Two-dimensional time series sample entropy algorithm: Applications to rotor axis orbit feature identification

Abstract

Traditional sample entropy algorithms are limited in their inability to analyze two-dimensional (2D) time series. Here, we describe a new feature algorithm for 2D time-series complexity and signal classification. This is a 2D sample entropy algorithm that includes the definitions of distance d and tolerance r in the 2D sample entropy algorithm on 2D signal scale and the difference between 2D and 1D sample entropies. The effectiveness of this algorithm in characterizing 2D signals was verified through simulated signal analysis. Then, by combining the 2D sample entropy algorithm with ensemble empirical mode decomposition (EEMD) and support vector machine (SVM) algorithms, we proposed a magnetically suspended rotor axis orbit feature identification and fault diagnosis method based on 2D sample entropy. This method was used to first perform EEMD of the 2D signals of a magnetically suspended rotor axis orbit to obtain several intrinsic mode functions (IMFs). We then calculated the 2D sample entropies of each IMF, and finally input the two-dimensional sample entropy as 2D feature vectors separately into the SVM, neural network, and logistic regression to identify the features of a rotor axis orbit. Finally, we compared the 1D sample entropy and variational mode decomposition (VMD) sample entropy. A comparison of experimental results showed that the 2D sample entropy algorithm can be used to characterize 2D signals, identify the features of the rotor axis orbit based on typical 2D signals, and identify and classify the rotor axis orbits under different fault conditions. The performance of this algorithm in feature identification is remarkably superior to that of 1D and VMD sample entropy algorithms. The availability of online diagnosis of this method was verified via speed testing.