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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。
Based on the regularization theory, a regularized Newton iteration method is established to solve the Poisson model parameters by adding regular factors to the iterative matrix, and an iterative formula is given. Based on the properties of the iterative matrix, based on the condition number calculation theory and the absolute value triangle inequality Principle is used to prove that there exists a regular factor such that the condition number of the iterative matrix is less than a certain value and the formula of the regular factor in the iterative process is deduced. Based on the observation data of the total settlement of six sections of the soft soil subgrade in Shaoyang-Huaihua Expressway, The regularized Newton iterative method not only makes the iterative process proceed smoothly but also obtains the smaller residual sum of squared values than the three-stage method, and the predicted settlement is more in line with the engineering practice.