﻿ 水库月径流概率预报研究 Probability Forecast of Monthly Reservoir Inflow

Journal of Water Resources Research
Vol.06 No.01(2017), Article ID:19754,8 pages
10.12677/JWRR.2017.61001

Probability Forecast of Monthly Reservoir Inflow

Shaokun He1,2, Shenglian Guo1,2, Zhangjun Liu1,2, Jiabo Yin1,2, Xushu Wu1,2

1State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan Hubei

2Hubei Provincial Collaborative Innovation Centre for Water Resource Security, Wuhan Hubei

Received: Jan. 25th, 2017; accepted: Feb. 18th, 2017; published: Feb. 21st, 2017

ABSTRACT

The Singular Spectrum Analysis (SSA) was applied to preprocess the original flow series, and Artificial Neural Network (ANN) and Support Vector Machine (SVM) were used to simulate and predict the reconstructed data series. The multivariate joint distribution based on copula function and probability forecast model were proposed. With a case study of Danjiangkou reservoir monthly inflow series, the probability forecast results were compared with that of deterministic model. It is shown that the probability forecast model not only can improve the accuracy of middle value prediction to a certain extent but also give probability interval, which helps reservoir managers to consider uncertainty quantitatively and provides technical support for decision-making.

Keywords:Singular Spectrum Analysis, Artificial Neural Networks, SVM, Copula, Conditional Distribution

1武汉大学水资源与水电工程科学国家重点实验室，湖北 武汉

2水资源安全保障湖北省协同创新中心，湖北 武汉

1. 引言

2. 研究方法

2.1. 奇异谱分析

2.1.1. 建立相空间

(1)

2.1.2. 奇异值变换

2.2. 人工神经网络模型

2.3. 支持向量机模型

(2)

(3)

2.4. 基于Copula函数的径流概率预报模型

2.4.1. Copula函数

Sklar提出可以将一个m维联合分布函数分解为m个边缘分布函数和一个Copula函数。Nelsen于1999年给出了copula函数的严格定义，即是把随机变量的m维联合分布函数分布函数与各自的边缘分布相连接的函数。即存在一个m-Copula函数C，使得对任意 [12] ：

(4)

(5)

2.4.2. 条件概率

(6)

(7)

(8)

2.5. 模型性能指标

3. 实例研究

3.1. 数据预处理

3.1.1. SSA参数的选择

Table 1. Cross-correlation function values between subseries and original series for different L

3.1.2. 预报因子的选取

3.2.实测流量的条件概率分布

3.2.1. 边缘分布的确定

(9)

3.2.2. 联合分布的建立

Figure 1. The autocorrelation and partial autocorrelation function for reconstructed series under L = 11

Table 2. Estimated parameters of marginal distribution and K-S test

3.2.3. 概率预报

(10)

3.3. 结果分析

Table 3. Performance indices of models during training and testing periods

Figure 2. Comparison of observed and probability forecasted monthly inflow and 90% confidence intervals during testing period

4. 结论

1) 概率预报可以在一定程度上整合不同模型的预测优势，提高预报精度。与单个模型方法相比，概率预报模型具有更大的优势。

2) 基于Copula方法的概率预报可以给出置信水平下的预报区间，有利于决策人员定量考虑预报的不确定性。

Probability Forecast of Monthly Reservoir Inflow[J]. 水资源研究, 2017, 06(01): 1-8. http://dx.doi.org/10.12677/JWRR.2017.61001

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