Research Papers: Structures and Safety Reliability

Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method

[+] Author and Article Information
Arvid Naess

Centre for Ships and Ocean Structures;
Department of Mathematical Sciences,
Norwegian University of Science
and Technology,
Trondheim NO-7491, Norway
e-mail: arvid.naess@ntnu.no

Oleh Karpa

Centre for Ships and Ocean Structures,
Norwegian University of Science
and Technology,
Trondheim NO-7491, Norway
e-mail: oleh.karpa@ntnu.no

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received September 30, 2013; final manuscript received December 3, 2014; published online January 20, 2015. Assoc. Editor: Lance Manuel.

J. Offshore Mech. Arct. Eng 137(2), 021602 (Apr 01, 2015) (7 pages) Paper No: OMAE-13-1091; doi: 10.1115/1.4029370 History: Received September 30, 2013; Revised December 03, 2014; Online January 20, 2015

In the reliability engineering and design of offshore structures, probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as, e.g., wave heights and wind speeds (WS), application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the average conditional exceedance rate (ACER) method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method, it is possible to provide an accurate estimate of the extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the true extreme value distribution. When it has been ascertained that this cascade has converged, an estimate of the extreme value distribution has been obtained. In this paper, it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will be demonstrated for measured coupled WS and wave height data.

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Grahic Jump Location
Fig. 1

Map of the part of Scandinavia with marked location

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Fig. 2

Coupled observations of WS data (ξ axis) and Hs data (total sea, η axis)

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Fig. 3

Comparison between ACER estimates for different degrees of conditioning. WS data.

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Fig. 4

Comparison between ACER estimates for different degrees of conditioning. Hs (total sea).

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Fig. 5

Plot of ɛ∧2(ξ) versus WS ξ on a logarithmic scale for the optimized parameter values; ξ1=14.5

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Fig. 6

Plot of ɛ∧2(η) against wave heights η on a logarithmic scale for the optimized parameter values; η1=4.5

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Fig. 7

Comparison between bivariate ACER surface estimates for different degrees of conditioning. E∧k(ξ,η) surfaces are plotted on a logarithmic scale.

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Fig. 8

Contour plot of the empirically estimated E∧2(ξ,η) surface (•), optimized GL, GL2(ξ,η), (°), and optimized logistical, AL2(ξ,η), (—) surfaces. Boxes indicate levels on a logarithmic scale

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Fig. 9

Contour plot of the return period levels for E∧2(ξ,η) surface (•), optimized AL, AL2(ξ,η), (—), and optimized GL, GL2(ξ,η), (°) surfaces. Boxes indicate return period levels in years.




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