随机微分方程在泄洪风险分析中的运用

Application of stochastic differential equations in risk analysis for flood relief

本文根据调洪过程中水库蓄洪量具有Ｗｉｅｎｅｒ过程特性的分析，建立了带有随机作用项的Ｉｔｏ随机微分方程，以描述和分析调洪过程中库水位的随机变化规律．在此基础上，给出了动态的泄洪风险表述，并通过Ｆｏｋｋｅｒ－Ｐｌａｎｃｋ向前方程，求解了与泄洪风险率紧密相关的库水位过程的概率密度分布．计算实例表明，运用随机微分方程进行水库的调洪演算，能够全面、正确地反映各种不确定性因素对库水位过程的影响，从而使泄洪风险分析建立在科学的基础上．

After analysing the Wiener process characteristics of reservoir capacity in flood regulation, the author proposes an Ito stochastic differential equation including random term to describe and analyse the stochastic rules of reservoir level hydrograph in flood routing process. An expression of active risk for the flood relief is given, and the probability densities of reservoir level hydrograph, which is related to the risk for the flood relief are computed by Fokker- Planck Equation. Analyzed and calculated results indicate that by using the stochastic differential equations in flood routing, the influence of various random factors on the reservoir level hydrograph can be comprehensively analyzed. Therefore, the method of risk analysis suggested by this paper is reasonable.