  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.
