Integrated design of fault detection systems in time-frequency domain

Problems related to the integrated design of robust fault detection (FD) systems are studied. First, it is revealed that due to the time window introduced to realize the 2-norm based evaluation function, an optimal design of a FD system with the 2-norm based evaluation function may not ensure the expected optimal performance when the system is realized in real applications. To solve this problem, an integrated design method of FD systems using the absolute value of residual signal as evaluation function is then proposed. It leads to a residual generator which is much easier to be realized. Different from the usual 2-norm based approaches whose mathematical basis is the relationship between the energy of the output and input signals of a dynamic system, a relationship between the instant power of the output signal and the energy of the past input signal of a dynamic system is established and further used for FD system design. Another new kind of evaluation function based on the absolute value of wavelet transform of residual signal and the corresponding integrated design approach for FD systems are further proposed