  Chatter identification and detection in machining processes has been an
active area of research in the past two decades. Part of the challenge in
studying chatter is that machining equations that describe its occurrence are
often nonlinear delay differential equations. The majority of the available
tools for chatter identification rely on defining a metric that captures the
characteristics of chatter, and a threshold that signals its occurrence. The
difficulty in choosing these parameters can be somewhat alleviated by utilizing
machine learning techniques. However, even with a successful classification
algorithm, the transferability of typical machine learning methods from one
data set to another remains very limited. In this paper we combine supervised
machine learning with Topological Data Analysis (TDA) to obtain a descriptor of
the process which can detect chatter. The features we use are derived from the
persistence diagram of an attractor reconstructed from the time series via
Takens embedding. We test the approach using deterministic and stochastic
turning models, where the stochasticity is introduced via the cutting
coefficient term. Our results show a 97% successful classification rate on the
deterministic model labeled by the stability diagram obtained using the
spectral element method. The features gleaned from the deterministic model are
then utilized for characterization of chatter in a stochastic turning model
where there are very limited analysis methods.
