A new parameter-free entropy based on fragment oscillation and its application in fault diagnosis

For finite time series, it is difficult to provide a convincing determination scheme for specifying relevant parameters of entropy. This article proposes a new entropy, σkEn, based on the amplitude fluctuations of time series segments. It uses the optimal variance estimation under the principle of minimizing AMSE(σˆ2) to adaptively select the window width, and then realizes the no-argument calculation process of volatility entropy through kernel density estimation. By testing with artificial data and applying to real-world data, it has been verified anti-noise and stability properties of σkEn. In a background noise environment with an intensity of 20%, σkEn distinguish various chaotic systems and random signals efficiently. In addition, this manuscript also proposes the plane of (σkEn,NkEn) and (σ̄,σkEn) , which also successfully identifies 6 types of chaotic systems, and 3 random noise signals. Furthermore, (<σ̄>,<σkEn>) curve exhibits different dynamical behavior patterns for these chaotic systems. Finally, we employ (σ̄,σkEn) as a feature and take 8 usual machine learning models, such as Liner Discriminant, Gaussian Naive Bayes and Subspace Discriminant, etc, to perform anomaly detection and fault classification tests on 6 open datasets. Given the appropriate classifiers, our method can achieve a classification accuracy of 100% for four tasks, and an average accuracy of over 96% for the remaining two. This is significantly superior than the accuracy obtained by using Permutation Entropy as a feature.