  Machining processes are most accurately described using complex dynamical
systems that include nonlinearities, time delays, and stochastic effects. Due
to the nature of these models as well as the practical challenges which include
time-varying parameters, the transition from numerical/analytical modeling of
machining to the analysis of real cutting signals remains challenging. Some
studies have focused on studying the time series of cutting processes using
machine learning algorithms with the goal of identifying and predicting
undesirable vibrations during machining referred to as chatter. These tools
typically decompose the signal using Wavelet Packet Transforms (WPT) or
Ensemble Empirical Mode Decomposition (EEMD). However, these methods require a
significant overhead in identifying the feature vectors before a classifier can
be trained. In this study, we present an alternative approach based on
featurizing the time series of the cutting process using its topological
features. We first embed the time series as a point cloud using Takens
embedding. We then utilize Support Vector Machine, Logistic Regression, Random
Forest and Gradient Boosting classifier combined with feature vectors derived
from persistence diagrams, a tool from persistent homology, to encode chatter's
distinguishing characteristics. We present the results for several choices of
the topological feature vectors, and we compare our results to the WPT and EEMD
methods using experimental turning data. Our results show that in two out of
four cutting configurations the TDA-based features yield accuracies as high as
97%. We also show that combining Bezier curve approximation method and parallel
computing can reduce runtime for persistence diagram computation of a single
time series to less than a second thus making our approach suitable for online
chatter detection.
