Probabilistic Graphical Modeling Of Distributed Cyber-Physical Systems

Probabilistic graphical models (PGMs) have been shown to efficiently capture the dynamics of physical systems as well as model cyber systems such as communication networks. This chapter focuses on some recent developments in applying PGMs as data-driven models for jointly analyzing cyber and physical properties of distributed complex systems. Among various PGM techniques, Bayesian networks and symbolic dynamic filtering are discussed with three use cases: spatial modeling, multiscale temporal modeling, and spatiotemporal interaction modeling. While spatial modeling deals with anomaly detection and root-cause analysis in large building systems, temporal modeling involves the online identification of dynamic modes of a complex system operation. Finally, spatiotemporal modeling aims to characterize casual dependencies among wind turbines in a large wind farm, both spatially and temporally, for predicting farm-wide power generation. The chapter concludes with key observations such as enhanced robustness and scalability in cyber-physical system modeling with PGMs along with recommendations for future research directions.