Analysis of Resilience Under Repair Strategy in Interdependent Mechatronic System

Existing works on the interdependent system have come to fruition based on the percolation theory and revealed that it possesses the great vulnerability due to the essential interdependency. However, how to effectively recover the performance of the interdependent system after cascading failures is still under research. In this article, we define an interdependent mechatronic system as an interdependent machine-electricity-communication network. By considering the behavior of the real-world system, we put forward an extended cascading failure model in which the non-giant component is also functional when its size proportion is not smaller than the proportion threshold
$\delta $
and it has the interdependent links from the other two subnetworks. Then, according to the measures of a node (i.e., single measures), the interdependent measures are proposed and the repair strategies are obtained by these measures to determine the order of repaired nodes. In order to accurately reflect the resilience in the interdependent mechatronic system, we adopt three metrics to quantify it, i.e., the change of the robustness, the recovery ability, and the critical number of repaired nodes. Finally, we study the relationship between
$\delta $
and the robustness, and apply different repair strategies to the analysis of the resilience in a real mechatronic system. The experiments show that the non-giant component plays a key role in the robustness and the resilience is affected by
$\delta $
when a few nodes fail to work. In addition, we obtain the optimal repair strategy from different aspects of the resilience. A striking finding is that in most instances, the repair strategies concerning the interdependent measures lead to the higher resilience compared with the ones concerning the single measures. Our work may provide insights to make a plan for repairing equipment so as to enhance the resilience of the interdependent mechatronic system.