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M. Meiyi, J. Stankovic, E. Bartocci, L. Feng:
"Predictive Monitoring with Logic-Calibrated Uncertainty for Cyber-Physical Systems";
ACM Transactions on Embedded Computing Systems, 20 (2021), 5s (101); S. 1 - 25.

Predictive monitoring---making predictions about future states and monitoring if the predicted states satisfy requirements-offers a promising paradigm in supporting the decision making of Cyber-Physical Systems (CPS). Existing works of predictive monitoring mostly focus on monitoring individual predictions rather than sequential predictions. We develop a novel approach for monitoring sequential predictions generated from Bayesian Recurrent Neural Networks (RNNs) that can capture the inherent uncertainty in CPS, drawing on insights from our study of real-world CPS datasets. We propose a new logic named Signal Temporal Logic with Uncertainty (STL-U) to monitor a flowpipe containing an infinite set of uncertain sequences predicted by Bayesian RNNs. We define STL-U strong and weak satisfaction semantics based on whether all or some sequences contained in a flowpipe satisfy the requirement. We also develop methods to compute the range of confidence levels under which a flowpipe is guaranteed to strongly (weakly) satisfy an STL-U formula. Furthermore, we develop novel criteria that leverage STL-U monitoring results to calibrate the uncertainty estimation in Bayesian RNNs. Finally, we evaluate the proposed approach via experiments with real-world CPS datasets and a simulated smart city case study, which show very encouraging results of STL-U based predictive monitoring approach outperforming baselines.

http://dx.doi.org/10.1145/3477032