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The use of complex networks for time series analysis has recently shown to beuseful as a tool for detecting dynamic state changes for a wide variety ofapplications. In this work, we implement the commonly used ordinal partitionnetwork to transform a time series into a network for detecting these statechanges for the simple magnetic pendulum. The time series that we used areobtained experimentally from a base-excited magnetic pendulum apparatus, andnumerically from the corresponding governing equations.The magnetic pendulumprovides a relatively simple, non-linear example demonstrating transitions fromperiodic to chaotic motion with the variation of system parameters. For ourmethod, we implement persistent homology, a shape measuring tool fromTopological Data Analysis (TDA), to summarize the shape of the resultingordinal partition networks as a tool for detecting state changes. We show thatthis network analysis tool provides a clear distinction between periodic andchaotic time series. Another contribution of this work is the successfulapplication of the networks-TDA pipeline, for the first time, to signals fromnon-autonomous nonlinear systems. This opens the door for our approach to beused as an automatic design tool for studying the effect of design parameterson the resulting system response. Other uses of this approach include faultdetection from sensor signals in a wide variety of engineering operations.

Dynamic State Analysis of a Driven Magnetic Pendulum using Ordinal Partition Networks and Topological Data Analysis