Robust Structure Identification of Industrial Cyber-Physical System From Sparse Data: A Network Science Perspective

Industrial cyber-physical systems (ICPSs) are deployed in many high-value facilities recently, and the monitoring of ICPS is more and more important. However, the prerequisite of ICPS monitoring is how to obtain an accurate network structure. In addition, the structure of ICPS may change over time and the observations data are limited and noisy. These situations make the ICPS network structure identification more difficult. In this article, we proposed the algorithm of temporal network identification from sparse data (ATNISD) to address these two issues simultaneously. First, we established the temporal network analysis model from the aspect of state equation and observation equation. Then, we analyze the characteristics of temporal networks in both time domain and space domain and propose a general framework of temporal networks structure identification, which is a combinatorial optimization problem. To improve the accuracy and alleviate the computational complexity, we decompose the combinatorial problem into small independent simple problems, which can be solved efficiently. The performance of the proposed algorithm is verified on synthetic evolutionary game dynamics on both homogeneous and heterogeneous temporal networks. The experimental results show that the proposed method can efficiently solve the problem of temporal networks structure identification from sparse data. Note to Practitioners—This article addresses the importance of network structure identification in industrial cyber-physical systems (ICPSs). The proposed method can effectively cope with the task of ICPS network structure identification in time-varying environments by exploiting the spatial and temporal features of networks in both time domain and space domain. The proposed algorithm can be implemented in typical slowing changing ICPS with or without observation noise, and it can decompose the combinatorial problem into small independent simple problems to improve the accuracy and release the computational complexity. Extensive simulation experiments demonstrate the accuracy and robustness of the proposed method for solving the structure identification task of temporal networks.