A generalized index for functionality-sensitive resilience quantification

The resilience index based on the integral of functionality/performance function within a time interval of interest has been widely used in the literature. However, it cannot fully reflect the sensitivity of the resilience of the object (e.g., structure or system) to the variation of functionality. In this paper, a generalized index is proposed to measure the resilience of structures and systems that is sensitive to the instantaneous functionality, as reflected by a generating function involved in the proposed resilience index. The mathematical properties of the proposed resilience model are discussed. It is proven that, the proposed index varies within [0,1], and is a monotone measure. If the generating function is a power function with α being the exponent (called α-fairness function), the additivity property (i.e., superadditivity, additivity, and subadditivity) of the resilience index is dependent on the value of α. It is also observed that the existing resilience index is a special case of the proposed one. A byproduct is that, with a properly selected generating function, the time-dependent reliability problem of an aging structure can also be described by the proposed resilience index. The applicability of the proposed resilience model is demonstrated through four examples.