The joint empirical mode decomposition-local mean decomposition method and its application to time series of compressor stall process

Abstract

This paper proposed a new time-frequency analysis approach that has good robustness and clear physical meaning of instantaneous frequency, namely the joint EMD (empirical mode decomposition)-LMD (local mean decomposition) method. The algorithm uses the output (that is intrinsic mode functions, IMFs) of EMD as the input of LMD, and can effectively avoid the negative frequency problem generated by the Hilbert transform (HT) in the Hilbert-Huang transform (HHT) method. The main idea is to first perform EMD decomposition on the time series data to obtain a series of IMFs, and then implement the LMD method for each IMF to obtain a series of product function (PFs), each of which is the product of a frequency modulated signal and an envelope function. Finally, the instantaneous frequency is directly obtained for each frequency modulated signal to obtain a non-negative value. The effectiveness of the joint EMD-LMD method for solving the instantaneous frequency of nonlinear and non-stationary time series is verified by the damped chirp Duffing waves. Then the joint EMD-LMD method is applied to the nonlinear and non-stationary stall processing data of a contra-rotating compressor. Finally, the method is further verified in the observation data of gravitational waves. The results show that the joint EMD-LMD method can be used to deal with complex nonlinear and non-stationary signals in the real world.