引用本文: 唐利民, 朱建军. 软土路基沉降泊松模型的正则化牛顿迭代法[J]. 武汉大学学报 ( 信息科学版), 2013, 38(1): 69-73.
TANG Limin, ZHU Jianjun. Regularized Newton Iterative Algorithm for Poisson Model of Soft Clay Embankment Settlement[J]. Geomatics and Information Science of Wuhan University, 2013, 38(1): 69-73.
 Citation: TANG Limin, ZHU Jianjun. Regularized Newton Iterative Algorithm for Poisson Model of Soft Clay Embankment Settlement[J]. Geomatics and Information Science of Wuhan University, 2013, 38(1): 69-73.

## Regularized Newton Iterative Algorithm for Poisson Model of Soft Clay Embankment Settlement

• 摘要: 基于正则化理论,通过添加正则因子到迭代矩阵中,建立了正则化的牛顿迭代法来求解泊松模型参数,给出了迭代公式;根据迭代矩阵性质,基于条件数计算理论和绝对值三角不等式原理,证明了存在正则因子使得迭代矩阵的条件数小于一定的数值,推导了迭代过程中正则因子的计算公式;结合邵阳-怀化高速公路软土路基六个断面的总体沉降板观测数据分析表明,正则化的牛顿迭代方法不仅使迭代过程顺利进行并获得比三段法更小的残差平方和值,且其预测沉降量较三段法更符合工程实际。

Abstract: According to general Newton iterative method for solving Poisson model parameters of soft clay embankment settlement would failure because the iterative matrix is ill-conditioned or close to singular,based on regularization theory,by adding a regular factor to iterative matrix,a regularized Newton iterative method was proposed for solving Poisson model parameters.The iterative formula was also given.Based on condition number calculation formula and absolute value triangle inequality principle,according to the properties of the iterative matrix,a regular factor which can make the iterative matrix's condition number less than a given value was proved.Calculation formula of regular factor in iterative procedure was also derived.Settlement data of six section subgrade in Shaoyang-Huaihua expressway were analysis using Poisson prediction model.The study show that the regularized Newton iterative method not only can get the residual sum of squares value small than general three-segment method and make the iterative process convergence,but also the predicted settlement accorded with measured values better.

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