Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

Global sensitivity analysis (GSA) plays an important role in uncertainty analysis and quantification. Conventional GSA for structures requires tackling two main challenges: (1) the incomplete probability information of inputs and (2) the effects caused by the static/dynamic correlation of random variables or stochastic processes. In this paper, two kinds of novel copula-based methods for variance-based GSA are proposed to address these challenges. Based on the known samples, the proposed methods can choose the optimal copula function to construct the joint distribution of inputs, and compute the global sensitivity indices combined with Monte Carlo (MC) simulation. Time-variant copula function is used to generate the samples of time series which are both auto-correlated and cross-correlated, and the proposed methods are extended to develop time-variant GSA of dynamic structures with correlated random variables and stochastic processes. Four engineering examples are given to illustrate the good applicability and capability of the proposed methods for the dependent model functions under incomplete probability information.