论文标题
使用顺序分区网络和拓扑数据分析对驱动的磁摆的动态状态分析
Dynamic State Analysis of a Driven Magnetic Pendulum using Ordinal Partition Networks and Topological Data Analysis
论文作者
论文摘要
在时间序列分析中，将复杂网络的使用用于检测各种应用程序的动态状态变化是有用的。在这项工作中，我们实现了常用的序数分区网络，以将时间序列转换为一个网络，用于检测简单磁性摆的这些状态变化。我们所使用的时间序列是从基础兴奋的磁摆仪实验中获得的，并从相应的管理方程式上从数值上获得。磁性摆有相对简单的，非线性的示例，该示例证明了从周期性到混乱运动的过渡，并提供了系统参数的变化。对于我们的方法，我们实施了持久的同源性，这是一种形状测量工具，从拓扑数据分析（TDA）总结了所得的序数分区网络的形状，作为检测状态变化的工具。我们表明，该网络分析工具在周期性和混沌时间序列之间提供了明确的区别。这项工作的另一个贡献是第一次成功地应用网络-TDA管道对非自治非线性系统的信号。这为我们的方法打开了大门，可以用作研究设计参数对所得系统响应的影响的自动设计工具。这种方法的其他用途包括从多种工程操作中的传感器信号检测到故障检测。
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.
