HISR Method for Parameter Inversion of Solute Transport through Unsaturated Soils
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摘要: 以非饱和土中溶质迁移参数反演问题为背景, 依据正则化方法的思路, 以Itakura Saito距离作为同伦函数中的平凡问题, 将同伦方法引入非线性参数反演问题的求解, 进而提出一种求解非线性参数反演问题的大范围收敛(HomotoyItakura SaitoRegularization, HISR) 方法.为保证迭代稳定性, 并同时削弱观测噪声的影响, 同伦参数的修正采用了连续化修正方法.本文将HISR方法应用于求解带有平衡及非平衡吸附效应的一维非饱和土中溶质迁移参数反演问题, 计算结果表明HISR方法具有大范围收敛性及计算稳健性, 同时有较强的抵抗观测噪声的能力.Abstract: Taken the parameter inversion of solute transport through unsaturated soils as the application background and homotopy method imported for solving the nonlinear parameter inversion problem, this paper presents a global convergence method, HISR (homotopy Itakura-Saito regularization) method. The Itakura-Saito distance between the iterative parameter value and the estimated parameter value was adopted as the trivial problem in the homotopy function based on the idea of regularization. Moreover, a continuous method is employed to modify the homotopy parameter during iteration in order to ensure the ability of the iteration and the capability of the noise resistance. Problems of parameter inversion of solute transport coupled with equilibrium and non-equilibrium effects through one-dimensional unsaturated soils are carried out as numerical examples, and the computational results clearly demonstrated the features of global convergence and stability of the HISR method. Besides, a favorable solution is obtained even though experimental quantities were contaminated heavily by noise by HISR method.
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图 1 实验室土柱实验(a) 及穿透曲线(b) 示意图
Fig. 1. Sketch map of laboratory soils column experiment (a) and breakthrough curve (BTC) (b)
图 1 实验室土柱实验(a) 及穿透曲线(b) 示意图
Fig. 1. Sketch map of laboratory soils column experiment (a) and breakthrough curve (BTC) (b)
图 2 模拟实验穿透曲线(○)、反演穿透曲线(实线) 与真实穿透曲线(虚线) 的拟合
a.噪声强度为4%;b.噪声强度为8%;c.噪声强度为10%;d.噪声强度为15%
Fig. 2. BTCs fitting of simulated experimental results, inverse results and true results
图 2 模拟实验穿透曲线(○)、反演穿透曲线(实线) 与真实穿透曲线(虚线) 的拟合
a.噪声强度为4%;b.噪声强度为8%;c.噪声强度为10%;d.噪声强度为15%
Fig. 2. BTCs fitting of simulated experimental results, inverse results and true results
表 1 模拟实验参数数值
Table 1. Value of simulated experimental parameters
表 1 模拟实验参数数值
Table 1. Value of simulated experimental parameters
表 2 不同初始值时的参数反演结果
Table 2. Numerical inversion results for different initial values of parameters
表 2 不同初始值时的参数反演结果
Table 2. Numerical inversion results for different initial values of parameters
表 3 不同噪声强度下的反演结果
Table 3. Numerical inversion value for different noise levels
表 3 不同噪声强度下的反演结果
Table 3. Numerical inversion value for different noise levels
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