基于有序划分网络和拓扑数据分析的驱动磁摆动态分析
Dynamic State Analysis of a Driven Magnetic Pendulum using Ordinal Partition Networks and Topological Data Analysis
摘要：
使用复杂网络的时间序列分析最近被证明是有用的工具，用于检测动态状态变化的各种应用。在这项工作中，我们实现了常用的有序分区网络转换成一个网络的时间序列检测这些状态变化的简单磁摆。所用的时间序列是从基激励磁摆装置的实验和相应的控制方程数值计算得到的，磁摆提供了一个相对简单的非线性例子，证明了随着系统参数的变化，从周期运动到混沌运动的转变。对于我们的方法，我们实现持久同源性，拓扑数据分析（TDA）的形状测量工具，总结所得到的有序分区网络的形状作为检测状态变化的工具。我们表明，这种网络分析工具提供了一个明确的区分周期和混沌时间序列。这项工作的另一个贡献是成功地应用网络TDA管道，第一次，从非自治非线性系统的信号。这为我们的方法打开了大门，可用作自动设计工具，用于研究设计参数对系统响应的影响。该方法的其他用途包括在各种工程操作中从传感器信号进行故障检测。
英文摘要：
The use of complex networks for time series analysis has recently shown to be useful as a tool for detecting dynamic state changes for a wide variety of applications. In this work, we implement the commonly used ordinal partition network to transform a time series into a network for detecting these state changes for the simple magnetic pendulum. The time series that we used are obtained experimentally from a base-excited magnetic pendulum apparatus, and numerically from the corresponding governing equations.The magnetic pendulum provides a relatively simple, non-linear example demonstrating transitions from periodic to chaotic motion with the variation of system parameters. For our method, we implement persistent homology, a shape measuring tool from Topological Data Analysis (TDA), to summarize the shape of the resulting ordinal partition networks as a tool for detecting state changes. We show that this network analysis tool provides a clear distinction between periodic and chaotic time series. Another contribution of this work is the successful application of the networks-TDA pipeline, for the first time, to signals from non-autonomous nonlinear systems. This opens the door for our approach to be used as an automatic design tool for studying the effect of design parameters on the resulting system response. Other uses of this approach include fault detection from sensor signals in a wide variety of engineering operations.
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