交互熵法在洪水频率分布参数估计中的应用研究
An Application of Cross Entropy Method to the Parameter Estimation in Flood Frequency Analysis

作者: 牛林森 , 宋松柏 :西北农林科技大学,水利与建筑工程学院,咸阳;

关键词: 交互熵分位数对约束参数估计洪水频率分析 Cross Entropy Fractile Constraints Parameter Estimation Flood Frequency Analysis

摘要: 本文研究基于分位数对约束下的交互熵进行洪水频率分布参数估计方法。以加拿大Feather河和陕北地区张村驿站年最大洪峰流量序列为例,选取GumbelGamma分布,基于最小交互熵原理,进行年最大洪峰流量序列分布参数估计,并根据估计参数推求洪峰流量频率曲线图。与矩法和极大似然法所求熵值比较,结果表明:交互熵法获得最小熵值,频率点距拟合亦取得满意效果。因此,在考虑分位数对约束的条件下,交互熵法能有效的估计分布参数,且较矩法和极大似然法优越。

Abstract: This paper studies on the application of fractile constrained cross-entropy to the estimation of dis- tribution parameters in flood frequency analysis. Based on the principle of minimum cross-entropy, two annual maximum flood peak series respectively in Feather River in Canada and Zhangcunyi Station in north- ern Shaanxi province with Gumbel distribution and Gamma distribution were employed to the parameter estimation of the four distribution functions. Four frequency curves with the estimated parameters were also plotted. Then, comparing the calculated cross-entropy values with those that are derived by traditional methods- MOM and MLM, it turned out that: by using cross entropy method, we got the minimum cross entropy values. The plotted theoretical frequency curves fit well with the empirical frequency curves. So, we can conclude that the quantile constrained cross-entropy method has the considerable merit in the flood frequency parameter estimation and is superior to the traditional methods-MOM and MLM.

文章引用: 牛林森 , 宋松柏 (2013) 交互熵法在洪水频率分布参数估计中的应用研究。 水资源研究, 2, 389-394. doi: 10.12677/JWRR.2013.26055

参考文献

[1] 董洁, 谢悦波, 翟金波. 非参数统计在洪水频率分析中的应用与展望[J]. 河海大学学报(自然科学版), 2004, 32(1): 23-26. DONG Jie, XIE Yuebo and ZHAI Jinbo. Application of non- parametric statistic approach to flood frequency analysis and prospect of its development trend. Journal of Hohai University (Natural Sciences), 2004, 32(1): 23-26. (in Chinese)

[2] 丛树铮, 胡四一. 洪水频率分析的现状与展望[J]. 水文, 1987, 6: 52-58. CONG Shuzheng, HU Siyi. Present situation and prospect of flood frequency analysis. Hydrology, 1987, 6: 52-58. (in Chi- nese)

[3] RAO, A.R., HAMED, K.H. Flood frequency analysis. New York: CRC Press LCC, 2000: 127-186.

[4] 马秀峰. 计算水文频率参数的权函数法[J]. 水文, 1984, 3: 1- 11. MA Xiufeng. The weighted function method applied in hydro- logic frequency parameters calculation. Hydrology, 1984, 3: 1- 11. (in Chinese )

[5] 陈元芳, 沙志贵, 陈剑池等. 具有历史洪水时P-III分布线性矩法的研究[J]. 河海大学学报, 2001, 29(4): 76-80. CHEN Yuanfang, SHA Zhigui, CHEN Jianchi, et al. Study on L- moments estimation method for P-III distribution with historical flood. Journal of Hohai University, 2001, 29(4): 76-80. (in Chi- nese)

[6] 李扬, 宋松柏. 高阶概率权重矩在洪水频率分析中的应用[J].水力发电学报, 2013, 32(2): 14-21. LI Yang, SONG Songbai. Application of higher-order probabil- ity-weighted moments to flood frequency analysis. Journal of Hydroelectric Engineering, 2013, 32(2): 14-21. (in Chinese)

[7] WANG, Q.J. Using higher probability weighted moments for flood frequency analysis. Journal of Hydrology, 1997, 194(1): 95-106.

[8] COHN, T.A., LANE, W.L. and BAIER, W.G. An algorithm for computing moments-based flood quantile estimates when his- torical flood information is available. Water Resources Research, 1997, 33(9): 2089-2096.

[9] DENG, J., PANDEY, M.D. and GU, D. Extreme quantile estima- tion from censored sample using partial cross-entropy and frac- tional partial probability weighted moments. Structural Safety, 2009, 31(1): 43-54.

[10] PANDY, M.D. Extreme quantile estimation using order statistics with minimum cross-entropy principle. Probabil-istic Engineer- ing Mechanics 2001, 16(1): 31-42.

[11] 茆诗松. 贝叶斯统计[M]. 北京: 中国统计出版社, 1999: 1-6. MAO Shisong. Bayesian statistics. Beijing: China Statistics Press, 1999: 1-6. (in Chinese)

[12] SHORE, J.E., JOHNSON, R.W. Axi-omatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Transformation on Information Theory, 1980, 26(1): 26-37.

[13] 黄振平. 水文统计学[M]. 南京: 河海大学出版社, 2008: 169- 171. HUANG Zhenping. Hydrological statistics. Nanjing: Hohai Uni- versity Press, 2008: 169-171. (in Chinese)

[14] LIND, N.C. and HONG, H.P. A cross entropy method in flood frequency analysis. Stochastic Hydrology and Hydraulics, 1989, 3(3): 191-192.

[15] LIND, N.C. and SOLANA, V. Fractile constrained entropy estimation of distributions based on scarce data. Civil Engineer- ing Systems, 1990, 7(2): 87-93.

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