基于粒子群算法的P-Ⅲ型分布极大似然估计研究  

Research on P-Ⅲ Distribution Maximum Likelihood Estimation Based on Particle Swarm Optimization Algorithm

作　　者：雷庆文 闫磊 鲁东阳 卜嘉骏 罗云 LEI Qing-wen;YAN Lei;LU Dong-yang;BU Jia-jun;LUO Yun(College of Water Conservancy and Hydropower,Hebei University of Engineering,Handan 056038,Hebei Province,China;Hebei Key Laboratory of Smart Water Conservancy,Hebei University of Engineering,Handan 056038,Hebei Province,China)

机构地区：[1]河北工程大学水利水电学院,河北邯郸056038 [2]河北工程大学河北省智慧水利重点实验室,河北邯郸056038

出　　处：《中国农村水利水电》2022年第7期128-131,139,共5页China Rural Water and Hydropower

基　　金：国家自然科学基金(51909053);河北省自然科学基金(E2019402076);河北省高等学校科学技术研究项目(QN2019132);河北工程大学创新基金项目(SJ010002123)。

摘　　要：皮尔逊Ⅲ型分布(P-Ⅲ)在水文频率分析中被广泛应用。采用极大似然法(MLE)估计其分布参数时,由于计算复杂,在应用上受到了很大限制。通过将对数似然函数作为粒子群算法(PSO)的适应度函数,利用优化算法求解参数极大似然估计的数值解,即PSO-MLE算法,能够有效克服传统计算方法的缺陷。针对存在似然方程无解问题的困扰,提出了一种在粒子寻优过程中约束均值和位置参数的改进型极大似然算法。以渭河流域年降雨量的水文频率分析为例,对比其他参数估计方法的RMSE、AIC、Filliben相关系数的计算结果,可以表明PSO-MLE法有较好的实际应用价值;结合蒙特卡罗随机模拟分析结果,从统计角度证明了PSO-MLE法的参数估计结果具有更好的无偏性和有效性。Pearson-Ⅲ distribution(P-Ⅲ)is widely used in hydrologic frequency analysis.Due to the complexity of calculation,the application of the maximum likelihood method(MLE)to estimate the P-Ⅲ distribution parameters is greatly limited. Using the logarithmic likelihood function as a fitness function of the particle swarm optimization algorithm(PSO),solving the numerical solution of the parameter maximum likelihood estimation,PSO-MLE using the optimization algorithm can effectively overcome the defects of traditional computational methods. A modified algorithm of the maximum likelihood is proposed to constrain the mean and position parameters during the optimization of particles for the problem of the likelihood equation. Taking the hydrological frequency analysis of annual rainfall in Weihe Basin as an example,comparing the RMSE,AIC,Filliben correlation coefficient of other parameter estimation methods can show that PSO-MLE method has good practical value and combined with the results of Monte Carlo stochastic simulation analysis,the parameter estimation results of the PSO-MLE method are more unbiased and effective.

关 键 词：极大似然估计 水文频率分析 P-Ⅲ型分布 数值计算 粒子群优化算法 

分 类 号：TV11[水利工程—水文学及水资源] P333.9[天文地球—水文科学]