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

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 64 ◽  
Author(s):  
Guilin Liu ◽  
Baiyu Chen ◽  
Song Jiang ◽  
Hanliang Fu ◽  
Liping Wang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Maximum Entropy ◽  
Wave Height ◽  
Joint Distribution ◽  
Height Function ◽  
Copula Function ◽  
Wave Period ◽  
Ocean Engineering ◽  
Joint Distribution Function ◽  
Design Wave Height

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.

scholarly journals Synchronous asynchronous encounter analysis of runoff between reservoirs based on Copula function

2019 ◽  
Vol 81 ◽  
pp. 01021
Author(s):  
Weidong Zhao ◽  
Jing Zhang
Keyword(s):  
Distribution Function ◽  
Water Resources ◽  
Water Supply ◽  
Joint Distribution ◽  
Goodness Of Fit ◽  
Copula Function ◽  
Joint Distribution Function ◽  
Goodness Of Fit Test ◽  
Flood Water ◽  
Encounter Probability

Based on goodness-of-fit test on Copula function, we got the best fitted joint distribution function of runoff between D and H reservoirs. Then we analyzed the synchronous asynchronous encounter probability of runoff. The synchronous encounter probability of runoff was 72.46%, while the asynchronous of dryness-wetness or wetness-dryness encounter probability was only 1.06% between D and H reservoirs. The results showed that the runoff conditions were not conducive to the runoff compensation. In order to satisfy the target of water supply, we should also study the reservoir optimization operation, store water in advance and exploit the reservoir regulating potentialities on flood water resources.

scholarly journals Method of Fusion Diagnosis for Dam Service Status Based on Joint Distribution Function of Multiple Points

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Zhenxiang Jiang ◽  
Jinping He
Keyword(s):  
Distribution Function ◽  
Joint Distribution ◽  
Copula Function ◽  
Joint Distribution Function ◽  
Multiple Points ◽  
Measuring Point ◽  
Diagnosis Method ◽  
T Copula ◽  
Abnormal Point

The traditional methods of diagnosing dam service status are always suitable for single measuring point. These methods also reflect the local status of dams without merging multisource data effectively, which is not suitable for diagnosing overall service. This study proposes a new method involving multiple points to diagnose dam service status based on joint distribution function. The function, including monitoring data of multiple points, can be established with t-copula function. Therefore, the possibility, which is an important fusing value in different measuring combinations, can be calculated, and the corresponding diagnosing criterion is established with typical small probability theory. Engineering case study indicates that the fusion diagnosis method can be conducted in real time and the abnormal point can be detected, thereby providing a new early warning method for engineering safety.

Revisiting statistical properties of surf parameter with characteristic wave parameters for single random waves including spectral bandwidth effects

2021 ◽  
pp. 147509022110353
Author(s):  
Dag Myrhaug ◽  
Hong Wang ◽  
Lars Erik Holmedal ◽  
Hongtao Li
Keyword(s):  
Wave Height ◽  
Joint Distribution ◽  
Parametric Model ◽  
Wave Period ◽  
Small Scale ◽  
Spectral Bandwidth ◽  
Joint Distributions ◽  
Wide Range ◽  
Rubble Mound ◽  
Rubble Mound Breakwaters

Results from a comparative study of the joint distribution of surf parameter and wave period are provided. First, two transformed joint distributions of wave height and wave period are compared. One of the distributions is a parametric model originating from a best fit to relatively broad-band field data covering a wide range of wave conditions, whilst the other distribution is theoretically based. It appears that the theoretically based distribution does not represent the features of the parametric model especially well, suggesting that parametric models should be used to describe relatively broad-banded data. Then, the theoretically based joint distribution of wave height and wave period is transformed to the joint distributions of surf parameter with wave height and wave period and it is demonstrated how these distributions are affected by the spectral bandwidth. Finally, the theoretically based distribution of wave height and wave period is also transformed to the joint distribution of wave runup time and wave period due to its relation to the stability of rubble-mound breakwaters. Comparisons are made with a limited set of data representing results from small-scale laboratory experiments related to stability of rubble-mound breakwaters. The agreement between measurements and predictions of the distribution of the surf parameter is fair, whilst the agreement is poorer for the probability of resonance.

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