Solution for time-dependent resilience in the presence of gradual deterioration of performance

In this paper, a closed-form method is developed for the evaluation of time-dependent resilience (so named as it is a function of the service time of interest) of an aging object (e.g., a structure or system). These structures and systems often suffer from the deterioration of performances in a harsh service environment, causing the decline of serviceability. They are thus expected to be sufficiently resilient during their service lives, i.e., to have the ability to withstand disruptions to their performances. The proposed method takes into account the uncertainty associated with the performance deterioration process, the availability of resources that support the performance recovery, and the impact of a changing environment. The accuracy and improved efficiency of the proposed method are demonstrated through three examples. It is also shown through sensitivity analysis that the impact of a changing environment, and the availability of recovery-supporting resources play an essential role in the time-dependent resilience. The proposed resilience method can also be used to efficiently guide the design of new structures that meet predefined resilience goals.