Parallel multi-scale entropy and it's application in rolling bearing fault diagnosis

As a prevalent tool for complexity measure of time series, multi-scale entropy has been utilized effectively to extract nonlinear dynamic features from rolling bearing vibration signals. However, the coarse-graining procedure of multi-scale entropy ignores the frequency-domain characteristics of the data, and finally leads to information aliasing and limited state identification capability. In this paper, the frequency characteristic changes of the data in the process of coarse-graining procedure are analyzed, and then a novel nonlinear dynamic method named parallel multi-scale entropy is proposed. In the proposed method, the aliasing effect caused by the reduction of data points is eliminated, and the final estimated sample entropy is replaced by the entropy average of multiple parallel intermediate series. Experimental results show that the proposed parallel multi-scale entropy holds better discrimination and stability compared with the original version, and can provide more excellent feature vectors for intelligent fault diagnosis.