基于Gamma函数表征及遗传算法参数率定的单位线推求方法  

A unit hydrograph derivation method based on Gamma function characterization and genetic algorithm for parameter optimization

作　　者：杨子昕 TANG Xiaonan YANG Zixin;TANG Xiaonan(Xi’an Jiaotong-liverpool University,Suzhou 215123,Jiangsu,China)

机构地区：[1]西交利物浦大学,江苏苏州215123

出　　处：《水利水电技术（中英文）》2021年第9期32-39,共8页Water Resources and Hydropower Engineering

基　　金：国家自然科学基金(11772270)。

摘　　要：单位线推求方法主要有试算法、分析法和最小二乘法等,数值法推求结果经常出现锯齿或负值的局部不合理现象,而试错法不能保证结果最优,这两大对立矛盾一直困扰实践应用中单位线的推求。本文提出一种由单位线函数化、单位线初始率定和单位线经验修正等步骤构成的单位线推求方法。以组成论为理论依据将流域水文系统视为一个广义集合,以Gamma函数表达流域汇流过程规律,并将Gamma函数参数化;以计算汇流过程与实测过程误差最小为约束条件,采用遗传算法率定Gamma函数参数,获得初始单位线;采用Collins迭代法对初始单位线进行局部修正,最终完成单位线推求。结合算例与试错法推求结果进行比较分析,表明该方法计算的流量过程精度要优于试错法,而洪量计算精度虽然低于试错法,但相对误差为1.00%,完全能够满足工程需要。同时,以Gamma函数表达单位线,其参数取值能够揭示流域汇流规律,可以对区域性汇流规律进行数字化空间分析。The unit hydrograph derivation methods mainly include trial-and-error approach, analysis method and least-square method. The numerical method often results in local irrationality of jagged or negative value, while the trial-and-error method does not guarantee the optimal result. These two contradictions have been faced in the unit hydrograph derivation in practical applications. Based on the composition theory, the hydrological system of watershed is regarded as a generalized set, the law of watershed confluence process is expressed by the Gamma function, and the Gamma function is parameterized. The initial unit hydrograph is obtained by using a genetic algorithm where the parameters of the Gamma function are calibrated based on the minimum error between the computed confluence process and the measured confluence process. The initial unit hydrograph is then locally modified by the Collins iteration method. Finally, the unit hydrograph is obtained. The results are compared and analyzed with examples and the trial-and-error method, showing that the accuracy of the flow hydrograph obtained by the proposed method is better than that of the trial-and-error method, while the accuracy of the flood calculation is lower than that of the trial-and-error method with a relative error of 1.0%, which can fully meet the engineering needs. At the same time, the unit hydrograph expressed by Gamma function, as parameter values can reveal the watershed confluence law, can carry out for the digital spatial analysis of regional confluence law.

关 键 词：单位线 GAMMA函数 遗传算法 Collins迭代法 

分 类 号：TV213.4[水利工程—水文学及水资源]