Copula in Resilience Assessment of the Built Environment

A copula is such a function that “couples” multiple one-dimensional marginal distribution functions to formulate a multivariate distribution function. The Gaussian copula is among the well-established copula types and has been widely used in literature. This is fundamentally motivated by the fact that the sum of independent Gaussian (normal) random variables also follows a normal distribution, with which a sequence of correlated normal variables can be treated as linear combinations of independent normal variables. Based on the Gaussian copula, one can employ the Nataf transformation method to generate samples for correlated variables, which is, in particular, useful in simulation-based studies. The application of Gaussian copula in the resilience evaluation of the built environment is discussed in this chapter, where spatially correlated random variables are involved. Through illustrative examples it is demonstrated that ignoring the spatial correlation of variables would not always lead to a conservative or nonconservative estimate of resilience, due to the impacts of other dominating factors such as the post-hazard recovery strategies. As a result, when evaluating the resilience of, for example, a building portfolio, or an infrastructure system, one would need to reasonably incorporate the correlation between the capacities and load effects of spatially distributed components, where the use of Gaussian copula is beneficial in constructing the joint distributions of the correlated variables.