A meshfree model without shear-locking for free vibration analysis of first-order shear deformable plates

Difficulty in imposing essential boundary conditions in the standard element-free Galerkin method (EFG) is due to the lack of Kronecker’s delta function property of shape functions generated by moving least square approximation (MLS). In this paper, we further apply a meshfree model based on the moving Kriging interpolation method (MK) to free vibration analysis of first-order shear deformable plates. The deflection and two rotation field variables of plate are approximated by the MK method, which is employed to construct the shape functions having the delta function property. With this approach, the drawback in enforcement of the boundary conditions caused by the MLS is now avoided. The present formulation is based on the first-order shear deformation plate theory (FSDT) associated with an effective elimination of the shear-locking phenomenon completely, and hence the approach is applicable to both moderately thick and thin plates. Numerical examples considering various aspect ratios and different boundaries are examined and solutions on natural frequencies obtained by the present method are then compared with existing reference solutions, and very good agreements are observed.     

Surfer在江西省遂川县金坑金矿找矿中的应用

以江西遂川金坑土壤化探采样为研究对象,对研究区内土壤中微量金属元素的化探数据进行了分析,运用Surfer软件对其进行残差计算,滤波分析,最终生成克立格网格,并对其进行平面等值线成图,用以对比趋势面生成等值线图,完成对化探异常的圈定,得出上下金坑为重点勘查区域的结论,为下一步确定勘查靶区提供了有力的技术支持。     

三维地质建模的应用示范——以白音诺尔铅锌矿为例

以国产DIMINE三维矿业软件为基础,系统收集整理了白音诺尔铅锌矿南矿段1号矿脉群750~800 m中段地质勘探资料,通过建立地质数据库,系统建立矿岩三维模型、数据的分析与处理以及资源储量估算整个流程,对比矿体与围岩模型特点、普通克里克估算方法与应用特点,研究结果表明：圈定矿体5条,模型显示矿体主要赋存在闪长玢岩与结晶灰岩接触带上,属典型的矽卡岩型矿床,空间展布形态呈囊状、大脉状、透镜状,整体北东走向;依据地质统计学理论,拟合求得理论变异函数应用于普通克里格估值,分别估算控制和探明资源量合计18.66万t,Pb+Zn品位为4.04%;与传统方法相较,普通克里格估算误差均在合理的范围之内,应用效果良好,估算精度高,可为矿山采矿设计提供参考,为实现矿山的数字化提供重要的理论依据。     

Response surface methodology with prediction uncertainty: A multi-objective optimisation approach

In the field of response surface methodology (RSM), the prediction uncertainty of the empirical model needs to be considered for effective process optimisation. Current methods combine the prediction mean and uncertainty through certain weighting strategies, either explicitly or implicitly, to form a single objective function for optimisation. This paper proposes to address this problem under the multi-objective optimisation framework. Overall, the method iterates through initial experimental design, empirical modelling and model-based optimisation to allocate promising experiments for the next iteration. Specifically, the Gaussian process regression is adopted as the empirical model due to its demonstrated prediction accuracy and reliable quantification of prediction uncertainty in the literature. The non-dominated sorting genetic algorithm II (NSGA-II) is used to search for Pareto points that are further clustered to give experimental points to be conducted in the next iteration. The application study, on the optimisation of a catalytic epoxidation process, demonstrates that the proposed method is a powerful tool to aid the development of chemical and potentially other processes.     

矿业地质统计学在我国的应用现状及对影响克立格估计的若干因素的研究

地质统计学已用于我国多个矿床的储量计算。变程Ａ是一个很稳健的变异参数，块金Ｃ０、基台Ｃ以及估计邻域的大小较大地影响着克立格估计。     

Mapping of background air pollution at a fine spatial scale across the European Union

Background

There is a need to understand much more about the geographic variation of air pollutants. This requires the ability to extrapolate from monitoring stations to unsampled locations. The aim was to assess methods to develop accurate and high resolution maps of background air pollution across the EU.

Methods

We compared the validity of ordinary kriging, universal kriging and regression mapping in developing EU-wide maps of air pollution on a 1 × 1 km resolution. Predictions were made for the year 2001 for nitrogen dioxide (NO₂), fine particles < 10 µm (PM₁₀), ozone (O₃), sulphur dioxide (SO₂) and carbon monoxide (CO) using routine monitoring data in Airbase. Predictor variables from EU-wide databases were land use, road traffic, population density, meteorology, altitude, topography and distance to sea. Models were developed for the global, rural and urban scale separately. The best method to model concentrations was selected on the basis of predefined performance measures (R², Root Mean Square Error (RMSE)).

Results

For NO₂, PM₁₀ and O₃ universal kriging performed better than regression mapping and ordinary kriging. Validation of the final universal kriging estimates with results from all validation sites gave R²-values and RMSE-values of 0.61 and 6.73 µg/m³ for NO₂; 0.45 and 5.19 µg/m³ for PM₁₀; and 0.70 and 7.69 µg/m³ for O₃. For SO₂ and CO none of the three methods was able to provide a satisfactory prediction.

Conclusion

Reasonable prediction models were developed for NO₂, PM₁₀ and O₃ on an EU-wide scale. Our study illustrates that it is possible to develop detailed maps of background air pollution using EU-wide databases.     

Kriging插值中条件数据点个数的选择

Kriging插值时使用的数据量越大,插值结果越可靠,但数据量对耗时的影响则呈指数增加。为了保证尽量多的数据参与Kriging插值,又能维持合理的计算耗时,必须正确地选择条件数据点个数。通过对地质统计学中Kriging插值算法的深入解析,利用Kriging插值中产生的平均权系数分析插值过程中的条件数据点个数的选择,当平均权系数最小时,找到这个平衡点,让插值过程中的计算在保证计算精度的同时,尽量减少计算耗时。并改变Kriging插值的维数、网格大小和变差函数的变程,分析所选择的条件数据点个数对此3种因素的敏感度,得到条件数据点个数选择40～60最为合适,主要的影响因素为计算维数。     

地质统计学方法在渗透系数空间变异性研究中的应用

以内蒙古自治区巴盟地区为例,利用地质统计学方法——泛克里格法对含水层渗透系数估值,并分析验证了对渗透系数服从对数正态分布和运用克里格方法能够取得的良好效果。     

应用析取克里格方法估计区域地下水埋深分布

本文比较了几种常用的估计土壤空间变异的计算方法，介绍了析取克里格的理论和计算方法，给出计算区域地下水埋深分布的实例，并对普通克里格和析取克里格的计算方差作了比较。     

岩心CT微观驱替实验的图像处理研究

针对CT微观驱替图像的特点,考虑图像中像素的空间分布,提出利用指示克里金方法分割图像.对不同驱替阶段的CT微观驱替图像进行分割,并和传统的简单阈值法的分割结果进行对比,在此基础上计算孔隙度等参数并结合室内实验结果进行了比较,验证了方法的有效性.结果表明,利用指示克里金方法分割CT微观驱替图像克服了传统分割方法的缺陷,因而能达到较好的分割效果.