基于多尺度最小二乘支持向量机优化的克里金插值方法

克里金插值方法根据待估位置点、已知样本数据点的位置关系和区域化变量的空间相关性,实现空间加权估计,满足估计的无偏性和最优性。传统方法理论模型形状固定且选择具有人为主观性,无法反映空间数据的变化趋势及其空间多尺度特征。本文为解决上述问题,提出了一种基于多尺度最小二乘支持向量机优化的克里金插值方法,此方法为拟合实验变异函数提供了一种新的思路。从实际样本数据的变化趋势出发,采用最小二乘支持向量机拟合实验变异函数,并利用不同尺度小波核反映不同尺度下的空间变化。最后,实验环节包括模拟和应用,模拟主要验证经多尺度最小二乘支持向量机优化后插值方法的科学有效性以及准确性,应用主要研究青岛市PM_2.5浓度时空分布特征,为城市生态科学防护及控制提供理论依据。结果表明,基于多尺度最小二乘支持向量机优化的克里金插值方法能够更好地刻画变异函数,反映不同尺度下的空间变化细节,从而在一定程度上提高插值的精度,是一种可选的克里金插值方法。

Kriging Interpolation Method Optimized by Multi-scale Least Squares Support Vector Machine

Kriging interpolation method realizes spatial weighted estimation that meets the unbiasedness and optimality according to the position relationship between the estimated location sites and the known sample sites and regionalized variable spatial correlation. Traditional theoretical model shape is fixed and chosen with subjectivity, which can't reflect the changing trend and multi-scale spatial characteristics. The choice of scale and the treatment of scale effects also need to be considered. To solve the problems above, we propose a method of kriging interpolation optimized by multi-scale least squares support vector machine (LS-SVM), which provides a new idea for fitting experimental variogram. Starting from the changing trend of the actual sample data, least squares support vector machine fits experimental variogram and the results conform to the spatial changing trend of data itself. Secondly, the wavelet kernel as the LS-SVM kernel function, parameters can be adjusted according to different parts of the nuclear, which is flexible and variable. Finally, the multi-scale wavelet kernel using wavelet multi-resolution characteristics, can reflect the different details of spatial changes, to avoid the single scale LS-SVM ignoring the spatial details of the problem. Followed that, the experiment includes simulation and application. Experimental simulation mainly verifies scientific validity and accuracy by the optimized interpolation of multi-scale least squares support vector machine. Meanwhile, experimental application research of PM_2.5 concentrations of temporal and spatial distribution provides the theoretical basis for city ecological protection and controlling. Final results show that kriging interpolation algorithm optimized by multi-scale least squares support vector machine is superior to the traditional method and single scale optimized kriging interpolation algorithm. It would be better to depict the variation function and reflect the different scales of spatial changes in details to further improve the accuracy of the interpolation to some extent, which is an optional kriging interpolation method.