Adaptive estimation of VMD modes number based on cross correlation coefficient

The variational mode decomposition (VMD) proposed recently is a kind of time-frequency signal analysis method. VMD has some advantages on signal decomposition such as high precision and noise robustness, but its serious shortcoming is that the number of modes (K) should be given in advance. And if the number is chosen inappropriately, VMD will lead to larger decomposition error. In this paper, the VMD method is introduced and the over- and under-segment characters of VMD are discussed. The cross correlation coefficients can express the similarity between the two signals. Cross correlation coefficients among VMD components and the original signal are used to judge whether over-segment takes place. As a result, the estimation method of VMD parameter K is proposed. Based on the method, the tri-harmonic signal and the vibration signals of ball bearings are analyzed in detail. The results show that the proposed method is feasible and effective.