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.
翻译:预测性监测 -- -- 预测未来状况并监测预测状态是否满足要求 -- -- 提供了支持网络物理系统决策的有希望的范例。现有的预测性监测工作主要侧重于监测个别预测,而不是顺序预测。我们开发了一种新的方法,以监测来自巴伊西亚经常性神经网络(RNN)的连续预测,这种预测可以捕捉CPS的内在不确定性,借鉴我们对真实世界CPS数据集研究的见解。我们提出了一个名为\emph{Signal Temalal Tyal Locic with Unciltiny}(STL-U)的新逻辑,以监测含有由巴伊西亚网络预测的无限一系列不确定序列的流水管。我们根据流管中所含的所有或某些序列是否满足要求来界定STL-U的强大和薄弱的满意度语义。我们还开发了各种方法,用以计算信任度水平的范围,保证流管方法能够强有力地(weakly)满足STL-U的公式。此外,我们开发了新标准,用以利用STL-U监测Simal-U的真实结果来校准Simlimlal Besturisal 研究,最终显示我们Sirl-Basislex的、鼓励的模型案例研究。