| A New Maximum Entropy Probability Function for the Surface Elevation of Nonlinear Sea Waves |
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| 作者姓名： | 张立振 徐德伦 |
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| 作者单位： | [1]Department of Applied Mathematics, Ocean University of China, Qingdao 266071, China [2]Physical Oceanography laboratory, Ocean University of China, Qingdao 266003, China |
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| 基金项目： | This work is financially supported by the National Natural Science Foundation of China （Grant No. 40490263 and No. 40276006） |
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| 摘 要： | Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.
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| 关 键 词： | 熵 概率密度函数 海洋工程 波浪 标高 非线性模型 |
| 收稿时间： | 2005-07-14 |
| 修稿时间： | 2005-10-08 |
A New Maximum Entropy Probability Function for the Surface Elevation of Nonlinear Sea Waves |
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| ZHANG Li-zhen , XU De-lun.A New Maximum Entropy Probability Function for the Surface Elevation of Nonlinear Sea Waves[J].China Ocean Engineering,2005,19(4):637-646. |
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| Authors: | ZHANG Li-zhen XU De-lun |
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| Abstract: | Based on the maximum entropy principle a new probability density function (PDF) f(x) for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f(x). Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits: (1) it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; (2) these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; (3) the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and (4) the PDF is simple in form and hence convenient for theoretical and practical uses. Laboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF. |
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| Keywords: | maximum entropy probability density function (PDF) Gram-Charlier PDF beta PDF |
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