Multivariate Compound Extreme Value Distribution Theory And Its Engineering Applications

Based on the measure theory and religious mathematics theory, a multivariate compound extreme distribution model is developed in this dissertation, which is composed of discrete random variable and a multivariate continuous random variable. In the model discrete random variable may be different frequencies that typhoon, hurricane, cold wave gale happened, as well as may be different sampling counts each year which is composed of randomness of ocean environment condition; multivariate continuous random variable is calamity ocean environment condition, which induced from typhoon or hurricane, that is probability distribution of corresponding eigenvalue such as wave height, wind velocity, storm surge.Since this model is employed to discuss extreme environment-extreme joint distribution, the rationality of the distribution function is proved in measure theory.Owing to different calculation methods of different engineering, calculation errors will be induced. So, in this dissertation, based on measure theory and using religious mathematical illation, we give two lemmas and three inferences that are used to estimate errors.The model is presented by the expression that is convenient for applying to engineering. The advantage of the expression is that it considers frequencies of typhoon or randomness of data-sampling and correlate structural non-symmetry, and includes the single variant compound extreme distribution proposed by proposed Liu et al.We adopt the over-threshold sampling method that is widely used in the world to select datum. According to some characteristic of extreme distribution theory and mathematical laws of over threshold and character of non Poisson distribution, and using the concept of point of no-return process, we expounded rationalityof selecting threshold value in theory. The Threshold is selected with the mean-res i duaI -1i fe piot.Furthermore, by using four kinds of figures such as probability figure, quantile chart, return level figure and density bar, the threshold value is confirmed, and its rationality is checked up. The selection of the threshold value in this dissertation is reasonable. It not only has theoretical basis, but a I so has exp licit method of se I ect i ng va I ue. 11 i s d i f f erent from the prev i ous experiential method with large randomicity.For multivariate compound extreme distribution model established in the dissertation, several examples are given so that readers can deeply understand meaning of engineering from different aspects.In the dissertation typhoon frequency and marginal distribution of extremes of wind and surge are analyzed by Using wind wave isochronous datum of East sea Shengshi in China, joint probability distribution is calculated, and then the validity of Poisson-Mixed-Gumbel compound extreme model and stability of calculating results are tested in contrast to mixed- Gumbel. Calculated wind velocity and wave height of 100 return joint design value, and compared with other probability model and traditional design method, analyzed sensitivity.Aiming at the problems of several kinds disadvantageous factors, on the basis of date team obtained from road-test water level apartness, and combined with multivariate compound extreme distribution model, the probabi I ity analysis was car r i ed out for des i gn water I eve I of extreme env i ronmenta I cond i t i on of shangha i city. The calculating method and results of design water level were obtained in common effect of astronomical spring tide, surge of Changjiang and wind storm surge. By analyzing a example of wind, wave isochronous datum from 1963 to 1988 i n Chao I i an i s I and, the author gave app I i cat i on of mu 11 i var i ate compound extreme distribution model such as solving wind, wave joint design value in a certain period condition. For long-term probability forecast, such as prevention of flood, reservoir attemperment, and weather calamity, the wide application of the new model is important.