水库调洪演算的随机数学模型
A Stochastic Mathematic Model for Reservoir Flood Routing
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摘要: 以介于微分方程和概率论之间的边缘数学分支随机微分方程的数学模型,对水库调洪过程中的随机现象和规律进行数学描述和分析,试图全面正确地综合各种不确定性因素对库水位随机过程的影响.根据水库蓄洪量具有Wiener过程特性的分析,推导了带有随机输入项和随机初始条件的调洪演算Ito方程.在此基础上,运用Fokker-Planck向前方程,求介了调洪过程库水位的概率密度分布.计算成果表明,运用随机微分方程进行水库的调洪演算,有利于正确分析水库调洪的随机过程和进一步开展水库泄洪风险分析.Abstract: A mathematic model of the stochastic differential equation (SDE) is applied to describe and analyze the random phenomena and their laws in the reservoir flood regulation procedures. According to the analysis of a Wiener process characteristics of the reservoir storage, an Ito Equation with a stochastic input term and a stochastic initial condition for reservoir flood routing is derived. And, by using the Fokker-Planck Equation, the probability density distributions of reservoir level hydrograph in the flood regulation procedure are solved. The calculated results show that the mathematic model of SDE in reservoir routing is favourab 1e in understanding the laws of the stochastic flood regulation procedure and developing risk analysis for flood relief.
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[1] 陆大(纟金).随机过程及其应用.北京:清华大学出版社,1986.537-541 [2] 徐祖信,郭子中.开敝式滋洪道泄洪风险计算.水利学报.1989, (4):50-54 [3] 张炳根,赵玉芝.科学与工程中的随机微分方程.北京:海洋出版社.1980. 251-278
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