Modeling constitutive relationship of 6013 aluminum alloy during hot plane strain compression based on Kriging method

Hot plane strain compression tests of 6013 aluminum alloy were conducted within the temperature range of 613?773 K and the strain rate range of 0.001?10 s?1. Based on the corrected experimental data with temperature compensation, Kriging method is selected to model the constitutive relationship among flow stress, temperature, strain rate and strain. The predictability and reliability of the constructed Kriging model are evaluated by statistical measures, comparative analysis and leave-one-out cross-validation (LOO-CV). The accuracy of Kriging model is validated by the R-value of 0.999 and the AARE of 0.478%. Meanwhile, its superiority has been demonstrated while comparing with the improved Arrhenius-type model. Furthermore, the generalization capability of Kriging model is identified by LOO-CV with 25 times of testing. It is indicated that Kriging method is competent to develop accurate model for describing the hot deformation behavior and predicting the flow stress even beyond the experimental conditions in hot compression tests.

Reliability Analysis of Flexure Hinge Based on Kriging Method

The uncertainty widely exists in the engineering practice.Therefore,it is necessary to research the effect of uncertainty on the structural system. In this paper,the reliability and sensitivity of the flexure hinge, which is the key component of the compliant mechanisms,are investigated. The results of the reliability analysis can effectively guide the engineer to design and optimize the flexure hinge. In order to improve the calculating efficiency,the kriging method is introduced to estimate the failure probability and reliability sensitivity.

Optimization of Sensor Orientation in Railway Wheel Detector, Using Kriging Method

Considering the importance of axle counter function in detecting the train wheels and determining the clearance or occupancy of a track section, it is important to ensure a safe and reliable performance of this system. In this paper, in order to improve the sensor performance, the authors have focused on the orientation of magnetic sensors’ coils. In order to improve the detection capability of the system, through measuring the induced voltage in the receiver coil, it is important to adjust the relative orientation of the transmitter and receiver coils. Due to the existence of infinite relative orientations, in order to determine the optimum orientation for the sensor coils, Kriging methods which is one of the Response Surface Methodologies (RSMs) is applied. Finite Element Method (FEM) is utilized to provide sample data, as inputs to the Kriging algorithm. The analysis not only provides the optimum relative orientation of the sensor coils, it also improves analysis time, comparing to field based measurements. The analysis results are validated by the laboratory based data implemented in the control and signaling laboratory of the school of railway engineering and also field based tests in Iranian railway.

A moving Kriging interpolation-based boundary node method for two-dimensional potential problems

In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.

A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.

基于Kriging模型与FORM的钢板组合梁桥结构优化设计

考虑材料参数的不确定性以及设计变量多重约束条件的影响,提出了基于可靠性分析的钢板组合梁桥结构优化设计方法。首先,利用拉丁超立方试验设计(Latin hypercube design,LHD)构建试验组合方案,并通过有限元分析获取试验设计组合下的最大挠度响应值。基于获取的训练样本,构建能够表征结构最大挠度值与随机输入之间映射关系的Kriging代理模型。基于建立的代理模型,以钢结构截面积最小化为目标函数,建立符合规范要求与可靠度约束的优化数学模型,并采用一阶可靠性方法(first order reliability method,FORM),实现设计变量优化。通过比较具有相同设计变量上限,但下限分别为初始值的80%和70%两种优化设计方案,评估了两者在相同阈值以及不同阈值下设计变量的优化结果。最后对方案二在阈值为17 mm下的优化结果进行极限状态验算。结果表明:两个优化设计方案在阈值为17 mm下的优化结果更具合理性,并且方案二在同一阈值下具有更高的优化程度。随着阈值增加,优化程度增加,且腹板高度在较大阈值下对结果影响更大,而翼缘宽度在较小阈值下影响更大。

A Size-Dependent Functionally Graded Higher Order Plate Analysis Based on Modified Couple Stress Theory and Moving Kriging Meshfree Method

A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.

Optimization of buckling load for laminated composite plates using adaptive Kriging-improved PSO:A novel hybrid intelligent method

An effective hybrid optimization method is proposed by integrating an adaptive Kriging(A-Kriging)into an improved partial swarm optimization algorithm(IPSO)to give a so-called A-Kriging-IPSO for maximizing the buckling load of laminated composite plates(LCPs)under uniaxial and biaxial compressions.In this method,a novel iterative adaptive Kriging model,which is structured using two training sample sets as active and adaptive points,is utilized to directly predict the buckling load of the LCPs and to improve the efficiency of the optimization process.The active points are selected from the initial data set while the adaptive points are generated using the radial random-based convex samples.The cell-based smoothed discrete shear gap method(CS-DSG3)is employed to analyze the buckling behavior of the LCPs to provide the response of adaptive and input data sets.The buckling load of the LCPs is maximized by utilizing the IPSO algorithm.To demonstrate the efficiency and accuracy of the proposed methodology,the LCPs with different layers(2,3,4,and 10 layers),boundary conditions,aspect ratios and load patterns(biaxial and uniaxial loads)are investigated.The results obtained by proposed method are in good agreement with the literature results,but with less computational burden.By applying adaptive radial Kriging model,the accurate optimal resultsebased predictions of the buckling load are obtained for the studied LCPs.

