Topological Feature Vectors for Chatter Detection in Turning Processes

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 utilize support vector machine classifier combined with feature vectors derived from persistence diagrams, a tool from persistent homology, to encode distinguishing characteristics based on embedding the time series as a point cloud using Takens embedding. 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 time series from a turning cutting test. Our results show that in most cases combining the TDA-based features with a simple Support Vector Machine (SVM) yields accuracies that either exceed or are within the error bounds of their WPT and EEMD counterparts.