Adaptive Meyer wavelet filters for machinery fault diagnosis based on harmonic infinite-taxicab norm and grasshopper optimization algorithm

Abstract

Meyer wavelet filters are the key building blocks of empirical wavelet transform. In mechanical fault diagnosis, however, the boundaries of Meyer wavelet filters are usually defined empirically. In order to solve the problems, this paper proposes a new index called harmonic infinite-taxicab norm to guide grasshopper optimization algorithm to primarily optimize a band-pass filter and thus, concurrently and secondarily optimize a low-pass filter and a high-pass filter of Meyer wavelet. The proposed index is inspired by spectral Lp/Lq norm and it is closely related to fault characteristic frequency of rotating machinery. In addition, only three Meyer wavelet filters are demanded in each iteration of optimization. The effectiveness of the proposed method is validated by comparing with fast kurtogram method on analyzing faulty bearing data and gearbox data.