﻿ 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

Journal of Water Resources Research
Vol.05 No.06(2016), Article ID:19294,8 pages
10.12677/JWRR.2016.56062

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

Yiming Hu1, Zhongmin Liang2, Jing Yang2, Jun Wang2, Binquan Li2

1Research Institute of Management Science, Business School, Hohai University, Nanjing Jiangsu

2College of Hydrology and Water Resources, Hohai University, Nanjing Jiangsu

Received: Nov. 26th, 2016; accepted: Dec. 9th, 2016; published: Dec. 19th, 2016

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.

Keywords:Non-Stationary, Design Flood, Equivalent Reliability Method, Bayesian Theory, Uncertainty Analysis

1河海大学商学院管理科学研究所，江苏 南京

2河海大学水文水资源学院，江苏 南京

1. 引言

2. 理论方法

2.1. “等可靠度”法描述

“等可靠度”法是梁忠民和胡义明等 [13] 提出的一种非一致性条件洪水设计值估计的方法。其核心思想是：在非一致性框架下，无论环境如何变化，都应保证非一致性条件下推求的洪水设计值对应的工程可靠度应与决策人员“规划”的工程设计可靠度一致。在非一致性条件下，决策人员只需按照一致性思维框架下的重现期概念提出其期望的工程设计标准(抗御年一遇洪水)和工程的设计运行周期(年)。因而，就可采用“等可靠度”法推求非一致性性条件下的洪水设计值。为便于使用，可将表述为非一致性条件下重现期为T年一遇的洪水设计值。进而，可度量非一致性条件下的工程洪水设计值，方便了工程决策和设计人员使用。

(1)

(2)

(3)

(4)

(5)

(6)

(7)

2.2. 参数估计不确定性对洪水设计值的影响

(8)

(1) 对于给定的设计重现期T和工程寿命，按式(5)计算工程的可靠度

(2) 从组系数参数中抽取一组，记为

(3) 按式(1)-(3)计算未来每个时刻t对应的分布参数，进而可得到每个时刻的概率分布函数。根据“等靠度”概念，即变化环境下工程设计可靠度与一致性条件下工程的设计可靠度相等，通过式(9)计算在变化环境下，T年重现期对应的设计值的估计值，记为

(9)

(4) 从组系数参数中再抽取一组，记为，根据步骤(3)，可获得T年重现期对应的设计值的第二个估计值；不断地从中抽取样本，并重复执行步骤(3)，直到抽完第组参数后，可获得设计值组估计值

(5) 将组T年重现期对应的设计值的估计值的经验分布作为设计值的分布，进而可计算T年重现期对应的设计值的点估计和区间估计，以定量评估模型参数不确定性对洪水设计值估计的影响。

3. 实例研究

GEV分布函数可表示如下，

(10)

(1) 模型1：PE3分布函数中的位置参数随着时间线性变化，而尺度参数和形状参数为常数。即，记为PE3-Loc。

(2) 模型2：PE3分布中位置参数和尺度参数随时间变化，形状参数为常数。即，记为PE3-Loc-Scl。

(3) 模型3：GEV分布函数中的位置参数随时间变化，而尺度参数和形状参数为常数。即，记为GEV-Loc。

Figure 1. Location and hydrological station at the Huanglongtan basin

Figure 2. Time series of peak flow

(4) 模型4：GEV分布函数中位置参数和尺度参数随时间变化，而形状参数为常数。即，记为GEV-Loc-Scl。

Table 1. AIC and BIC for assessing the model performance

Figure 3. The designed peak flow with different return periods for PE3-Loc-Scl model

4. 结论

Figure 4. The 90% confident interval of 15-day flood design value with different return periods under the conditions of different engineering lifetimes

Uncertainty Analysis of Equal Reliability Principle Based Estimation of Design Flood in the Framework of Bayesian Theory[J]. 水资源研究, 2016, 05(06): 530-537. http://dx.doi.org/10.12677/JWRR.2016.56062

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