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

发布时间：2018-06-27 05:35

本文选题：普通克里金 + 泛克里金　；参考：《岩土力学》2014年S2期

【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。
[Abstract]:Spatial distribution characteristics of geotechnical parameters because of the autocorrelation and cross-correlation between sampling data, geotechnical parameters of unknown points can be interpolated or extrapolated by specific methods. The classical mathematical statistical method is difficult to determine the surrounding data sample points and the corresponding interpolation coefficients. Firstly, the distance weighted ordinary kriging algorithm, the pankrikriging algorithm (UK) and the cokriging algorithm (CK) in geostatistics are introduced. Because the moving distance weighted OK algorithm can not measure the singularity of local space, the multifractal theory will be introduced to make up this defect. Taking the Expo axis area (525m in length and 80m in width) of Expo 2010 Shanghai as the engineering background, there are 42 soil drilling holes in the region, and the cohesion force is the three important physical and mechanical indexes of the typical silty clay layer. The internal friction angle and compression modulus verify the above algorithm. For the cohesion of geotechnical parameters and the angle of internal friction, the prediction accuracy is from high to low to multifractal joint model (MK), cokriging model (CK), pankrikriging model (UK), general kriging model (OK), and for the compression modulus of geotechnical parameters, The corresponding order is the position exchange between the pankrikriging model and the ordinary Kriging model. The results show that the auxiliary information is helpful to improve the precision of data prediction in the analysis of the spatial field of geotechnical parameters, and the multifractal joint model is helpful to analyze the local singularity of the space.
【作者单位】：上海应用技术学院轨道工程系;解放军理工大学国防工程学院;同济大学地下建筑与工程系;
【基金】：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)
【分类号】：TU45

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