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.
The NBA Finals got off to an explosive start Thursday night as the Golden State Warriors picked up the win in Game 1 with an overtime 124-114 win over the Cleveland Cavaliers despite LeBron James scoring 51 points on the night. The Cavaliers almost had a perfect start to the 2018 NBA Finals after many had written off their chances of beating the reigning champions. With the game tied at 106, James' side had the chance to win as J.R. Smith collected the rebound after George Hill missed his second free throw. They had 4.6 seconds left in regulation time to make another shot, but Smith decided against the shot and ran to the perimeter thinking they were ahead when the game was actually tied. This took the game into overtime where the Warriors blitzed the Cavaliers outscoring them 17-7 to take Game 1 of the best of seven series.
The Wednesday night crowd stayed to hear from Tesla and SpaceX CEO Elon Musk, who arrived almost an hour late because of some "landing gear issue" with his plane. It was somewhat ironic coming from the guy whose company recently landed a space rocket vertically on a floating drone barge. Musk, like Bezos, is deeply interested in space travel. His company SpaceX is already worth billions, having won government contracts to send supplies into space. His greater mission is to send humans to Mars, a goal he said is attainable by 2024.
One of the major factors hindering the use of qualitative simulation techniques to reason a,bout the behavior of complex dynamical systems is intractable branching due to a phenomenon called chatter. This paper presents two general abstraction techniques that solve the problem of chatter. Eliminating the problem of chatter significantly extends the range of models that can be tractably simulated using qualitative simulation. Chatter occurs when a variable's direction of change is constrained only by continuity within a region of the state space.