Resilience modeling for an engineered network with multimodal performance under multiple recurrent hazards

Modeling the resilience of an engineered network exposed to multiple recurrent hazards has attracted increasing attention. Among all the unresolved technical challenges, two of them must be investigated more carefully. First, recurrent hazards lead to repeated catastrophic and wear-induced failures, and maintenance actions of the nodes and links in the network, making the network performance exhibit a multimodal shape over time. There is a lack of methods for modeling such a multimodal performance curve, especially when the periods of impact of these hazards overlap. Second, it is difficult to interpret and assess the vulnerability and recoverability of the network with multimodal performance as it repeatedly shows rising, falling, or even steady trends under these multiple overlapping hazards. In this paper, we quantify the resilience of an engineered network that is subject to multiple recurrent hazards and exhibits multimodal performance over time. We first model the network performance by investigating the availability of each node or link under multiple recurrent hazards. Next, a segment division algorithm that reflects the operator's sensitivity to the performance variation trend is developed to divide the network's multimodal performance curve into multiple segments, each exhibiting a distinct variation trend. Based on this, two resilience metrics are proposed to reflect both the network performance level and its variation rate. The merits of the two metrics are highlighted by comparing them with some benchmark alternatives. Several managerial insights, such as the criticality of nodes and links, are illustrated through a case study on a heating pipeline network.