Convex Environmental Contours for Non-Stationary Processes

TL;DR

This paper develops a theoretical framework for convex environmental contours applicable to non-stationary processes, enhancing marine structure design by accounting for increasing extreme sea-states.

Contribution

It generalizes existing convex contour theory to non-stationary environmental processes, providing new definitions and minimal conditions for their existence.

Findings

Established existence conditions for convex contours in non-stationary processes

Proposed two definitions based on exceedance times and quantiles

Included empirical examples demonstrating contour construction methods

Abstract

Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we consider convex contours based on the assumption of convex failure sets. We provide a rigorous foundation for the existence of such contours when the underlying environmental factors are modelled by a general, possibly non-stationary, process. This constitutes a generalisation of existing theory and is done to properly account for empirically observed increases in extreme sea-states. Two definitions are proposed, based respectively on averages or quantiles of exceedence times, along with minimal conditions on the environmental processes to guarantee existence. In order to illustrate these methods we give two examples, including an empirical study containing a method for constructing contours based on the presented theory.