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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。
Rainfall is one of the most important disaster loads in municipal engineering and civil engineering. Its probability structure plays an important role in the analysis of corresponding stochastic systems. However, the commonly used probability models often fail to characterize the probability structure of rainfall. Therefore, for the generalized density evolution equation of linear stochastic process and its formal analytical solution, the probability density transformation solution that can be directly used in stochastic static system analysis is derived and the δ sequence approximation algorithm is developed. If the random data is regarded as the self-mapping system, the above method can be conveniently used for the probabilistic structure analysis of random data. Using the above method, this paper analyzes the probability structure of rainfall in Chongqing and obtains the approximate solution of the maximum daily rainfall probability density function. The approximate solution of the maximum daily rainfall probability density function is obtained from the equi-pitch frequency histogram and the equiphannel frequency histogram and the empirical cumulative distribution function Accuracy, credibility. Unfortunately, the true probability density function is complicated and not practical. Therefore, a linear combination model describing complex probability structure is proposed and a practical probabilistic model of maximum daily rainfall is given through trial and error method, which lays the foundation for subsequent stochastic system analysis.