The paper focuses on the problem of robust fault detection using analytical methods and soft computing. Taking into account the model-based approach to Fault Detection and Isolation (FDI), possible applications of analytical models, and first of all observers with unknown inputs, are considered. The main objective is to show how to employ the bounded-error approach to determine the uncertainty of soft computing models (neural networks and neuro-fuzzy networks). It is shown that based on soft computing models uncertainty defined as a confidence range for the model output, adaptive thresholds can be described. The paper contains a numerical example that illustrates the effectiveness of the proposed approach for increasing the reliability of fault detection. A comprehensive simulation study regarding the DAMADICS benchmark problem is performed in the final part.
The paper deals with the problems of designing observers and unknown input observers for discrete-time Lipschitz non-linear systems. In particular, with the use of the Lyapunov method, three different convergence criteria of the observer are developed. Based on the achieved results, three different design procedures are proposed. Then, it is shown how to extend the proposed approach to the systems with unknown inputs. The final part of the paper presents illustrative examples that confirm the effectiveness of the proposed techniques. The paper also presents a MATLAB® function that implements one of the design procedures.