ATOMIC DECOMPOSITION METHOD BASED ON ADAPTIVE CHIRPLET DICTIONARY

Abstract

We propose an atomic decomposition method (AD) based on adaptive chirplet dictionary for decomposing multicomponent nonstationary signals with polygonal instantaneous frequencies (IFs). These signals are waveforms of the very general form ∑ Ai(t) cos (φi(t)), where the phase φi(t) is time-varying and the amplitude Ai(t) is slowly varying. Different from the traditional four-parameters chirplet, the one applied in this paper only contains two parameters (chirp offset and chirp rate) and its IF can be regarded as a line on the time–frequency (TF) plane. The idea is to use matching pursuit (MP) algorithm to search for the chirplets, which provide the best trade-off between complexity and goodness of fitting and chain the chirplets together adaptively as to form the desired signals. Our particular application in conjunction with this problem is the decomposition of meshing frequency component and its modulating frequency components in gear fault diagnosis. This strategy is general and may be applied in many other problems. We complement our study with numerical experiments showing that our algorithm boasts of many advantages, such as favorable TF resolution, strong noise robust property (NRP), good decomposition precision, and acceptable algorithm efficiency and is highly competitive compared to the current TF analysis methods.