Multivariate reliability method using the environment contour model based on C-vine copulas

This study aims to develop a new technique for deriving the reliability index in original physical space using C-vine copula models integrated with the environmental contour method. In the proposed approach, the minimum of the reliability index is considered an objective function, whereas the coordinates on the environmental contour satisfying the limit state equation are treated as the constraint. These components are formulated as a non-linear constrained optimisation problem. The validity of this method is illustrated through four examples of its application, and the computed reliability index is compared with the results yielded by the existing sampling method. The findings confirm the superiority of the proposed technique. Compared with sampling simulation techniques, it is easier to obtain the critical environmental contour and the design point. Due to a pair-copula construction technique being applied to obtain high-dimensional vine copula models, the multivariate environmental contours are determined, which overcomes the limitation of existing contour line methods that are only used for solving low-dimensional problems. Unlike the first-order reliability method constructed in standard normal space, this new algorithm solves in the original physical space of random variables, making the calculation principles more transparent and easier to understand.