Marginal and total exceedance probabilities of environmental contours.
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| Title: | Marginal and total exceedance probabilities of environmental contours. |
|---|---|
| Authors: | Mackay, Ed1 (AUTHOR) e.mackay@exeter.ac.uk, Haselsteiner, Andreas F.2,3 (AUTHOR) |
| Source: | Marine Structures. Jan2021, Vol. 75, pN.PAG-N.PAG. 1p. |
| Subjects: | Probability theory, Magnitude (Mathematics), Structural failures, Probability density function, Structural reliability, Coordinates |
| Abstract: | 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, corresponding to marginal exceedance probabilities under rotations of the coordinate system. 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 space or the 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 maximum value of each variable along an environmental contour and the total probability outside the contour. 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-h 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 marginal exceedance probabilities of the maximum values of each variable 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 highlight that to choose an appropriate contour method, some understanding about the shape of a structure's failure surface is required. • Different contour definitions can give significant differences in design conditions. • Return periods of largest values on contours can differ by orders of magnitude. • Structural failure probabilities can be significantly affected by choice of contour. • Appropriate choice of contour definition requires knowledge of structural response. [ABSTRACT FROM AUTHOR] |
| Copyright of Marine Structures is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Marginal and total exceedance probabilities of environmental contours. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mackay%2C+Ed%22">Mackay, Ed</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> e.mackay@exeter.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Haselsteiner%2C+Andreas+F%2E%22">Haselsteiner, Andreas F.</searchLink><relatesTo>2,3</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Marine+Structures%22">Marine Structures</searchLink>. Jan2021, Vol. 75, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Magnitude+%28Mathematics%29%22">Magnitude (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+failures%22">Structural failures</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+density+function%22">Probability density function</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+reliability%22">Structural reliability</searchLink><br /><searchLink fieldCode="DE" term="%22Coordinates%22">Coordinates</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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, corresponding to marginal exceedance probabilities under rotations of the coordinate system. 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 space or the 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 maximum value of each variable along an environmental contour and the total probability outside the contour. 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-h 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 marginal exceedance probabilities of the maximum values of each variable 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 highlight that to choose an appropriate contour method, some understanding about the shape of a structure's failure surface is required. • Different contour definitions can give significant differences in design conditions. • Return periods of largest values on contours can differ by orders of magnitude. • Structural failure probabilities can be significantly affected by choice of contour. • Appropriate choice of contour definition requires knowledge of structural response. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Marine Structures is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.marstruc.2020.102863 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Probability theory Type: general – SubjectFull: Magnitude (Mathematics) Type: general – SubjectFull: Structural failures Type: general – SubjectFull: Probability density function Type: general – SubjectFull: Structural reliability Type: general – SubjectFull: Coordinates Type: general Titles: – TitleFull: Marginal and total exceedance probabilities of environmental contours. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mackay, Ed – PersonEntity: Name: NameFull: Haselsteiner, Andreas F. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 09518339 Numbering: – Type: volume Value: 75 Titles: – TitleFull: Marine Structures Type: main |
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