Towards Utilizing Topological Data Analysis for Studying Machining Models
Wednesday, February 19, 2014 - 1:30pm - 2:30pm
Delay differential equations (DDEs) appear in many models in science and engineering either as an intrinsic component or as a modeling decision. Machining dynamics are an important example of processes that include delays as an intrinsic part of the system. The infinite dimensionality of DDEs significantly complicates the resulting analysis from both an analytical and numerical perspective. Recent developments in the theory of DDEs have helped with obtaining more accurate mathematical models for capturing the process dynamics. However, even though machining processes are known to be stochastic, the majority of existing machining models are deterministic. Further, data analysis methods for DDEs are either few or non-existant largely due to the non-Markovian nature of these systems. This talk briefly discusses the challenges associated with DDEs and how they are incorporated into machining dynamics models. We also discuss some new results which suggest that topological data analysis, specifically persistent homology, can be a very useful tool for analyzing numerical and experimental time series corresponding to time delay systems.