A time-frequency domain fault detection approach based on parity relation and wavelet transform

Problems related to the design of robust residual generators have been studied. The main objective of our study is to make use of the simple time domain design form of the parity relation based approach and the frequency domain analysis known by the H₂-optimization approach, in order to improve the system performance without an essential increase in computation. We establish a relationship between the parity relation based and the H₂ optimal residual generators and show that the optimal parity vector v_s converges to the H₂-optimal post-filter with s→∞. Making use of the fact that the H₂-optimal post-filter is a narrow band filter and the well known time-frequency domain properties of the wavelet transform, a time-frequency domain approach is developed, which allows us to design a residual generator based on the wavelet transform. The significant property of such kind of residual generators is its simple form, low order and high performance. The main results are illustrated by examples