贝叶斯框架下等可靠度法推求洪水设计值的不确定性分析

Uncertainty Analysis of Equal Reliability Principle Based Estimation of Design Flood in the Framework of Bayesian Theory

摘要: 气候变化及人类活动的影响破坏了现行洪水频率分析方法中对洪水极值系列需满足一致性的假定。在非一致性条件下，如何推求给定设计标准下的洪水设计值是目前的研究热点及难点。“等可靠度”法是提出的一种面向非一致性洪水设计值估计的方法，其考虑了工程设计寿命对设计值估计的影响。然而，该方法中需要估计的模型参数通常较多，参数估计的不确定性不可避免地会导致洪水设计值估计的不确定性。本文应用贝叶斯理论研究“等可靠度”法推求洪水设计值时，参数估计不确定性对洪水设计值的影响。在获得设计值的期望估计(点估计)的同时，还可通过置信区间估计来定量评估设计值的不确定性。

Abstract: The traditional hydrological frequency analysis depends on the assumption that the flood series should be stationary, which has been influenced by climate change and human activities. Under non-stationary conditions, how to refer the design flood with a given design standard is a hot topic. The recently proposed equal reliability method is expected to solve this problem. The equal reliability principle considers the impact of engineering lifetime on the estimation of design flood. However, more parameters need to be estimated by the equal reliability method. The uncertainty of parameter estimation unavoidably results in uncertainty of design flood. Therefore, the Bayesian theory is applied to analyze the impact of parameter uncertainty on design flood, which provides the expected values and confidence intervals of the design floods.