Multiwavelet construction via an adaptive symmetric lifting scheme and its applications for rotating machinery fault diagnosis

Multiwavelets and the lifting scheme are two important developments of wavelet theory. Multiwavelets outperform scalar wavelets in many applications due to their better properties. The lifting scheme is a method to construct a new wavelet with prescribed properties. In this paper, multiwavelets are integrated with the lifting scheme, synthesizing their advantages. Due to multiple wavelet bases, the lifting scheme of multiwavelets is more flexible than that of scalar wavelets. With supplement of a symmetric condition, a novel adaptive symmetric lifting scheme of multiwavelets is presented. Kurtosis is chosen to be the performance measurement of lifting coefficients, and the genetic algorithm is used to optimize the free parameters in the lifting scheme. The proposed method, constructing a new multiwavelet via an adaptive lifting scheme, is applied to analyze the simulation of a rolling bearing and gearbox vibration signals. The results demonstrate that the adaptive symmetric lifting of multiwavelets is more effective in extracting fault features of rotating machinery than conventional diagnosis techniques with scalar wavelets and non-adaptive multiwavelets.