A Novel Feature for Fault Classification of Rotating Machinery: Ternary Approximate Entropy for Original, Shuffle and Surrogate Data

Abstract

Existing works have paid scant attention to the multivariate entropy of complex data. Thus, existing methods perform poorly in fully exposing the nature of complex data. To mine a rich vein of data features, this paper applies a shuffle and surrogate approach to complex data to decouple probability density information from correlation information and then obtain shuffle data and surrogate data. Furthermore, this paper applies approximate entropy (ApEn) to individually estimate complexities and irregularities of the original, the shuffle, and the surrogate data. As a result, this paper develops a ternary ApEn approach by integrating the ApEn of the original, shuffle, and surrogate data into a three-dimensional vector for describing the dynamics of complex data. Next, the proposed ternary ApEn approach is compared with conventional temporal statistics, conventional ApEn, two-dimensional energy entropy based on empirical mode decomposition or wavelet decomposition, and binary ApEn using both gear vibration data and roller-bearing vibration data containing different types and severity of faults. The results suggest that the ternary ApEn approach is superior to the other methods in identifying the conditions of rotating machinery.