CDSTTN: A Data Imputation Method for Cyber-Physical Systems by Causal Dense Spatial–Temporal Transformer Network

Data-driven technique of artificial intelligence is a main receipt to model the uncertainty of cyber-physical systems. Based on large-scale sensor network, big data can be collected, and used to represent, understand and control the system. However, due to the issue of communication failures and cyberattacks, the collected data is often damaged and corrupted, which leads to terrible model training and low performance. To address this issue, a data missing imputation method is proposed based on causal dense spatial-temporal transformer network (CDSTTN). This model specially designs a module to recognize causal network on the observation variables, and then combine the network with densely connected spatial-temporal transformer modules. The results show that the causal module improves the performance of CDSTTN, and provides more causal interpretability. Moreover, extensive ablation studies are also conducted to show the contribution of CDSTTN to accelerating the model training process. Through comprehensive experimental comparison, the proposed model reaches the state-of-the-art performance compared to the other baseline models, which indicates it may provide some insight into the commonly encountered data missing problems in cyber-physical systems.