基于最大熵原理的非Rayleigh海浪波高的统计分布

Probability Distribution of Wave Heights of Non-Rayleigh Sea Waves Based on the Maximum Entropy Principle

在最大熵原理的基础上，通过解一个条件变分问题导出一种适用于描述非Rayleigh海浪波高H统计分布的概率密度函数f4（H）=aH^re^-βH^4，并将其参量α，β，γ以H的1～4阶分布矩（H^m^——m=1，2，3，4）显式地表示出来。用实验室风浪槽中不同风速下和不同风区处实测的36组风浪波高数据对上式进行验证，并与至今仍被广泛应用的瑞利波高概率密度函数加以比较。结果显示瑞利概率密度函数显著的偏离实验数据，而上式则与各组实测波高分布均符合良好。

A maximum entropy probability density function（PDF） for the wave height H of non-Rayleigh sea waves f4（H）=aH^re^-βH^4,, is derived through solving a conditional variation problem based on the maximum entropy principle, and its parameters a, 13 and 7 are expressed explicitly in terms of the distribution moments of H （H^m^--,m = 1,2, 3, 4）, To test the validity, the maximum entropy distribution is compared with thirty-six observed the above distributions of wave heights measured at different wind speeds and fetches in a wind-wave tunnel, along with the Rayleigh PDF which has been Widely employed to describe the distribution of sea wave heights. The results shown that while the Reyleigh PDF deviates significantly form the observed distributions, the above PDF agree quite well with them.