Fault diagnosis based on numerical differentiation using wavelet transform

This paper proposes a novel fault diagnosis scheme based on numerical differentiation. Specifically, wavelet transform is utilized to estimate the numerical derivatives of known signals. And then, based on the algebraic observability of the fault, fault estimation is achieved by certain algebraic operations on a set of known signals and their numerical derivatives. The proposed fault diagnosis method is not limited to estimate the magnitude of a single fault. When there are multiple faults occurred simultaneously, it is also effective. In this paper, the proposed fault diagnosis scheme is applied to estimate the gyroscope faults in a satellite attitude determination subsystem. Simulation results are given to demonstrate the performance of the proposed method.