Fault detection using adaptive thresholds for nonlinear systems: A Preserving order observer approach

This paper presents an adaptive thresholds based fault detection (FD) approach using preserving order observers for a family of nominal and disturbed nonlinear systems. Based on cooperativity and dissipativity systemic properties, and providing an adequate initialization, a pair of observers that preserve the partial order with respect to the real state values are provided. The interval estimation is exploited for the design of upper and lower adaptive thresholds for Fault Detection. The proposed methodology is developed for the nominal case, where the nonlinear model is completely known, and is extended for the uncertain case, where the adaptive threshold is designed in the presence of perturbations and uncertainties. A computational methodology expressed in terms of linear matrix inequalities (LMI) is provided for the tuning of the observers parameters. The workability of the proposed methodology is illustrated by numerical simulations in an electromechanical system.