软土路基沉降泊松模型参数求解的多项式Landweber迭代法

Polynomial Landweber iterative method for solving Poisson model parameters in soft subgrade settlement

针对求解泊松沉降分析模型参数由于迭代矩阵病态导致的迭代不收敛问题,基于矩阵变换理论,导出了经典Landweber迭代公式,提出了一种软土路基沉降泊松模型的多项式Landweber迭代法,给出了计算公式。基于非线性最小二乘原理,给出了公式中参数因子的确定方法和计算公式。以某高速公路的软土路基断面观测数据对算法进行了验证和分析,结果表明,所提方法有效避免了迭代矩阵病态导致的迭代不收敛情形,选择合适的参数因子后可获得理想的路基沉降分析结果。

Solving Poisson model parameters in settlement analysis will fail when the iterative matrix is ill-conditioned. Based on the matrix transformation theory, the classical Landweber iteration formula is derived, and a polynomial Landweber iterative method of Poisson model for soft soil subgrade settlement is proposed. The formula is also given. According to the nonlinear least-squares principle, the methods and formulas for parameter factors in the formula are given. The observed data of soft soil roadbed in expressways are analyzed using this method. The results show that the polynomial Landweber iterative method can effectively avoid the convergence situation which the ill-posed iterative matrix. Ideal embankment settlement results are achieved when the parameter factors are accuately selected.