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, σ k E n , based on the amplitude fluctuations of time series segments. It uses the optimal variance estimation under the principle of minimizing A M S E ( σ ˆ 2) 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 σ k E n. In a background noise environment with an intensity of 20%, σ k E n distinguish various chaotic systems and random signals efficiently. In addition, this manuscript also proposes the plane of (σ k E n , N k E n) and (σ ̄ , σ k E n) , which also successfully identifies 6 types of chaotic systems, and 3 random noise signals. Furthermore, (< σ ̄ > , < σ k E n >) curve exhibits different dynamical behavior patterns for these chaotic systems. Finally, we employ (σ ̄ , σ k E n) as a feature and take 8 usual machine learning models, such as Linear 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. • Based on volatility of fragments, we introduce an parameter-free entropy, σ k E n. • Optimal estimator and KDE yield a stable, anti-noise complexity measurement. • Distinguish various deterministic and stochastic singles in noisy environment. • Test on 6 open dataset, get 100% accuracy in 4 diagnosis tasks, 96% in other 2. [ABSTRACT FROM AUTHOR]