| 王占盛,陈健,戎虎仁,杨定强.土性参数各向异性随机场的表征与建模方法[J].计算力学学报,2021,38(1):29~36 |
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| 土性参数各向异性随机场的表征与建模方法 |
| Characterization and modeling of anisotropic random field of soil parameters |
| 投稿时间：2020-02-19 修订日期：2020-07-22 |
| DOI：10.7511/jslx20200219001 |
| 中文关键词: 随机场 各向异性 参数反演 矩阵分解法 |
| 英文关键词:random field anisotropy parameter inversion matrix decomposition |
| 基金项目:国家自然科学基金青年项目（51908344）；中国博士后科学基金面上项目（2018M643821XB）资助项目. |
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| 中文摘要: |
| 土性参数在空间上的相关性具有各向异性，因此对各向异性随机场表征与建模方法的研究具有重要的意义。本文首先通过对相关函数的分析，将各向异性相关的问题归结到相关距离函数的探讨上，给出了一种描述参数各向异性相关的方法；其次分析了目前常用的两种随机场反演方法在处理各向异性问题所面临的问题，（1）局部平均划分法只适合横观各向同性随机场的生成，难以处理任意的各向异性问题，（2）矩阵分解法反演随机场时，随机场网格数会受到计算机计算能力的限制，难以处理大型的随机场反演问题。针对以上两点问题，基于相关函数的快速衰减特性改进了矩阵分解法，并将改进的矩阵分解法与局部平均划分法进行了反演精度对比，同时用改进的矩阵分解法反演了旋转横观各向同性随机场，结果表明用改进的矩阵分解法处理各向异性问题是适用的。 |
| 英文摘要: |
| The spatial correlation of soil parameters is anisotropic,so the research on modeling methods of an anisotropic random field is of great significance.In this paper,firstly,by analyzing the correlation function,the problem of anisotropic correlation is reduced to the discussion of correlation distance function,and then a method to describe the anisotropic correlation of parameters is given.Secondly,the problems faced by two kinds of random field inversion methods in dealing with anisotropic problems are analyzed:(1) the local average partition method is only suitable for the generation of transversely isotropy random fields.It is difficult to deal with arbitrary anisotropic problems.(2) When matrix decomposition method is used to invert a random field,the grid number of the random field will be limited by the computing power of the computer,so it is difficult to deal with a large-scale random field inversion.Aiming at solving the above two problems,this paper improves the matrix decomposition method based on the fast attenuation characteristics of correlation function,and compares the inversion accuracy of the improved matrix decomposition method with the local average division method.At the same time,the improved matrix decomposition method is used to invert the rotational transversal isotropic random field.The results show that the improved matrix decomposition method is applicable to the anisotropic random field problem. |
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