Comparison analysis of sampling methods to estimate regional precipitation based on the Kriging interpolation methods： A case of northwestern China

The accuracy of spatial interpolation of precipitation data is determined by the actual spatial variability of the precipitation, the interpolation method, and the distribution of observatories whose selections are particularly important. In this paper, three spatial sampling programs, including spatial random sampling, spatial stratified sampling, and spatial sandwich sampling, are used to analyze the data from meteorological stations of northwestern China. We compared the accuracy of ordinary Kriging interpolation methods on the basis of the sampling results. The error values of the regional annual pre-cipitation interpolation based on spatial sandwich sampling, including ME （0.1513）, RMSE （95.91）, ASE （101.84）, MSE （？0.0036）, and RMSSE （1.0397）, were optimal under the premise of abundant prior knowledge. The result of spatial stratified sampling was poor, and spatial random sampling was even worse. Spatial sandwich sampling was the best sampling method, which minimized the error of regional precipitation estimation. It had a higher degree of accuracy compared with the other two methods and a wider scope of application.

基于自适应多保真度Co-Kriging代理模型的地下水污染源反演识别

为高效率高精度地进行地下水污染源反演识别,综合运用高保真度和低保真度地下水溶质运移数值模拟模型,研究应用集成差分进化算法的Co-Kriging方法建立模拟模型的多保真度代理模型;在此基础上,探索应用马尔科夫链蒙特卡洛(MCMC)-DREAM_((D))算法,并采用自适应更新多保真度代理模型策略进行地下水污染源反演识别.为验证上述方法的有效性和可行性,开展了数值算例研究.结果表明:相比仅基于高保真度模型输入-输出样本构建的Kriging代理模型,联合运用高保真度和低保真度模型输入-输出样本构建的Co-Kriging代理模型对模拟模型的逼近精度更高;耦合多保真度Co-Kriging代理模型和MCMC-DREAM_((D))算法能够得到较高精度的污染源反演结果,且能够大幅度减小计算负荷;同时,采用自适应更新多保真度代理模型策略能够进一步提高污染源反演识别精度.

基于LHS-Kriging-DW的页岩气集输管道内腐蚀预测模型研究

为了准确预测页岩气集输管道的内腐蚀速率,对DW(DeWarrd)模型进行修正,运用LHS(拉丁超立方抽样)优化的Kriging(克里金方法)对修正DW进行训练以建立模型并验证。通过高清漏磁检测器检测某页岩气集输管道内腐蚀速率,基于PIPESIM模拟该管道现场工况,运用多元非线性回归修正DW模型。运用LHS-Kriging对修正DW模型进行训练并优化,运用建立的模型对另一相邻管道进行了腐蚀速率的预测和现场开挖验证。现场内检测的结果显示:管线在几处低洼积液处发生了严重的腐蚀,因此引入了持液率作为修正因子修正DW模型。选择样本数为500用于LHS-Kriging-DW模型时误差较小。在实例运用中,10个开挖检测点有9个都在预测结果的95%置信区间内,这说明建立的腐蚀速率模型可用于指导现场内腐蚀直接评价等相关工作。

Kriging与Breitung融合的可靠性分析方法

针对一阶可靠性方法在处理非线性极限状态函数时精度不足,以及Breitung方法在随机变量维度较高时计算效率低的问题,提出融合Kriging模型与Breitung方法的可靠性分析策略。采用一阶可靠性方法求解极限状态函数的最大可能失效点,并基于迭代过程中产生的样本点训练Kriging模型。通过Breitung方法计算Kriging模型在最大可能失效点各方向上的曲率,并据此构建近似抛物面。为避免Breitung方法概率公式中的奇异解问题,引入鞍点近似来计算近似抛物面的失效概率。通过3个数值算例和一个复合材料压力容器的工程实例对比一阶可靠性方法、Breitung方法以及融合Kriging与Breitung的可靠性分析方法的效率与精度。结果显示,融合Kriging与Breitung的可靠性分析方法不仅提高了计算效率,并且求解过程稳定,具有较高的求解精度。

利用Kriging插值方法研究山东龙口北马镇农田土壤养分的空间变异

以山东省龙口市北马镇1000hm2的科技示范区为研究区,在地理信息系统平台ArcGIS上,采用GeostatisticalAnalyst地统计分析模块中的Kriging插值方法研究土壤养分的空间变异性。该分析过程中,发现影响分析工作结果精度的是Kriging插值模型的选择及Cross Validation交叉验证法的检验与系数修正。数据分析结果表明,龙口市北马镇0～20cm耕层土壤中碱解氮、速效钾含量空间相关性中等,速效磷含量具有强烈的空间相关性,有机质含量空间相关性较弱。

