一种基于稀疏正则化的地下水点污染源识别法

An identification method for groundwater point pollution source identification based on sparse regularization

提出了一种基于稀疏正则化的方法识别地下水点污染源。首先,对地下水一维对流-弥散方程时域有限元格式进行拉普拉斯变换得到频域方程,然后建立以l1范数项为约束的地下水点污染源识别问题的目标函数,从而克服空间分布稀疏的点污染源识别问题的不适定性;接着,利用交替优化法进行迭代求解。研究结果表明,所提方法能在噪声条件下有效识别地下水点污染源的位置和强度变化。

This paper proposes a method based on sparse regularization to identify groundwater point pollution sources.Firstly,the time domain finite element discretized equation of groundwater one-dimensional convection-diffusion equation is used to obtain the frequency domain equation by Laplace transform,and then the objective function of the groundwater point pollution source identification problem constrained by the l1 norm term is established,thus overcoming the ill-posed problem of the point source identification due to sparse spatial distribution.The identification equation is then solved iteratively using the alternating optimization method.The research results show that the proposed method can effectively identify the position and intensity changes of groundwater pollution sources under noise conditions.