Predictive Monitoring with Logic-Calibrated Uncertainty for Cyber-Physical Systems

TL;DR

This paper introduces a novel logic-based approach called STL-U for monitoring sequential predictions in Cyber-Physical Systems using Bayesian RNNs, effectively capturing uncertainty and improving decision support.

Contribution

It develops STL-U, a new logic for monitoring uncertain sequences, and methods to calibrate Bayesian RNN uncertainty estimates, advancing predictive monitoring in CPS.

Findings

STL-U outperforms baseline methods in real-world datasets.

The approach effectively calibrates uncertainty in Bayesian RNNs.

Experimental results show improved monitoring accuracy.

Abstract

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 \emph{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 if 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 datasets and a simulated smart city case study, which show very encouraging results of STL-U based predictive monitoring approach outperforming baselines.