Small Fault Detection of Discrete-Time Nonlinear Uncertain Systems

This article investigates the problem of small fault detection (sFD) for discrete-time nonlinear systems with uncertain dynamics. The faults are considered to be "small" in the sense that the system trajectories in the faulty mode always remain close to those in the normal mode, and the magnitude of fault can be smaller than that of the system's uncertain dynamics. A novel adaptive dynamics learning-based sFD framework is proposed. Specifically, an adaptive dynamics learning approach using radial basis function neural networks (RBF NNs) is first developed to achieve locally accurate identification of the system uncertain dynamics, where the obtained knowledge can be stored and represented in terms of constant RBF NNs. Based on this, a novel residual system is designed by incorporating a newmechanism of absolute measurement of system dynamics changes induced by small faults. An adaptive threshold is then developed for real-time sFD decision making. Rigorous analysis is performed to derive the detectability condition and the analytical upper bound for sFD time. Simulation studies, including an application to a three-tank benchmark engineering system, are conducted to demonstrate the effectiveness and advantages of the proposed approach.