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Safety and Reliability

# The Hermite Moment Model for Highly Skewed Response With Application to Tension Leg Platforms

[+] Author and Article Information
Myoungkeun Choi

Department of Civil Engineering, Texas A&M University, 3136 TAMU, College Station, TX 77843-3136myoungchoi@gmail.com

Bert Sweetman

Department of Civil Engineering, Texas A&M University, 3136 TAMU, College Station, TX 77843-3136sweetman@tamu.edu

J. Offshore Mech. Arct. Eng 132(2), 021602 (Mar 10, 2010) (8 pages) doi:10.1115/1.4000398 History: Received August 14, 2008; Revised June 17, 2009; Published March 10, 2010; Online March 10, 2010

## Abstract

A new addition to the statistical Hermite moment model of extremes is introduced for use on processes with high skewness and near-Gaussian kurtosis. The monotone limits of the existing model are expressed as ellipses in response moment space and a new methodology is introduced that combines hardening and softening models to overcome these limits. The result is that any fractile of a distribution described by its first four statistical moments can be transformed to or from the Gaussian. An example application to a tension leg platform is presented.

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## Figures

Figure 8

Statistical moments based on short durations used to predict 90 min maximum. All statistics based on 20 simulations.

Figure 1

Various regions of model applicability

Figure 2

Practical, softening monotone and hardening monotone limits in Hermite moment space

Figure 3

Combination of nonmonotone hardening and softening models into a single monotonic transformation. (a) Region III: softening-hardening-softening required for piecewise monotone (α3=−0.2651, α4=3.0072, and t=4400 s). (b) Region IV: hardening-softening-hardening required for piecewise monotone (α3=−0.2402, α4=2.9885, and t=4700 s).

Figure 4

Tension leg platform

Figure 5

Hermite extreme value estimation: a single realization with statistical moments shifting between monotone and nonmonotone models used to predict 90 min maximum

Figure 6

PDF comparison: standardized softening-hardening-softening, hardening-softening-hardening, and monotone responses (4700 s, 5000 s, and 5300 s in Table 1)

Figure 7

Histogram of 4100 s simulated response compared with theoretical PDFs based on α3=−0.2654 and α4=3.0360

## Errata

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