Xie Jieren, Xu Guanghua, Chen Xiaobi, Zhang Xun, Chen Ruiquan, Yang Zengyao, Fang Churui, Tian Peiyuan, Wu Qingqiang, Zhang Sicong
School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China.
State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, 710049, China.
Sci Rep. 2024 Aug 5;14(1):18103. doi: 10.1038/s41598-024-68693-0.
This paper presents a novel approach to the phase space reconstruction technique, fractional-order phase space reconstruction (FOSS), which generalizes the traditional integer-order derivative-based method. By leveraging fractional derivatives, FOSS offers a novel perspective for understanding complex time series, revealing unique properties not captured by conventional methods. We further develop the multi-span transition entropy component method (MTECM-FOSS), an advanced complexity measurement technique that builds upon FOSS. MTECM-FOSS decomposes complexity into intra-sample and inter-sample components, providing a more comprehensive understanding of the dynamics in multivariate data. In simulated data, we observe that lower fractional orders can effectively filter out random noise. Time series with diverse long- and short-term memory patterns exhibit distinct extremities at different fractional orders. In practical applications, MTECM-FOSS exhibits competitive or superior classification performance compared to state-of-the-art algorithms when using fewer features, indicating its potential for engineering tasks.
本文提出了一种相空间重构技术的新方法，即分数阶相空间重构（FOSS），它推广了传统的基于整数阶导数的方法。通过利用分数阶导数，FOSS为理解复杂时间序列提供了一个新视角，揭示了传统方法未捕捉到的独特特性。我们进一步开发了多跨度转移熵分量法（MTECM-FOSS），这是一种基于FOSS的先进复杂性测量技术。MTECM-FOSS将复杂性分解为样本内和样本间分量，从而更全面地理解多变量数据中的动态变化。在模拟数据中，我们观察到较低的分数阶可以有效滤除随机噪声。具有不同长期和短期记忆模式的时间序列在不同分数阶处呈现出明显的极值。在实际应用中，当使用较少特征时，MTECM-FOSS与最先进的算法相比表现出具有竞争力或更优的分类性能，表明其在工程任务中的潜力。
