CityPM: Predictive Monitoring with Logic-Calibrated Uncertainty for Smart Cities

We present CityPM, a novel predictive monitoring system for smart cities, that continuously generates sequential predictions of future city states using Bayesian deep learning and monitors if the generated predictions satisfy city safety and performance requirements. We formally define a flowpipe signal to characterize prediction outputs of Bayesian deep learning models, and develop a new logic, named {Signal Temporal Logic with Uncertainty} (STL-U), for reasoning about the correctness of flowpipe signals. CityPM can monitor city requirements specified in STL-U such as "with 90% confidence level, the predicated air quality index in the next 10 hours should always be below 100". We also develop novel STL-U logic-based criteria to measure uncertainty for Bayesian deep learning. CityPM uses these logic-calibrated uncertainty measurements to select and tune the uncertainty estimation schema in deep learning models. We evaluate CityPM on three large-scale smart city case studies, including two real-world city datasets and one simulated city experiment. The results show that CityPM significantly improves the simulated city's safety and performance, and the use of STL-U logic-based criteria leads to improved uncertainty calibration in various Bayesian deep learning models.