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

Area of Science:

• Ocean Engineering
• Probability Theory
• Statistical Modeling

Background:

• Wave height and wave period are critical oceanic factors influencing wave randomness.
• Accurate calculation of design wave height is essential in ocean engineering.
• Existing models may be limited by assumptions like weak nonlinearity or narrow spectra.

Purpose of the Study:

• To derive a novel periodic maximum entropy distribution function.
• To develop a double entropy joint distribution function for wave height and period.
• To enhance the applicability and accuracy of wave characteristic analysis in ocean engineering.

Main Methods:

• Derivation of a periodic maximum entropy distribution using coordinate transformation and variational problems.
• Construction of a double entropy joint distribution function utilizing Copula function structures.
• Application of the derived function to engineering cases for recurrence level assessment.

Main Results:

• A four-parameter periodic maximum entropy distribution function was successfully derived.
• A double entropy joint distribution function for wave height and period was established.
• The new joint distribution function demonstrated superior performance in fitting data and wider applicability to nonlinear waves.

Conclusions:

• The double entropy joint distribution function overcomes limitations of traditional methods, including nonlinearity and narrow spectrum assumptions.
• This function provides more accurate and reliable recurrence level estimations than single-variable extreme value distributions or traditional joint distributions.
• The derived function offers improved applicability for diverse nonlinear wave scenarios in ocean engineering.