A New Approach for Environmental Contour and Multivariate De-Clustering

Abstract

When the long term behaviour of a floating unit is assessed, the environmental contour concept is often applied together with IFORM (Inverse First Order Reliability Method). This approach avoids direct computation on all sea-states, which is computationally very demanding, and most often simply not feasible. Instead, only a few conditions (the contour) are assessed and results in an accurate estimate of the long term extreme. However, most of available methods to derive the contour require the knowledge of the joint distribution of the different random variables (waves, wind, current...), which is often difficult to derive accurately. In fact, some complex dependences exist and are attempted to be simplified in too few coefficients. Another limitation of current environmental contour is its difficulty to deal with the dependence issue. Indeed, extreme sea-states arise by groups (storms, hurricanes...) and are not independent. While de-clustering techniques exist and are quite straightforward in univariate problems, this becomes difficult when the number of dimension increases. In an attempt to tackle those challenges, this paper presents a novel approach to derive IFORM contours. The method does not require any joint distribution and makes use of much more degrees of freedom to capture the dependence between variables. It also allows for an easy de-clustering. The approach is illustrated on two locations, using actual hindcast data of significant wave height and period; the resulting contours are compared to the ones obtained with more traditional methods.

Long-term extreme response of an offshore turbine: How accurate are contour-based estimates?

“…The second simplification is related to the assumption about the failure surface, made in the construction of the contour. IFORM contours [4] (and various alternative formulations [46,47], which we also refer to here as IFORM methods) are based on the assumption that a structure's failure surface can be linearized at the design point (the point on the failure surface with the highest probability of occurrence). Under this assumption, multivariate extreme sets are defined as half-plane regions, corresponding to the linearized failure surface, which contain a fixed probability level a.…”

“…serial correlation on environmental contours and estimates of longterm extreme loads has been discussed in Refs. [15,47]. The two challenges associated with offshore wind turbines, dealing with the non-monotonic response and jointly dealing with wind and wave variables, are less understood.…”

Environmental contours as Voronoi cells

“…Environmental contours continues to be an active area of research, and several modified approaches have been suggested in recent years, e.g., a dynamical IFORM method [19], a modified approach to account for non-monotonic behaviour of the responses [20], an approach including preprocessing and principal component analysis prior to estimating IFORM contours [21], contours for sub-populations such as directional sectors or seasonality [22,23], contours for a combination of circular and linear variables [24], contours for copula-based joint distributions [25,26] and contours based on a direct IFORM approach [27]. Contours for buffered failure probabilities were proposed in [28] and contours based on a particular version of the inverse second order reliability method (ISORM) were derived in [29].…”

“…The term in brackets correspond to the Hessian on a Riemann manifold, and we may therefor write A(θ) = Hess(C(θ)) + g(θ)C(θ). (27)…”

Marginal and total exceedance probabilities of environmental contours

“…In the following we assume that a model has been estimated for the joint distribution and contours are to be derived from the joint distribution. There is a wide range of definitions of environmental contours, such as the isodensity contour methods proposed by Haver [13,27], NORSOK [28, p. 12] and DNV GL [29,Section 3.7.2.4], methods based on joint exceedance regions [24], or methods based on univariate analyses [30]. In the present work we focus on four types of contour, namely IFORM, ISORM, DS and HD contours, due to their analogous definitions in terms of either marginal or total exceedance probabilities.…”