Optimized C-vine copula and environmental contour of joint wind-wave environment for sea-crossing bridges

Sea-crossing bridges are subjected to wind-wave environment, of which the extreme values obtained by univariate and bivariate distributions often overestimate the effects of wind and wave on the bridges. This study thus proposes an optimized canonical vine (C-vine) copula for constructing the joint probability distribution and environmental contour of mean wind speed, significant wave height and peak wave period for sea-crossing bridges. Multivariate correlation analysis is first recommended to identify the key variable. The one-step optimization method is then proposed to find the optimized C-vine copula which is more accurate and less uncertain compared with the currently-used method. The environmental contour of the three variables is also derived and its effectiveness is verified in terms of copula principles. The proposed approach is finally applied to a real seacrossing bridge site with the measurement data of mean wind speed, significant wave height and peak wave period. The results show that the key variable can be reasonably selected and the one-step optimization method significantly improves the accuracy compared with the currently-used method. The obtained environmental contour can provide the appropriate design values of wind and wave.