A comparative study on ApEn, SampEn and their fuzzy counterparts in a multiscale framework for feature extraction

Feature extraction from vibration signals has been investigated extensively over the past decades as a key issue in machine condition monitoring and fault diagnosis. Most existing methods, however, assume a linear model of the underlying dynamics. In this study, the feasibility of devoting nonlinear dynamic parameters to characterizing bearing vibrations is studied. Firstly, fuzzy sample entropy (FSampEn) is formulated by defining a fuzzy membership function with clear physical meaning. Secondly, inspired by the multiscale sample entropy (multiscale SampEn) which is originally proposed to quantify the complexity of physiological time series, we placed approximate entropy (ApEn), fuzzy approximate entropy (FApEn) and the proposed FSampEn into the same multiscale framework. This led to the developments of multiscale ApEn, multiscale FApEn and multiscale FSampEn. Finally, all four multiscale entropies along with their single-scale counterparts were employed to extract discriminating features from bearing vibration signals, and their classification performance was evaluated using support vector machines (SVMs). Experimental results demonstrated that all four multiscale entropies outperformed single-scale ones, whilst multiscale FSampEn was superior to other multiscale methods, especially when analyzed signals were contaminated by heavy noise. Comparisons with statistical features in time domain also support the use of multiscale FSampEn.