In previous work [1], empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of [1] where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis [52]. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.MCS: 37A25, 37D45, 37N25, 93B05, 94C15, 05C80, 92D30

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The objective of this work is to identify failure modes and detect the onset of process anomalies in additive manufacturing (AM) processes, specifically focusing on fused filament fabrication (FFF). We accomplish this objective using advanced Bayesian nonparametric analysis of in situ heterogeneous sensor data. Experiments are conducted on a desktop FFF machine instrumented with a heterogeneous sensor array including thermocouples, accelerometers, an infrared (IR) temperature sensor, and a real-time miniature video borescope. FFF process failures are detected online using the nonparametric Bayesian Dirichlet process (DP) mixture model and evidence theory (ET) based on the experimentally acquired sensor data. This sensor data-driven defect detection approach facilitates real-time identification and correction of FFF process drifts with an accuracy and precision approaching 85% (average F-score). In comparison, the F-score from existing approaches, such as probabilistic neural networks (PNN), naïve Bayesian clustering, support vector machines (SVM), and quadratic discriminant analysis (QDA), was in the range of 55–75%.

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