农田土壤微量元素的空间变异及Kriging估值

采用差分式GPS定位的方法,在山东省龙口市北马镇面积为10 km2的科技示范区内采用200 m×170 m网格式设置205个土壤采样点。用EDTA提取-原子吸收分光光度计测定法对示范区土壤微量元素铜、锌、铁、锰、硼的有效态含量进行了测定分析。在此基础上,选择Arcinfo地理信息系统软件,采用GeostatisticsAnalyst地统计分析模块中的Kriging插值方法对微量元素的空间变异性进行研究,该工作的关键是Kriging插值模型的选择及Cross-Validation交叉验证法的检验与系数修正。结果表明,龙口市北马镇0～20 cm耕层土壤中铜、锌、铁、锰、硼微量元素含量空间相关性中等,其中锌空间变异性相对较强,铜空间变异性相对弱一些。

基于Kriging方法的空间散乱点插值

给出的一种距离加权插值方法借鉴地质统计学中的Ｋｒｉｇｉｎｇ 方法，在空间数据场满足给定的统计分布特征的前提假设下进行插值．通过对帽状曲面函数的插值结果的观察，可以看出该方法可以获得良好的插值效果．

基于改进的Kriging法区域似大地水准面精化

利用常规的Kriging法进行GPS高程拟合时,由于模型误差和公共点误差的存在,其拟合内符合精度值并不为零。通过对已知点拟合残差进行改正得到一种改进的Kriging法来精化区域似大地水准面。通过实测数据对比改进的Kriging法与Kriging法的GPS高程拟合精度,结果表明:改进的Krig-ing法的拟合精度明显优于Kriging法,该方法能有效削弱模型误差和公共点误差引起的拟合残差。

用Kriging方法构建中纬度区域电离层TEC地图

提出了中国中北部及周边(30°N～55°N,70°E～140°E范围内)区域电离层电子浓度总含量(TEC)地图(简称CNC TEC Map)的Kriging算法.比较了目前被广泛使用的电离层模型(Klobllchar,IRI和JPL GIM)与真实的TEC分布的符合情况;比较了常数漂移(普通Kriging方法)、线性漂移和二次漂移的Kriging方法;在三种不同的时间分辨率(5min,30min和120min)下,比较了Kriging算法、就近插值算法和多项式回归算法(5阶)绘制CNC TEC Map的效果.结果显示在本文研究区域内常用的电离层模型与真实TEC分布存在较大的区别;使用普通Kriging方法就可以较好的表示华北地区TEC分布;Kriging方法的结果优于其余两种插值算法,尤其是当时间分辨率提高到5min时,Kriging算法的优势比较明显.

基于Kriging方法Argo数据重构太平洋温度场研究

采用Kriging算法，将2007年1～12月份期间获得的太平洋海域的Argo剖面浮标资料重新构成3°×3°的月平均海温场。重构的温度场能较好地揭示太平洋暖流区、西边界流系的季节性变化和西边界流系强温度锋面。将插值数据与同一时期的实测数据进行比较。结果表明Kriging算法得到的海表温度最大误差0．7℃，平均误差0．3℃，平均相对误差0．7％，平均标准误差0．06℃，计算结果令人满意。进一步利用重构的太平洋表层及水下4个断面的温度场分析了太平洋海域的温度分布格局及季节变化，赤道海区表层暖水占主体，随着水深增加，东部冷水迅速往东扩展，在200m时冷水基本把北上的太平洋暖水切断。

土壤含水量的Kriging和Cokriging估值研究

分析了田间同深度土壤含水量的半方差和不同深度土壤含水量的交互半方差特征 ,探讨了土壤含水量的Kriging和Cokriging估值方法。研究表明 ,同深度土壤含水量与不同深度的土壤含水量之间均具有显著的空间相关性 ,用Kriging方法进行土壤含水量的估值精度较传统方法高。加入浅层土壤含水量用Cokriging方法来估测深层土壤含水量 。

基于监测及Kriging方法的京津冀地区大气污染物暴露分布研究

为了实现充分利用已有环境监测站点数据进行人群精细化暴露评估的目的,同时解决某些待测人群社区周边无监测站点时数据的选择问题,以保定市作为大气高污染研究城市,基于现场监测和Kriging(克里金插值)空间分析方法,明确了在研究大气污染物人群暴露时,某一个固定监测站污染物数据的代表性问题.研究表明:对于大气中φ(SO 2)、φ(NO 2)、颗粒物及其组分,空气质量监测点位的代表性一般为5~6 km;对于φ(CO)、φ(O 3)和φ(VOCs),它们在城市不同地区的空间分布更为均匀,空气质量监测点位的代表性范围更大.通过使用Radial Basis Functions(径向基函数,RBF)、Local Polynomial Interpolation(局部多项式插值,LPI)、Inverse Distance Weighting(反距离权重插值,IDW)、Kriging、Kernel Smoothing(内核平滑插值,KS)和Diffusion Kernel(内核扩散插值,DK)等6种空间分析方法对大气污染物浓度进行预测发现,Kriging方法对大气污染物浓度预测时可使预测值和实测值间的偏差小于10%,准确度最高.因此,在进行某城市某点位的污染物人群暴露浓度预测时,若该点位周边5 km以内有空气质量监测点位,则可用该点位的监测值代替;若5 km以内没有空气质量监测点位,则可基于最近监测点位的污染物浓度进行Kriging空间插值,从而获得该点位的污染物暴露水平.