Improved Method for Calculating Exceedance Probabilities of Environmental Contours

Abstract

Environmental contours is commonly applied in e.g. ship design. The aim of this thesis is to study different methods of constructing environmental contours of sea states, and look at properties of these. Especially we will look at estimation of exceedance probabilities. Estimation of exceedance probabilities are done through Monte Carlo simulation. This is not a trivial task, since in principal we have to examine an unlimited amount of possible failure regions. In this thesis we use a new method of doing this. The method will be used on a number of examples where the joint distribution of the sea states is estimated from real data. We will also explore the case when the joint distribution is a mixture of distributions. This is of interest since it can model e.g, seasonal variations or variations of wave directions. For all examples we will compare the new method to former methods of estimating exceedance probabilities. Traditionally, environmental contours are constructed based on the well-known Rosenblatt transformation. There is, however, a challenge to this approach; due to the effects of the transformation, the probabilistic properties of the resulting environmental contour can be difficult to interpret. The tendency is for Rosenblatt contours to have exceedance probabilities higher than desired. In this thesis we will use our new method to evaluate the Rosenblatt contour and use the evaluation as basis to adjust the contours to the desired exceedance probability. Finally, we will compare the adjusted Rosenblatt contours to the contours constructed by Monte Carlo simulations, to see which contour is best in different applications.