基于EnKF法的无资料地区河道断面形状反演研究

Inversion Study of the Shape of River Cross-sections in Ungauged Regions Based on EnKF Method

针对无资料地区河道断面反演中使用优化算法和概率密度等数学方法在算法寻优过程中易陷入局部最优解的问题,提出了基于集合卡尔曼滤波(EnKF)和粒子群优化(PSO)耦合的方法实现对无资料地区河道断面的反演计算,即通过粒子群优化算法对缺失断面进行初始化,形成一个梯形的初始断面,再通过EnKF不断对初始断面进行修正,并通过理想案例对所提方法进行验证。结果表明,模型的R~2、N_(NSE)均高于0.99,相对均方差小于0.04。考虑到工程实际中的观测误差,选取0.1%、1%、5%、10%的观测误差对缺失断面、PSO初始断面及EnKF法修正断面的水动力模拟误差进行评价,发现误差随选取的误差不同整体呈现正态分布,但EnKF法面对不同的观测误差均可保持一个很高的模拟精度,R~2均高于0.98,相对均方差均小于0.06 m,N_(NSE)均高于0.98。可见所提方法具有较高的可行性。

Aiming at the falling into locally optimal solution shortcomings of optimization algorithm and probability density method for inversion of river cross-sections in ungauged regions,this paper proposed a combination of Ensemble Kalman Filter(EnKF) method and particle swarm optimization algorithm(PSO).The PSO was used to initialize the missing section to form a trapezoidal initial section.Then the EnKF was used to correct the initial section,and the proposed method was verified by the ideal case.The results show that the R~2 and N_(NSE) of the model are higher than 0.99,and the relative mean square error is less than 0.04.Considering the observation errors in the engineering practice,the observation errors of 0.1%,1%,5% and 10% were selected to evaluate the hydrodynamic simulation errors of the missing section,the PSO initial section and the corrected section by the EnKF method.It is found that the errors are normally distributed with the selected errors,but the overall distribution is normal with different errors.But the EnKF method can maintain a high simulation accuracy with different observation errors,the R~2 is higher than 0.98,the relative mean square deviation(RMSD) is less than 0.06 m,and the N_(NSE) is higher than 0.98.Thus,the proposed method has a high feasibility.