基于双层规划的普通克里金插值方法研究

Ordinary Kriging approach for spatial interpolation based on bi-level programming

采用双层规划描述了普通克里金法中理论变异函数模型参数求解问题.针对传统变异函数模型参数求解过程中容易受人为不确定性因素影响的问题,建立了以交叉验证统计结果最优和个体样本满足最优无偏线性估计为目标的双层规划模型,并给出了相应的求解方法.该方法根据交叉验证结果优化调整上层系统随机给定的变异函数模型参数,可以减少变异函数模型参数求解过程中人为不确定等因素的影响,从而可以获得合理的理论变异函数模型参数和较好的空间插值结果最后,以土壤pH值为例,通过与加权最小二乘法比较验证了采用该方法的有效性和合理性.

The bilevel programming is applied to obtain the optimal spatial interpolation results by optimizing the variogram parameters of ordinary Kriging method.A bilevel programming model regarding the most optimal cross-validation statistics and optimal unbiased linear estimation of every measured data as the targets is established for reducing the impact of human uncertainties.On this basis,the optimal variogram parameters and spatial interpolation statistics can be obtained consequently.Finally,the pH values of soil data is employed as a case to verify the efficacy and reasonability of the model by comparing with the weighted least squares method.