Modeling and monitoring of a multivariate spatio-temporal network system

With the development of information technology, various network systems are created to connect physical objects and people by sensor nodes or smart devices, providing unprecedented opportunities to realize automated interconnected systems and revolutionize people's lives. However, network systems are vulnerable to attacks, due to the integration of physical objects and human behaviors as well as the complex spatio-temporal correlated structures of the network systems. Therefore, how to accurately and effectively model and monitor a network system is critical to ensure information security and support system automation. To address this issue, this article develops a multivariate spatio-temporal modeling and monitoring methodology for a network system by using multiple types of sensor signals collected from the network system. We first propose a Multivariate Spatio-Temporal Autoregressive (MSTA) model by integrating a Gaussian Markov Random Field and a vector autoregressive model structure to characterize the spatio-temporal correlation of the network system. In particular, we develop an iterative model learning algorithm that integrates the Bayesian inference, least squares, and a sum square error-based optimization method to learn the network structure and estimate parameters in the MSTA model. Then, we propose two spatio-temporal control schemes to monitor the network system based on the MSTA model. Numerical experiments and a real case study of an IoT network system are presented to validate the performance of the proposed method.