粒子群优化协同克里金法在确定山地斜坡土层厚度中的应用

Application of cooperative Kriging method based on particle swarm optimization in estimation slope soil thickness

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。

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.