| 地基沉降预测模型的正则化算法 |
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| 引用本文： | 唐利民. 地基沉降预测模型的正则化算法[J]. 岩土力学, 2010, 31(12): 3945-3948 |
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| 作者姓名： | 唐利民 |
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| 作者单位： | 1.中南大学 信息物理工程学院，长沙 410083；2.长沙理工大学 交通运输工程学院，长沙 410004 |
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| 基金项目： | 国家自然科学基金（No. 40874005）；湖南省科技计划项目（No. 2008SK3054）。 |
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| 摘 要： | 通过分析地基沉降预测模型，指出最小二乘的病态性会导致模型参数求解失败。应用正则化理论，基于矩阵求逆理论，提出了一种沉降预测模型参数的正则化无偏估计算法，说明了新算法的无偏性和方差最小性。在一定条件下，证明了新算法中正则参数的存在性，并给出了正则参数的计算公式。结合文献和工程实例进行的分析表明，新算法降低了矩阵条件数，减轻矩阵病态程度，能有效求得地基沉降预测模型参数。
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| 关 键 词： | 地基沉降 预测模型 正则化 正则参数 病态矩阵 |
| 收稿时间： | 2009-04-23 |
Regularization algorithm of foundation settlement prediction model |
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| TANG Li-min. Regularization algorithm of foundation settlement prediction model[J]. Rock and Soil Mechanics, 2010, 31(12): 3945-3948 |
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| Authors: | TANG Li-min |
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| Affiliation: | 1. School of Info-Physics and Geomatics Engineering, Central South University, Changsha 410083, China; 2. School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410004, China |
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| Abstract: | I11-conditioning of least squares will lead to parameter solving failure. Based on analysis of foundation settlement prediction model and matrix inversion theory, using regularization theory, a new regularization unbiased estimation settlement prediction model algorithm is proposed. Unbiased and minimal variance of this new algorithm is described according to statistical theory. Existence of regularization parameter in the new algorithm is proofed in some condition. Calculation formula of regularization parameter is also given. Analyses with literatures and engineering examples show that the algorithm proposed not only reduces the matrix condition number and alleviates matrix ill-conditioning degree, but also can get the prediction model parameters effectively. |
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| Keywords: | foundation settlement prediction model regularization regularization parameter ill-conditioning matrix |
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