Rapid Detection of Small Oscillation Faults via Deterministic Learning

Detection of small faults is one of the most important and challenging tasks in the area of fault diagnosis. In this paper, we present an approach for the rapid detection of small oscillation faults based on a recently proposed deterministic learning (DL) theory. The approach consists of two phases: the training phase and the test phase. In the training phase, the system dynamics underlying normal and fault oscillations are locally accurately approximated through DL. The obtained knowledge of system dynamics is stored in constant radial basis function (RBF) networks. In the diagnosis phase, rapid detection is implemented. Specially, a bank of estimators are constructed using the constant RBF neural 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, and the average L₁ norms of the residuals are taken as the measure of the differences between the dynamics of the monitored system and the dynamics of the training normal mode and oscillation faults. 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 novelty of the paper lies in that the modeling uncertainty and nonlinear fault functions are accurately approximated and then the knowledge is utilized to achieve rapid detection of small oscillation faults. Simulation studies are included to demonstrate the effectiveness of the approach.