Extreme-value Distributions Of Run Lengths In Wave Group

Wave group is a group of continuous large waves in random wave train.Wave group has important influence on the stability of seawall,the rolling motion of ship,the overflow of dam top,the vibration of pile column structure and so on.The wave numbers of wave groups whose wave height is greater than a certain level are called positive run length.We study the distribution of the maximum and minimum of the positive run length of wave groups by using the travel theory,the statistical theory of the run and the first order Markov chain.The specific research contents and conclusions are as follows:（1）The numerical simulation steps of wave group are introduced in detail,and the numerical simulation program of wave group is written with Matlab,and the reference formula for the selection of numerical simulation duration and parameter M is given.（2）The analysis method of the existing theory of the maxima wave group run length is explored,and two shortcomings are found:firstly,the incompleteness of the wave height sequence is not considered;secondly,the relation between total run length,total run number,total wave height number and positive and negative run length is not fully considered.（3）In this paper,an improved analysis method for the run length of the extreme value of the wave group is proposed.The relation between the total and positive and negative run in the wave height sequence is fully considered.The theoretical formulas for calculating the maximum value of the positive run length of wave group are obtained by step-by-step theoretical simplification,and the original theoretical formula,the improved theoretical formula and the numerical simulation results are compared.The formula has the same distribution effect.（4）Based on the analysis of the wave group minimum positive run length,the distribution of wave group minimum positive run length is given theoretical results are compared with the numerical simulation results.When the interception level is H_1%,the fitting effect is good.（5）The joint distribution of the maximum positive run length and the corresponding maximum wave height in the maximum positive run length of wave groups is studied.The cumulative probability distribution function of the joint distribution under three conditions and nine conditions is established by using the Copula function.The establishment of the joint distribution can provide reference for the dynamic design of the Marine structure.（6）The time history change of dynamic response displacement of isolated single pile top under the action of wave group is analyzed from the angle of wave group positive continuous length.Based on the previous work in the field of wave group extreme run length,the probabilistic characteristics of wave group extreme run length were further studied,which enriched the theory of wave group extreme run length distribution,and provided a new analytical approach and method for the problems encountered in ocean and offshore engineering.