多测度加权克里金法在高边坡变形稳定性分析中的应用

针对传统的克里金法仅以欧式距离测度描述空间结构相关性的不足，基于最小方差准则提出了综合曼氏、欧式和切氏三种距离测度的多测度加权克里金方法，同时给出了一种简便的替代最小方差准则的改进定权准则。利用小湾水电站2号山梁高边坡监测点不同季节的变形速率数据进行实例计算，结果表明多测度加权克里金法提高了插值精度与可靠性，且改进定权准则的估计值接近理论最优值。应用所提出方法得到的2号山梁高边坡2004年春夏秋冬多时相变形速率场，有效地揭示了高边坡自下而上牵引式变形逐步得到控制并趋于平稳的演化特征，为边坡变形稳定性评估与防治提供依据。

Weighted Kriging Method for Deformation Stability Analysis of Steep Slopes Using Multi-distance Measures

The defect of traditional Kriging is pointed out, that is only Euclidean distance measure is used to describe spatial structure correlation. Then, on the basis of minimum variance criteria, this article presents the weighted Kriging using multi-distance measures, including Manhattan distance, Euclidean distance, and Chebyshev distance. Moreover, the modified weighting method is developed for the iterative criteria. Because different distance measure has different ability of detecting spatial correlation, the multi-Kriging would be very helpful to improving interpolation precision and reliability. A case is studied from the deformation monitoring data of the Number Two steep slope at Xiaowan hydropower station in 2004. It is shown that multi-Kriging generally outperforms traditional single-Kriging, especially for multi-Kriging with the modified weighting criteria. Bottom-up towing deformation mechanism of this steep slope is clearly revealed by multi-temporal deformation velocity fields of four seasons derived from multi-Kriging. Thus, this research provides important references for stability evaluation and prevention of this steep slope.