Abstract The uncertainty of initial water level being above the designed flood limited water level and the uncertainty of inflow caused by flood forecast error can cause flood risk in real-time reservoir flood operation. A risk analysis model for reservoir flood regulation under two-dimensional uncertainties based on Bayesian network is proposed. The nodes of Bayesian network are determined and the network structure is established with expert knowledge; the parameter learning is conducted with the training samples obtained from Monte Carlo simulation. Thereafter, through the prior probability inference without posterior information and the posterior probability inference with given posterior information, the variation of flood risk is analyzed under singular-factor uncertainty and two-factors uncertainties. The case study of Xianghongdian Reservoir using a flood of 100 years return period indicates: the risk resulted from inflow uncertainty is greater than that of the uncertainty of initial water level; there is a certain complementarity between the uncertainties of inflow and initial water level, and the combination risk is between the results of two single-factor risk levels. Moreover, Bayesian Network is able to conduct bi-directional inferences and infer the probability distribution of any other node, which has practical value for risk assessment and control of reservoir flood control operation.

中文翻译：

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基于贝叶斯网络的考虑二维不确定性的水库防洪运行风险分析

摘要 初始水位高于设计洪水限水位的不确定性和洪水预报误差导致的入流不确定性会导致水库实时洪水运行中的洪水风险。提出了一种基于贝叶斯网络的二维不确定性下水库调洪风险分析模型。确定贝叶斯网络的节点，利用专家知识建立网络结构；参数学习是用蒙特卡罗模拟得到的训练样本进行的。此后，通过无后验信息的先验概率推断和给定后验信息的后验概率推断，分析了单因素不确定性和双因素不确定性下洪水风险的变化。以100年重现期洪水为例，向洪店水库案例研究表明：入水不确定性风险大于初始水位不确定性风险；进水量的不确定性与初始水位之间存在一定的互补性，组合风险介于两个单因素风险水平的结果之间。并且，贝叶斯网络能够进行双向推断，推断任意其他节点的概率分布，对水库防洪作业的风险评估和控制具有实用价值。组合风险介于两个单因素风险水平的结果之间。并且，贝叶斯网络能够进行双向推断，推断任意其他节点的概率分布，对水库防洪作业的风险评估和控制具有实用价值。组合风险介于两个单因素风险水平的结果之间。而且，贝叶斯网络能够进行双向推断，推断任意其他节点的概率分布，对水库防洪作业的风险评估和控制具有实用价值。