Similar Fault Isolation of Discrete-Time Nonlinear Uncertain Systems: An Adaptive Threshold Based Approach

In this paper, a new concept of “similar fault” is introduced to the field of fault isolation (FI) of discrete-time nonlinear uncertain systems, which defines a new and important class of faults that have small mutual differences in fault magnitude and fault-induced system trajectories. Effective isolation of such similar faults is rather challenging as their small mutual differences could be easily concealed by other system uncertainties (e.g., modeling uncertainty/disturbances). To this end, a novel similar fault isolation (sFI) scheme is proposed based on an adaptive threshold mechanism. Specifically, an adaptive dynamics learning approach based on the deterministic learning theory is first introduced to locally accurately learn/identify the uncertain system dynamics under each faulty mode using radial basis function neural networks (RBF NNs). Based on this, a bank of sFI estimators are then developed using a novel mechanism of absolute measurement of fault dynamics differences. The resulting residual signals can be used to effectively capture the small mutual differences of similar faults and distinguish them from other system uncertainties. Finally, an adaptive threshold is designed for real-time sFI decision making. One important feature of the proposed sFI scheme is that: it is capable of not only isolating similar faults that belong to a pre-defined fault set (used in the training/learning process), but also identifying new faults that do not match any pre-defined faults. Rigorous analysis on isolatability conditions and isolation time is conducted to characterize the performance of the proposed sFI scheme. Simulation results on a practical application example of a single-link flexible joint robot arm are used to show the effectiveness and advantages of the proposed scheme over existing approaches.