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Entropy 2019, 21(1), 64; https://doi.org/10.3390/e21010064

Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height

1
College of Engineering, Ocean University of China, Qingdao 266100, China
2
College of Engineering, University of California Berkeley, Berkeley, CA 94720, USA
3
School of Management, Xi’an University of Architecture and Technology, Xi’an 710055, China
4
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
5
School of Forest Resources and Conservation, University of Florida, Gainesville, FL 32611, USA
*
Author to whom correspondence should be addressed.
Received: 6 November 2018 / Revised: 5 January 2019 / Accepted: 9 January 2019 / Published: 14 January 2019
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Abstract

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. View Full-Text
Keywords: maximum entropy function; copula function; recurrence level maximum entropy function; copula function; recurrence level
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Liu, G.; Chen, B.; Jiang, S.; Fu, H.; Wang, L.; Jiang, W. Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height. Entropy 2019, 21, 64.

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