ABSTRACT:

The Rayleigh-Stokes model has been widely applied to represent the probability distribution function of crests and troughs of weakly nonlinear random processes. In this study, the parameter estimates for the three-parameter Rayleigh-Stokes probability distribution function are obtained from application of two moment-based empirical parameter estimation methods, i.e. conventional method of moments and method of linear moments. Monte-Carlo simulations are utilized to compare the performance of these parameter estimation approaches in estimating the parameters of the Rayleigh-Stokes distribution and also to evaluate the uncertainty of the extreme statistics. Additionally, the effect of sample size on the uncertainty of the model statistics is evaluated. Finally, the Rayleigh-Stokes model is utilized to estimate the probability distribution function of disturbed wave crests beneath a mini-TLP and the model performance is evaluated.

INTRODUCTION

The Rayleigh-Stokes model is a well-known probability distribution function in the field of ocean wave mechanics and is widely utilized to estimate the probability distribution function of weakly non-linear wave crests. The model initially developed by Tayfun (1980) for offshore wave crests was based on the assumptions that:

  1. waves can be modeled as a narrow-banded random process and consequently the wave crests of the linear waves follow the Rayleigh law (Longuet- Higgins 1952), and

  2. wave elevations can be approximated by second order Stokes wave theory.

In the Tayfun's Rayleigh-Stokes model the distribution structure was derived analytically and the underlying model parameter were obtained from its theoretical relation with the significant wave height and mean wave period. The model structure and the estimate of model parameter were subsequently modified by other researches (Arhan and Plaisted 1981, Kriebel and Dawson 1991 and 1993, Tung and Huang 1985, Tayfun 2006). However, the different representations of the second-order Rayleigh-Stokes model converge to almost identical results for deepwater conditions.

Keywords:
extreme statistics, subsea system, engineering, rayleigh-stoke model, error distribution, offshore, crest, molm, distribution parameter, model parameter
Subjects:
Offshore Facilities and Subsea Systems, Information Management and Systems
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2011. The International Society of Offshore and Polar Engineers
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