Elimination of end effects in empirical mode decomposition by mirror image coupled with support vector regression

Abstract

The treatment of end effects is one of the most important open problems related to the EMD (Empirical Mode Decomposition) method. This work proposes a new approach that couples the mirror expansion with the extrapolation prediction of regression function to solve this problem. The algorithm includes two steps: the extrapolation of the signal through Support Vector (SV) regression at both endpoints to form the primary expansion signal, then the primary signal is further expanded through extrema mirror expansion and EMD is performed on the resulting signal to obtain reduced end effects. If there is not enough length for the signal to meet the need of finding the length of the data available for expanding the signal, a direct extrapolation towards the outside of the signal at the endpoint is executed by the estimate model, and the length of extrapolation points is controlled by the first local extremum. Applications of the proposed approach to the decomposition of a digital modeling signal and three segment signals from the observed earthquake signal by the EMD method are presented, and all of the results are compared with those on the basis of the traditional mirror expansion approach and the extrapolation estimate expansion based on the SV regression, which shows that the most satisfactory result can be obtained for the elimination of end effects in EMD method by mirror image coupled with SV regression.