| 克里金算法与多重分形理论在岩土参数随机场分析中的应用 |
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| 引用本文： | 王长虹,朱合华,钱七虎.克里金算法与多重分形理论在岩土参数随机场分析中的应用[J].岩土力学,2014,35(Z2):386-392. |
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| 作者姓名： | 王长虹 朱合华 钱七虎 |
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| 作者单位： | 1.上海应用技术学院 轨道工程系，上海 200235；2. 同济大学 地下建筑与工程系，上海 200092； 3.解放军理工大学 国防工程学院，南京 210007 |
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| 基金项目： | 国家自然科学基金（No. 51208303）；国家973计划（No. 2011CB013800-G）；上海市教委青年教师培养计划（No. yyy11007）；上海市教委科技创新计划（No. 14ZZ162）。 |
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| 摘 要： | 岩土参数的空间分布特征由于存在取样数据之间自相关和互相关的特性,未知点的岩土参数属性可通过特定的方法内插或外推,经典的数理统计方法难以确定周围的数据样本点以及相应的插值系数。首先介绍地统计学中基于距离加权的普通克里金(ordinary kriging,OK)算法、泛克里金算法(UK)和协克里金算法(CK)。由于基于滑动距离加权的OK算法无法度量局部空间的奇异性,将引入多重分形理论弥补该缺陷。以2010上海世博会的世博轴区域(长525 m,宽80 m)为工程背景,区域内共有42个取土钻孔,以典型的粉质黏土层3个重要的物理力学指标,即黏聚力、内摩擦角和压缩模量验证以上算法。对于岩土参数黏聚力和内摩擦角,预测精度由高至低为多重分形联合模型(MK)、协克里金模型(CK)、泛克里金模型(UK)、普通克里金模型(OK);对于岩土参数压缩模量,相应的顺序为泛克里金模型和普通克里金模型位置互换。研究结果证明,在岩土参数空间场的分析中,辅助信息有助于提高数据预测精度,并且多重分形联合模型有助于分析空间局部的奇异性。
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| 关 键 词： | 普通克里金 泛克里金 协克里金 多重分形 随机场 |
| 收稿时间： | 2014-03-26 |
Application of Kriging methods and multi-fractal theory to estimate of geotechnical parameters spatial distribution |
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| WANG chang-hong,ZHU He-hua,QIAN Qi-hu.Application of Kriging methods and multi-fractal theory to estimate of geotechnical parameters spatial distribution[J].Rock and Soil Mechanics,2014,35(Z2):386-392. |
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| Authors: | WANG chang-hong ZHU He-hua QIAN Qi-hu |
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| Institution: | 1. Department of Rail Track Engineering, Shanghai Institute of Technology, Shanghai 200235, China; 2. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China 3. Engineering Institute of National Defense Engineering, PLA University of Science and Technology, Nanjing 210007, China |
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| Abstract: | Due to spatial auto-correlation and inter-correlation among geotechnical observed data, the spatial geotechnical characteristics distribution at unknown location has to be extrapolated or interpolated by some special methods. However, classical statistical methods could not rationally resolve the problems which include selection of sample points, and comparison of spatial estimating weights between bilateral data. The distance-weighted ordinary Kriging (OK), universal Kriging (UK), and co-Kriging (CK) prediction methods for scattered data are introduced at first, which are known as the Kriging family in global geostatistics. Moreover, multi-fractal theory combining with co-Kriging (MK) is presented to depict the local singularity which should be ignored by Kriging of sliding weighted average algorithm. The performance is compared in different typical geotechnical parameters: cohesion coefficient c, friction angle and compression modulus . This study is based on the main axis (525 m long, 80 m wide) of Expo 2010 area of Shanghai, geotechnical test samples come from 42 boreholes. The performance of the different model fitness used in this study is MK, CK, OK and UK from the best to poor for parameters c and , and for parameter simulation, the sequence is MK, CK, UK and OK. The results prove that, in the most geotechnical occasions, auxiliary information would improve the prediction accuracy, and MK theory is useful tool to measure local singularity. |
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| Keywords: | ordinary Kriging(OK) universal Kriging(UK) co-Kriging(CK) multi-fractal(MK) random field |
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