Small oscillation fault detection for a class of nonlinear systems with output measurements using deterministic learning

Early detection of small faults is an important issue in the literature of fault diagnosis. In this paper, for a class of nonlinear systems with output measurements, an approach for rapid detection of small oscillation faults is presented. Firstly, locally accurate approximations of unknown system dynamics and fault functions are achieved by combining a high gain observer and a deterministic learning (DL) theory. The obtained knowledge of system dynamics for both normal and fault modes is stored in constant RBF networks. Secondly, a bank of dynamical estimators are constructed for all the normal mode and oscillation faults. The knowledge obtained through DL is reused with a nonhigh-gain design. The occurrence of a fault can be detected if one of residual norms of a fault estimator becomes smaller than that of the normal estimator in a finite time. A rigorous analysis of the detectability properties of the proposed fault detection scheme is also given, which includes the fault detectability condition and the fault detection time. The attractions of the paper lie in that with output measurements, the knowledge of modeling uncertainty and nonlinear faults is obtained and then is utilized to enhance the sensitivity to small faults.