Robust Consistency-Based Diagnosis of Nonlinear Systems by Set Observation

Abstract

Achieving robustness and a high fault sensitivity simultaneously is one of the most important goals of diagnosis system design. The idea of the so-called passive approach, which has been given relatively little attention in literature so far, is to include the effects of measurement and model uncertainties in the residual. In the subsequent residual evaluation, these uncertainties can then be accounted for such that false alarms can be precluded.Following this passive approach, we present a new model-based diagnosis algorithm based on state-set observation of nonlinear continuous-time systems. A set-valued observer following the well-known predictor-corrector scheme is used to calculate a set of system states. These sets are consistent with the underlying system model as well as with the discrete measurements including both model and measurement uncertainties. In the prediction step, a validated ODE solving method is applied for calculation of the consistent state set. To the authors knowledge, such a nonlinear continuous-time set-valued observer has not yet been used for diagnosis tasks. The performance of the method is demonstrated using measured data of fault-free and faulty operation of an inverted pendulum as a benchmark system.