基于概率密度演化理论的重庆市降雨概率结构研究

降雨作为市政工程和土木工程领域重要的灾害荷载之一,其概率结构对相应随机系统的分析有着至关重要的作用。然而,常用的概率模型往往不能很好地描述降雨的概率结构。为此,针对线性虚拟随机过程的广义密度演化方程及其形式解析解,导出了可直接用于随机静力系统分析的概率密度变换解,并发展了δ序列逼近算法。若将随机数据视为自映射系统,则上述方法可方便用于随机数据的概率结构分析。采用上述方法,该文分析了重庆市降雨的概率结构,获得了最大日降雨量概率密度函数的近似解,并由等间距的频数直方图和等频数直方图以及经验累积分布函数验证了近似解的准确性、可信性。遗憾的是,真实的概率密度函数复杂而不便于实用。因此,该文建议了一种描述复杂概率结构的线性组合模型,并通过试算法给出了最大日降雨量的实用概率模型,为后续的随机系统分析奠定基础。

PROBABILISTIC ANALYSIS OF RAINFALL IN CHONGQING BASED ON PROBABILITY DENSITY EVOLUTION THEORY

As one of hazard actions in the field of municipal engineering and civil engineering,the probabilistic structure of rainfall is very important for the analysis of stochastic systems involved in rainfall.However,it is difficult for modeling the probabilistic structure of rainfall by a traditional probability density function,sometimes it is impossible.In this work,a new technique coming from probability density evolution theory is proposed to describe the probabilistic structure of rainfall.Based on the analytical solution for generalized density evolution equations of a virtual random process,the transiting solution of a probability density function and its approximation via a family of δ sequences are derived.This transiting solution promotes probability density evolution theory from dynamical systems to static systems.Obviously,it is applicable to the probability analysis of random data,which can be viewed as a self-mapping static system.Therefore,the probabilistic structure of rainfall in Chongqing can be obtained by this method,verified by the frequency histogram of an equal interval,a frequency histogram of equal probability and empirical cumulative distribution functions.In order to build up a simple and practical model for the complicated,a class of linear combined model based on traditional probability density functions is put forward,and linear combined models for maximum daily rainfall are obtained by try and error.