Rapid detection of oscillation faults via deterministic learning

In this paper, we propose an approach for rapid detection of nonlinear oscillation systems. The approach consists of two phases: the training (learning) phase and the test (diagnosis) phase. In the training or learning phase, for an oscillation system in both normal and fault modes, a partial persistence of excitation (PE) condition is guaranteed to be satisfied by using localized radial basis function (RBF) networks, and the system dynamics underlying the normal and fault oscillations are locally-accurately approximated. The obtained knowledge of system dynamics is stored in constant RBF networks. In the test or diagnosis phase, rapid detection is implemented by utilizing the learned knowledge of system dynamics. Specially, a bank of estimators are constructed using the constant RBF networks to represent the training normal and fault modes. By comparing the set of estimators with the test monitored system, a set of residuals are generated. The occurrence of a test oscillation fault can be rapidly detected according to the smallest residual principle. A rigorous analysis of the performance of the detection scheme is also given. The significance of the paper lies in that an intelligent fault detection approach is presented for a class of nonlinear oscillation systems, in which knowledge of modeling uncertainty and nonlinear faults is firstly obtained and then is utilized to achieve rapid and sensitive detection of small oscillation faults.