基于系统微分响应的暴雨强度公式参数优化  

Parameter optimization of rainstorm intensity formula based on system differential response method

作　　者：李琼芳[1,2] 许树洪 周正模 和鹏飞 杜尧 虞美秀 陈启慧[1] LI Qiongfang;XU Shuhong;ZHOU Zhengmo;HE Pengfei;DU Yao;YU Meixiu;CHEN Qihui(College of Hydrology and Water Resources,Hohai University,Nanjing 210098,China;Yangtze Institute for Conservation and Development,Nanjing 210098,China)

机构地区：[1]河海大学水文水资源学院,江苏南京210098 [2]长江保护与绿色发展研究院,江苏南京210098

出　　处：《水资源保护》2022年第5期8-16,共9页Water Resources Protection

基　　金：国家自然科学基金面上项目(51879069);江苏省水利科技项目(2018002);国家自然科学青年科学基金(51909058)。

摘　　要：暴雨强度公式参数的优化求解本质是一个高维非线性优化问题,目前常采用的优化求解方法是在以误差平方和为目标函数的基础上通过智能算法优化求解参数。为研究这类方法的合理性,通过随机抽样、参数空间网格化方法分析了常用暴雨强度公式参数求解方法的局限性,评价了常用智能算法的参数优化能力,进而提出了基于系统微分响应的暴雨强度公式参数优化方法。结果表明:以均方误差作为目标函数对非线性函数求解参数会增加额外参数解;在没有有效确定参数范围的情况下,随机抽样很难获得满足精度要求的参数样本,在有效确定参数范围后,目标函数的响应面上仍会存在无穷多个局部最优值,且很多局部最优的目标函数与全局最优近乎相同;以粒子群算法、SCE-UA算法为代表的随机搜索优化算法会因为参数初始取值范围过大、目标函数响应面局部最优参数解数量过多等问题而难以获得参数真值;提出的基于系统微分响应的暴雨强度公式参数优化方法能够快速寻找到参数真值,不仅效率高且能够避免陷入局部最优。The parameter optimization of rainstorm intensity formula is a high-dimensional and nonlinear optimization problem.The commonly used intelligent algorithms for parameter determination are applied by taking the sum of squared errors as their objective function.To investigate the rationality of these algorithms,random sampling and parameter space meshing method were used to evaluate their limitation and optimization ability,and then the system differential response method for parameter optimization of the rainstorm intensity formula was proposed.The results show that taking the mean square error as the objective function to solve the parameters of nonlinear function will produce additional parameter solutions;it is difficult to obtain parameter samples meeting the precision requirements through random sampling if the parameter range is not effectively constrained,and there exist infinite local optima on the objective function surface with different parameter information even if the parameter range is effectively constrained,with many local optima being almost the same as the global optimum;it is also difficult to obtain the real values of parameters using random search optimization algorithms,including the particle swarm optimization algorithm and shuffled complex evolution algorithm due to the large initial parameter value range and redundant local optima on the objective function surface;the system differential response method for parameter optimization of rainstorm intensity formula can quickly search the real values of parameters,and the method is not only efficient but also can avoid falling into local optima.

关 键 词：暴雨强度公式 参数优化 目标函数 随机抽样 系统微分响应 镇江市 

分 类 号：P333.9[天文地球—水文科学]