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软土路基沉降泊松模型参数求解的多项式Landweber迭代法

唐利民

唐利民. 软土路基沉降泊松模型参数求解的多项式Landweber迭代法[J]. 岩土工程学报, 2013, 35(zk2): 853-856.
引用本文: 唐利民. 软土路基沉降泊松模型参数求解的多项式Landweber迭代法[J]. 岩土工程学报, 2013, 35(zk2): 853-856.
shu
TANG Li-min. Polynomial Landweber iterative method for solving Poisson model parameters in soft subgrade settlement[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(zk2): 853-856.
Citation: TANG Li-min. Polynomial Landweber iterative method for solving Poisson model parameters in soft subgrade settlement[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(zk2): 853-856.
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软土路基沉降泊松模型参数求解的多项式Landweber迭代法  English Version

  • 唐利民

基金项目: 中国博士后科学基金项目（2013M531776）
详细信息
    作者简介:

    唐利民(1978- )，男，广西桂林人，在站博士后，讲师，工程师，主要从事岩土工程反问题方面的研究。E-mail: tlmttt@163.com。

  • 中图分类号: TU43

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

  • 1. Key Laboratory of Road Structure & Material of Ministry of Communications, Changsha 410004, China; 2. Changsha University of Science & Technology, Changsha 410004, China

摘要

    摘要
  • 摘要: 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。
    Abstract: 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.
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    • 参考文献(12)
  • [1] 朱志铎, 周礼红. 软土路基全过程沉降预测的Logistic模型应用研究[J]. 岩土工程学报, 2009, 31(6): 965-969. (ZHU Zhi-duo, ZHOU Li-hong. Application of Logistic model in settlement prediction during complete process of embankment construction[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(6): 965-969. (in Chinese))
    [2] 赵明华, 龙 照, 邹新军. 路基沉降预测的Usher模型应用研究. [J].岩土力学, 2008, 29(11): 2973-2981. (ZHAO Ming-hua, LONG Zhao,ZOU Xin-jun.Prediction of roadbed settlement by Usher model[J]. Rock and Soil Mechanics, 2008, 29(11): 2973-2981. (in Chinese))
    [3] TANG Li-min. A regularization homotopy iterative method for ill-posed nonlinear least squares problem and its application[J]. Applied Mechanics and Materials, 2011(90-93): 3268-3273.
    [4] 邓英尔, 谢和平. 全过程沉降预测的新模型与方法[J]. 岩土力学, 2005, 26(1): 1-4. (DENG Yin-er, XIE He-ping. New model and method of forecasting settlement during complete process of construction and operation[J]. Rock and Soil Mechanics, 2005, 26(1): 1-4. (in Chinese))
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    [7] А.Н.吉洪诺夫, В.Я.阿尔先宁. 不适定问题的解法[M]. 王秉忱译. 北京: 地质出版社, 1979: 142-174. (TIKHONOV A N, ARSENIN В Я. Solutions of ill-posed problems[M]. WANG Bing-chen, translate. Beijing: Geological Press, 1979: 142-174. (in Chinese))
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    [9] LANDWEBER L. An iteration formula for fredholm integral equations of the first kind amer[J]. J Math, 1951, 73: 615-624.
    [10] HANKE M, NEUBAUER A, SCHERZER O. A Convergence Analysis of the Landweber Iteration for Nonlinear Ill-posed Problems[J]. Numer Math, 1995, 72: 21-37.
    [11] KU¨GLER P. A derivative-free landweber iteration for parameter identifiation in certain elliptic pdes[J]. Inverse Problems, 2003, 19: 1407-1426.
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出版历程
  • 收稿日期:  2013-07-16
  • 发布日期:  2013-11-24

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