Fault Detection for Nonlinear Discrete-Time Systems via Deterministic Learning

Abstract

This paper presents a fault detection scheme for nonlinear discrete-time systems based on the recently proposed deterministic learning (DL) theory. The scheme consists of two phases: the learning phase and the detecting phase. In the learning phase, the discrete-time system dynamics underlying normal and fault modes are locally accurately approximated through deterministic learning. The obtained knowledge of system dynamics is stored in constant RBF networks. In the detecting phase, a bank of estimators are constructed using the constant RBF networks to represent the learned normal and fault modes. By comparing the set of estimators with the monitored system, a set of residuals are generated, and the average L ₁ norms of the residuals are used to compare the differences between the dynamics of the monitored system and the dynamics of the learning normal and fault modes. The occurrence of a fault can be rapidly detected in a discrete-time setting.