Liu Guilin, Chen Baiyu, Jiang Song, Fu Hanliang, Wang Liping, Jiang Wei
College of Engineering, Ocean University of China, Qingdao 266100, China.
College of Engineering, University of California Berkeley, Berkeley, CA 94720, USA.
Entropy (Basel). 2019 Jan 14;21(1):64. doi: 10.3390/e21010064.
Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period.
波高和波周期是用于描述波浪随机性的重要海洋环境因素。在海洋工程领域，设计波高的计算具有重要意义。本文通过坐标变换和求解条件变分问题，推导了一个具有四个待定参数的周期最大熵分布函数。还推导了波高和波周期的双熵联合分布函数。该函数借助Copula函数的结构，由最大熵波高函数和最大熵周期函数推导得出。波高和波周期的双熵联合分布函数不受弱非线性限制，也不受正态随机过程和窄谱限制。此外，由于它包含许多待定参数，能够更细致地拟合观测数据，更广泛地适用于各种情况下的非线性波浪。工程实例表明，由双熵联合分布函数得出的重现水平高于使用波高或波周期单变量的极值分布得出的重现水平，也高于传统的波高和波周期联合分布函数得出的重现水平。
