3-Dimensional direct sampling-based environmental contours using a semi-parametric joint probability model

Abstract

Environmental contours are often utilized in response analysis and design of offshore structures. Properly modeling the multivariate joint probability distributions (JPD) of ocean environmental variables (e.g., wind speed, wave height, and wave period) is fundamental to constructing environmental contours. In this paper, we present an environmental contour construction procedure based on the direct sampling method. The procedure is a semi-parametric joint probability model designed to build the multivariate JPD of ocean environmental variables using a log-transformed kernel density estimation (KDE)-Paretotails approach to calculate statistical characteristics and estimate the marginal cumulative distributions (MCDs) and the vine copula using bivariate copulas as building blocks to fully define the complex dependence structures between MCDs. Furthermore, the importance sampling technique, which can easily be generalized to any dimension, was used to generate kept samples. The proposed model can accommodate three or higher dimensional direct sampling-based environmental contours and was shown by GOF tests to be well suited to building the multivariate JPDs of ocean environmental variables.