王桂林 向林川 孙帆

摘 要：克里金法是广泛应用的空间插值方法，但仅考虑单一因素的普通克里金法在确定山地斜坡土层厚度中存在较大误差。针对普通克里金法中的不足之处，提出了一种确定土层厚度的基于粒子群优化的协同克里金法。该方法首先用粒子群优化算法拟合半变异函数，然后将该函数用于以高程值作为辅助变量的协同克里金法中，并根据均方根误差来评价土层厚度的不确定性。将该方法应用于重庆万盛某边坡土层厚度的确定，通过交叉验证，结果表明：与普通克里金插值法相比较，考虑高程的协同克里金法插值的均方根误差降低了39.32%;基于粒子群优化的普通克里金法和协同克里金法的均方根误差分别降低了28.79%和48.45%。基于粒子群优化的协同克里金插值法对提高土层厚度的插值精度有较大作用。

关键词：克里金;协同克里金;土层厚度;空间插值;粒子群优化算法

中图分类号：TU191.1

文献标志码：A  文章编号：1674-4764（2018）06-0060-07

Application of cooperative Kriging method based on particle swarm

optimization in estimation slope soil thickness

Wang Guilin1，2 ， Xiang Linchuan2，Sun Fan2

（a.Key Laboratory of New Technology for Construction of Cities in Mountain Area， Ministry of Education;

b.School of Civil Engineering， Chongqing University， Chongqing 400045， P.R. China）

Abstract： The Kriging method is widely used for the spatial interpolation. However， the conventional Kriging method which only considers a singer factor generally leads to a considerable inaccuracy. In this paper， a cooperative kriging method based on particle swarm optimization is proposed to estimate the soil thickness distribution. Estimation is divided into two steps. Firstly， the particle swarm optimization is used to fit the semi-variance function. Secondly， the cooperative Kriging method which uses the altitude as an auxiliary variable is employed for estimation. In addition， a root mean square error is obtained to evaluate the estimation uncertainty of soil thickness. The proposed method is applied to estimate the soil thickness of a slope in Wansheng， Chongqing. It shows that compared with the conventional method， the cooperative Kriging approach improves the estimation accuracy by reducing the standard deviation by 39.32%， indicating that the proposed method is advantageous in improving the accuracy of spatial interpolation.

Keywords：Kriging; Co-Kriging; soil thickness; spatial interpolation; particle swarm optimization

隨着中国城镇化进程的不断推进，为了更有效地保护优质耕地，国土资源部提出了开展低丘缓坡等未利用土地开发试点的工作。残坡积土是低丘缓坡重要的组成部分，高质量的残坡积土层厚度信息在土地资源管理、工程建设、地质灾害预警预报等方面具都有重要意义。获取比较精确的土层厚度数据的方法之一是布设高密度的钻孔，但由于受到经济水平、技术手段和地形条件的限制，钻孔点的数量是一定的，这为确定土层厚度带来了较大的误差。……