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Ocean Engineering

Prediction of Extreme Tether Tension for a TLP by the AUR and ACER Methods

[+] Author and Article Information
A. Naess

Centre for Ships & Ocean Structures and Department of Mathematical Sciences,  Norwegian University of Science and Technology, NO-7491 Trondheim, Norwayarvidn@math.ntnu.no

C. T. Stansberg

MARINTEK AS, NO-7491 Trondheim, Norwaycarl.t.stansberg@marintek.sintef.no

O. Batsevych

Kongsberg Maritime, NO-3194 Horten, Norwayoleksandr.batsevych@kongsberg.com

J. Offshore Mech. Arct. Eng 134(2), 021103 (Dec 02, 2011) (9 pages) doi:10.1115/1.4004954 History: Received December 10, 2009; Revised October 19, 2010; Published December 02, 2011; Online December 02, 2011

The paper presents a study of the extreme value statistics related to measurements on a scale model of a large tension leg platform (TLP) subjected to random waves in a wave basin. Extensive model tests were carried out in three irregular sea states. Time series of the motion responses and tether tension were recorded for a total of 18 three hour tests (full scale). In this paper we discuss the statistics of the measured tether tension. The focus is on a comparison of two alternative methods for the prediction of extreme tether tension from finite time series records. One method is based on expressing the extreme value distribution in terms of the average upcrossing rate (AUR). The other is a novel method that can account for statistical dependence in the recorded time series by utilizing a cascade of conditioning approximations obtained by defining the average conditional exceedance rates (ACER). Both methods rely on introducing a specific parametric form for the tail part of the extreme value distribution. This is combined with an optimization procedure to determine the parameters involved, which allows prediction of various extreme response levels.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Heidrun TLP as seen from the side

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Figure 2

Short time series samples of wave elevation and tether tension T10, with a ringing event caused by a steep wave

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Figure 3

Cumulative peak distribution of tether tension T10. 18-hours, test 3210. —-: fitted Rayleigh distribution; --: fitted Weibull distribution to tail data.

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Figure 4

Power spectrum of tension in tether T10

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Figure 5

Log plot of empirical AUR (—-) with extrapolation by optimally fitted curve (--), Sea state 1. -·-: optimized 95% confidence band; ····: reanchored empirical 95% confidence band. logq = −0.5479, b = 10,953.1, a = 0.1678, c = 0.3667.

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Figure 6

Optimal transformed plot of empirical AUR (—-) with extrapolation by optimally fitted curve (--), Sea state 1. ····: empirical 95% confidence band.

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Figure 7

Log plot of empirical ACER ɛk(η), k= 1, 2, 3, 4, Sea state 1

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Figure 8

Log plot of empirical ACER ɛ3(η) (—-) with extrapolation by optimally fitted curve ( --), Sea state 1. -·-: optimized 95% confidence band; ····: reanchored empirical 95% confidence band. logq = −2.5717, b = 15,730.3, a = 0.0609, c = 0.4327.

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Figure 9

Optimal transformed plot of empirical ACER ɛ3(η) (—-) with extrapolation by optimally fitted curve (--), Sea state 1. ····: empirical 95% confidence band.

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Figure 10

Log plot of empirical AUR (—-) with extrapolation by optimally fitted curve ( --), Sea state 2. -·-: optimized 95% confidence band; ····: reanchored empirical 95% confidence band. logq = −2.5913, b = 9487.68, a = 0.0059, c = 0.6673.

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Figure 11

Optimal transformed plot of empirical AUR (—-) with extrapolation by optimally fitted curve ( --), Sea state 2. ····: empirical 95% confidence band.

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Figure 12

Log plot of empirical ACER ɛk(η), k = 1, 2, 3, 4, Sea state 2

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Figure 13

Log plot of empirical ACER ɛ3(η) (—-) with extrapolation by optimally fitted curve ( --), Sea state 2. -·-: optimized 95% confidence band; ····: reanchored empirical 95% confidence band. logq = 5.7730, b = 4301.65, a = 0.7426, c = 0.2768.

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Figure 14

Optimal transformed plot of empirical ACER ɛ3(η) (—-) with extrapolation by optimally fitted curve ( --), Sea state 2. ····: empirical 95% confidence band.

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Figure 15

Log plot of empirical AUR (—-) with extrapolation by optimally fitted curve ( --), Sea state 3. -·-: optimized 95% confidence band; ····: reanchored empirical 95% confidence band. logq = 5.4643, b = 998.587, a = 0.3480, c = 0.3533.

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Figure 16

Optimal transformed plot of empirical AUR (—-) with extrapolation by optimally fitted curve ( --), Sea state 3. ····: empirical 95% confidence band.

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Figure 17

Log plot of empirical ACER ɛk(η), k = 1, 2, 3, 4, Sea state 3

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Figure 18

Log plot of empirical ACER ɛ3(η) (—-) with extrapolation by optimally fitted curve ( --), Sea state 3. -·-: optimized 95% confidence band; ····: reanchored empirical 95% confidence band. logq = 0.4915, b = 5548.4, a = 0.0337, c = 0.5386.

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Figure 19

Optimal transformed plot of empirical ACER ɛ3(η) (—-) with extrapolation by optimally fitted curve ( --), Sea state 3. ····: empirical 95% confidence band.

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