基于变步长梯度正则化算法识别分数阶地下水污染模型参数

Identification of the Model Parameters of Fractional Order Groundwater Pollution by Gradient Regularization Method with Variable Step

针对一维的地下水污染迁移过程中的非"菲克"扩散现象,建立分数阶对流-扩散偏微分方程.对于其参数识别的问题,采用隐式差分格式离散控制方程,设计变步长的梯度正则化算法重构地下水污染迁移模型参数.数值结果表明:变步长的梯度正则化算法能快速有效地识别地下水污染迁移模型参数;当正则化参数取0.000 1和分数微分阶数趋于2.0时,该算法计算精度高、收敛速度快、稳定性好,具有重要的应用价值.

One-dimension fractional order convection-diffusion partial differential equation is established to describe the non-Fick phenomenon in the groundwater pollution migration process.In order to identify the model parameters,the implicit scheme is adopted to discrete the controlling equation,and a gradient regularization method with variable step is designed to reconstruct the parameters.Numerical results have verified that the proposed algorithm is an effective method to inverse the model parameters.When the regularization parameter is 0.0001 and the fractional differential exponent approaches 2.0,the algorithm is of high precision,fast convergence,good stability and important application value.