Environmental Contour Lines: A Method for Estimating Long Term Extremes by a Short Term Analysis

Haver, Sverre; Winterstein, Steven R.

doi:10.5957/smc-2008-067

Cited by 38 publications

(35 citation statements)

References 3 publications

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“…For other types of structures, one may consider e.g., material quality, effects of erosion or corrosion as environmental quantities. 3 In some papers, such as [5], the failed states are defined as the states such that g(x, V ) < 0. This is just a matter of choice of notation.…”

Section: The Failure Probability Reliability and Approximation Methodsmentioning

confidence: 99%

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Buffered environmental contours

Dahl¹,

Huseby²

2018

Safety and Reliability – Safe Societies in a Changing World

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The main idea of this paper is to use the notion of buffered failure probability from probabilistic structural design, first introduced by [14], to introduce buffered environmental contours. Classical environmental contours are used in structural design in order to obtain upper bounds on the failure probabilities of a large class of designs. The purpose of buffered failure probabilities is the same. However, in constrast to classical environmental contours, this new concept does not just take into account failure vs. functioning, but also to which extent the system is failing. For example, this is relevant when considering the risk of flooding: We are not just interested in knowing whether a river has flooded. The damages caused by the flooding greatly depends on how much the water has risen above the standard level.

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Section: The Failure Probability Reliability and Approximation Methodsmentioning

confidence: 99%

“…A realistic model of the environmental loads and the resulting response is crucial for structural reliability analysis of mechanical constructions exposed to environmental forces. See [19] and [3]. For applications of environmental contours in marine structural design, see e.g., [1], [4], [9], [11] and [2].…”

Section: Introductionmentioning

confidence: 99%

Buffered environmental contours

Dahl¹,

Huseby²

2018

Safety and Reliability – Safe Societies in a Changing World

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“…So, we define a model for X and a model for Y conditional on X. There exist many examples in the literature of models within this conditional framework with applications in extremes, e.g., the conditional extreme value model (Heffernan and Tawn, 2004;Fougeres and Soulier, 2012), the Weibull-log normal distribution (Haver and Winterstein, 2009, henceforth the Haver-Winterstein distribution), and hierarchical models (Eastoe, 2019). Although conditional models are easy to interpret, it can be rather difficult to study the extremes of both Y and (X, Y ) within this class.…”

Section: Introductionmentioning

confidence: 99%

“…First, we consider the model described in Haver and Winterstein (2009), used to explain the dependence between extreme significant wave height and their associated wave periods. Secondly, we investigate the model of Heffernan and Tawn (2004).…”

Section: Introductionmentioning

confidence: 99%

Extremal Characteristics of Conditional Models

Tendijck¹,

Tawn²,

Jonathan³

2022

Preprint

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Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since the copula and marginals are not expressed in closed forms. We consider bivariate conditional models that specify the distribution of X and the distribution of Y conditional on X. We provide tools to quantify implicit assumptions on the extremes of this class of models. In particular, these tools allow us to approximate the distribution of the tail of Y and the coefficient of asymptotic independence η in closed forms. We apply these methods to a widely used conditional model for wave height and wave period. Moreover, we introduce a new condition on the parameter space for the conditional extremes model of Heffernan and Tawn (2004), and prove that the conditional extremes model does not capture η, when η < 1.

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“…Extreme responses of marine structures are often calculated using the environmental contour method [1,2]. The environmental contour method provides a computationally efficient approximation to a full long-term analysis [3], sometimes referred to as the 'all sea states approach'.…”

Section: Introductionmentioning

confidence: 99%

Marginal and total exceedance probabilities of environmental contours

Mackay,

Haselsteiner

2020

Preprint

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Various methods have been proposed for defining an environmental contour, based on different concepts of exceedance probability. In the inverse first-order reliability method (IFORM) and the direct sampling (DS) method, contours are defined in terms of exceedances within a region bounded by a hyperplane in either standard normal space or the original parameter space. The IFORM and DS contours at exceedance probability α pass through points with marginal exceedance probability α. In contrast, the more recent inverse second-order reliability method (ISORM) and highest density (HD) contours are defined in terms of an isodensity contour of the joint density function in either standard normal or original parameter space, where an exceedance is defined to be anywhere outside the contour. Contours defined in terms of the total probability outside the contour are significantly more conservative than contours defined in terms of marginal exceedance probabilities. In this work we study the relationship between the marginal exceedance probability of the highest point along an environmental contour and the total probability outside the contour. It is shown that the marginal exceedance probability of the contour maximum can be orders of magnitude lower than the total exceedance probability of the contour, with the differences increasing with the number of variables. For example, a 50-year ISORM contour for two variables at 3-hour time steps, passes through points with marginal return periods of 635 years, and the marginal return periods increase to 10,950 years for contours of four variables. It is shown that the ratios of marginal to total exceedance probabilities for DS contours are similar to those for IFORM contours. However, the exceedance probabilities of the maximum values along an HD contour are not in fixed relation to the contour exceedance probability, but depend on the shape of the joint density function. Examples are presented to illustrate the impact of the choice of contour on simple structural reliability problems, for cases where the use of contours defined in terms of either marginal or total exceedance probabilities may be appropriate. The examples show that, to choose an appropriate contour method, some understanding about the shape of a structure's failure surface is required.

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Environmental Contour Lines: A Method for Estimating Long Term Extremes by a Short Term Analysis

Cited by 38 publications

References 3 publications

Buffered environmental contours

Buffered environmental contours

Extremal Characteristics of Conditional Models

Marginal and total exceedance probabilities of environmental contours

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