复合极值分布理论及其工程应用

Multivariate Compound Extreme Value Distribution and Its Application

复合极值分布理论在国际上公开发表以来得到了国内外的大量引用和应用。本文就该理论由一维拓宽至多维进行了理论论述 ,并对其不同模式在海岸、海洋和水利工程中的应用做了实例计算。

With the development of offshore engineering, the joint probability study for extreme sea environments has been a subject of increasing interest to both mathematicians and engineers. However, the conventional multivariate probability distribution models do not describe the distribution of the occurrences of extreme sea states induced by Typhoon, Hurricane or winter storm, and thus fail to reflect the probability characteristics of sea environments in all their aspects. Extreme sea environments are typically to be found in storms like Typhoon, and the occurrences of such storms in certain sea areas, varying from year to year, may be fitted to a discrete distribution. By compounding the discrete distribution with a multivariate continuous distribution of some extreme sea environments, a new kind of distribution—Multivariate Compound Extreme Value Distribution(MCEVD) is obtained in this paper.The first part of this paper proposes two types of MCEVD: Poisson-Nested Logistic Trivariate Compound Extreme Distribution and Poisson-Gumbel Mixed Compound Extreme Distribution.The second part of this paper proposes the stochastic simulation technique for MCEVD. Both the theoretical solutions and stochastic simulation techniques are used in predicting disaster prevention design water level for Shanghai city, in designing of platform deck clearance wave overtopping of breakwaters in the Hong-Kong sea areas, and in flood(peak, voluame, frequency) analysis fo the Yangze River.