Robustness assessment of cyber–physical systems with weak interdependency

With the increasing integration of information and communication technologies, cyber–physical systems are ubiquitous in our daily life. It is very meaningful to study the robustness of such critical systems to meet the needs of modern society. However, previous models of cascading failures are based on the assumption that once a node fails, its counterpart in other networks fails immediately. This strong assumption may not be true in practice where networks may have emergency procedures to buffer against cascades. In this paper, we propose an interdependent model that matches interdependent networks by allowing nodes to survive when their counterparts fail. We establish the weak interdependency across networks via two failure propagation probabilities which quantify the likelihood that a node survives when its counterpart fails. Based on the model we proposed, we perform simulations on both theoretical and realistic networks, and study how the failure propagation probabilities affect the robustness of cyber–physical systems under three patterns of initial attacks. The results show that the failure propagations in two directions are dissymmetric. And the system is more sensitive to the failures propagated from the power network to the communication network.