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Integrated design approach of fault detection systems based on wavelet transform

Problems related to the integrated design of robust fault detection (FD) systems are studied. Firstly, a problem of the 2-norm based approaches is discussed, i.e. due to the necessary length of the time window introduced to realize the 2-norm based residual evaluation function of a FD system, the expected optimal performance of the FD system may not be achieved when the system is realized in real applications. Then a new kind of evaluation function based on the absolute value of the wavelet transform (WT) of the residual signal and the corresponding integrated design approach for the FD systems are proposed. Different from the usual 2-norm based approaches whose mathematical basis is the relationship between the whole energy of the output and input signal of a dynamic system, a relationship between the instant power of the WT of the output signal and the energy of the past input signal of a dynamic system is established and further used for the FD system design. It solves the problem in the 2-norm based method, and the resulting FD system is easy to implement, and can detect faults very rapidly with a low miss detection ratio.