Inferring spatial-temporal properties from data is important for many complex systems, such as additive manufacturing systems, swarm robotic systems and biological networks. Such systems can often be modeled as a labeled graph where labels on the nodes and edges represent relevant measurements such as temperatures and distances. We introduce graph temporal logic (GTL) which can express properties such as "whenever a node's label is above 10, for the next 3 time units there are always at least two neighboring nodes with an edge label of at most 2 where the node labels are above 5". This paper is a first attempt to infer spatial (graph) temporal logic formulas from data for classification and identification. For classification, we infer a GTL formula that classifies two sets of graph temporal trajectories with minimal misclassification rate. For identification, we infer a GTL formula that is informative and is satisfied by the graph temporal trajectories in the dataset with high probability. The informativeness of a GTL formula is measured by the information gain with respect to given prior knowledge represented by a prior probability distribution. We implement the proposed approach to classify the graph patterns of tensile specimens built from selective laser sintering (SLS) process with varying strengths, and to identify informative spatialtemporal patterns from experimental data of the SLS cooldown process and simulation data of a swarm of robots.
We present a novel unsupervised deep learning approach that utilizes the encoder-decoder architecture for detecting anomalies in sequential sensor data collected during industrial manufacturing. Our approach is designed not only to detect whether there exists an anomaly at a given time step, but also to predict what will happen next in the (sequential) process. We demonstrate our approach on a dataset collected from a real-world Additive Manufacturing (AM) testbed. The dataset contains infrared (IR) images collected under both normal conditions and synthetic anomalies. We show that the encoder-decoder model is able to identify the injected anomalies in a modern AM manufacturing process in an unsupervised fashion. In addition, it also gives hints about the temperature non-uniformity of the testbed during manufacturing, which is what we are not aware of before doing the experiment.
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