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Research Papers: Ocean Engineering

On the Estimation of Ocean Engineering Design Contours

[+] Author and Article Information
Philip Jonathan

Shell Projects & Technology,
Brabazon House,
Manchester M22 0RR, UK
e-mail: philip.jonathan@shell.com

Kevin Ewans

Sarawak Shell Bhd,
eTiQa Twins (Level 23, Tower 1),
Kuala Lumpur 50450, Malaysia
e-mail: kevin.ewans@shell.com

Jan Flynn

Shell International Exploration and Production,
P.O. Box 60,
AB Rijswijk 2280, The Netherlands
e-mail: jan.flynn@shell.com

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received May 3, 2011; final manuscript received April 25, 2014; published online July 16, 2014. Assoc. Editor: John Halkyard.

J. Offshore Mech. Arct. Eng 136(4), 041101 (Jul 16, 2014) (8 pages) Paper No: OMAE-11-1040; doi: 10.1115/1.4027645 History: Received May 03, 2011; Revised April 25, 2014

Understanding extreme ocean environments and their interaction with fixed and floating structures is critical for offshore and coastal design. Design contours are useful to describe the joint behavior of environmental, structural loading, and response variables. We compare different forms of design contours, using theory and simulation, and present a new method for joint estimation of contours of constant exceedance probability for a general set of variables. The method is based on a conditional extremes model from the statistics literature, motivated by asymptotic considerations. We simulate under the conditional extremes model to estimate contours of constant exceedance probability. We also use the estimated conditional extremes model to estimate other forms of design contours, including those based on the first-order reliability method (FORM), without needing to specify the functional forms of conditional dependence between variables. We demonstrate the application of new method in estimation of contours of constant exceedance probability using measured and hindcast data from the Northern North Sea, the Gulf of Mexico, and the North West Shelf of Australia, and quantify their uncertainties using a bootstrap analysis.

Copyright © 2014 by ASME
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References

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Ewans, K. C., and Jonathan, P., 2014, “Evaluating Environmental Joint Extremes for the Offshore Industry,” J. Mar. Syst., 130, pp. 124–130. [CrossRef]
Jonathan, P., Ewans, K. C., and Randell, D., 2013, “Joint Modeling of Environmental Parameters for Extreme Sea States Incorporating Covariate Effects,” Coastal Eng., 79, pp. 22–31. [CrossRef]
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Figures

Grahic Jump Location
Fig. 1

Contours C1-C4 (see Sec. 3) corresponding to the HSTP model (see Sec. 4) (equivalent to a 1 in 1000 event of HS marginally): C1 (dashed black), C2 (solid gray), C3 (dashed gray), and C4 (solid black). Also shown is a random sample of 1000 values from the model.

Grahic Jump Location
Fig. 2

True (gray) and estimated (black) contour C1 corresponding to the HSTP model (equivalent to a 1 in 1000 event of HS marginally), as a function of angle θ, for θ ∈ [0,360). HS(θ) is the solid line, and TP(θ) is the dashed line. Thick lines correspond to the bootstrap median, thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 3

True (gray) and estimated (black) contour C2 corresponding to the HSTP model (equivalent to a 1 in 1000 event of HS marginally), as a function of angle θ, for θ ∈ [0,360). HS(θ) is the solid line, and TP(θ) is the dashed line. Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 4

True (gray) and estimated (black) contour C3 corresponding to the HSTP model (equivalent to a 1 in 1000 event of HS marginally), as a function of angle θ, for θ ∈ [0,360). HS(θ) is the solid line, and TP(θ) is the dashed line. Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 5

True (gray) and estimated (black) contour C4 corresponding to the HSTP model (equivalent to a 1 in 1000 event of HS marginally), as a function of angle θ, for θ ∈ [0,360). HS(θ) is the solid line, and TP(θ) is the dashed line. Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 6

Estimated contours of constant exceedance probability, one-sided in HS, (equivalent to 10-, 100-, and 1000-yr HS marginally), for measured Northern North Sea sample. Also shown is the sample.

Grahic Jump Location
Fig. 7

Estimated contours of constant exceedance probability, one-sided in HS, (equivalent to 10-, 100-, and 1000-yr HS marginally), for hindcast Northern North Sea sample. Also shown is the sample.

Grahic Jump Location
Fig. 8

Estimated contours of constant exceedance probability, one-sided in HS, (equivalent to 10-, 100-, and 1000-yr HS marginally), for measured Gulf of Mexico sample. Also shown is the sample.

Grahic Jump Location
Fig. 9

Estimated contours of constant exceedance probability, one-sided in HS, (equivalent to 10-, 100-, and 1000-yr HS marginally), for hindcast North West Shelf of Australia sample. Also shown is the sample.

Grahic Jump Location
Fig. 10

Estimated contour of constant exceedance probability, one-sided in HS (equivalent to the 100-yr HS marginally), for measured Northern North Sea sample, as a function of angle θ, for θ ∈ [0,360). HS(θ) (solid), and TP(θ) (dashed). Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 11

Estimated contour of constant exceedance probability, one-sided in HS (equivalent to the 100-yr HS marginally), for hindcast Northern North Sea sample, as a function of angle θ, for θ ∈ [0,360). HS(θ) (solid), and TP(θ) (dashed). Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 12

Estimated contour of constant exceedance probability, one-sided in HS (equivalent to the 100-yr HS marginally), for measured Gulf of Mexico sample, as a function of angle θ, for θ ∈ [0,360). HS(θ) (solid), and TP(θ) (dashed). Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 13

Estimated contour of constant exceedance probability, one-sided in HS (equivalent to the 100-yr HS marginally), for hindcast North West Shelf of Australia sample, as a function of angle θ, for θ ∈ [0,360). HS(θ) (solid), and TP(θ) (dashed). Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 14

Estimated contour of constant probability density on standard normal scale (C1), equivalent to the 100-yr HS marginally, for measured Northern North Sea sample, as a function of angle θ, for θ ∈ [0,360). HS(θ) (solid), and TP(θ) (dashed). Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 15

Estimated contour of constant probability density on standard normal scale (C1), equivalent to the 100-yr HS marginally, for hindcast Northern North Sea sample, as a function of angle θ, for θ ∈ [0,360). HS(θ) (solid), and TP(θ) (dashed). Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 16

Estimated contour of constant probability density on standard normal scale (C1), equivalent to the 100-yr HS marginally, for measured Gulf of Mexico sample, as a function of angle θ, for θ ∈ [0,360). HS(θ) (solid), and TP(θ) (dashed). Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

Grahic Jump Location
Fig. 17

Estimated contour of constant probability density on standard normal scale (C1), equivalent to the 100-yr HS marginally, for hindcast North West Shelf of Australia sample, as a function of angle θ, for θ ∈ [0,360). HS(θ) (solid), and TP(θ) (dashed). Thick lines correspond to the bootstrap median and thin lines to a bootstrap 95% uncertainty band.

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