as well as sliding mode (SM) theory were used to develop a novel robust TS-SM-observer for a class of nonlinear systems. Conditions for stability and the decay of the observer were derived based on linear matrix inequalities (LMIs). These conditions guarantee stability on the one hand and on the other hand provide a direct design method of the observer.

Another significant scientific contribution lies in the extension of the proposed fault diagnosis approach to an online adaptation of the error sensitivity. It is proposed to adapt the error thresholds online at the current operating condition with their respective maximum possible uncertainties. This results in greatly increased error sensitivity at operating conditions with small model uncertainties. In operating phases with large model uncertainties false alarms are being prevented. The basic idea is to determine the current operating condition by means of a Bayesian classifier and also customize the error thresholds to the a priori defined uncertainties of the different operating state.

The effectiveness of the proposed approaches to solving problems from engineering practice was demonstrated by the successful use of several technical systems.