Non-stationary variogram models for geostatistical sampling optimisation: An empirical investigation using elevation data

A problem with use of the geostatistical Kriging error for optimal sampling design is that the design does not adapt locally to the character of spatial variation. This is because a stationary variogram or covariance function is a parameter of the geostatistical model. The objective of this paper was to investigate the utility of non-stationary geostatistics for optimal sampling design. First, a contour data set of Wiltshire was split into 25 equal sub-regions and a local variogram was predicted for each. These variograms were fitted with models and the coefficients used in Kriging to select optimal sample spacings for each sub-region. Large differences existed between the designs for the whole region (based on the global variogram) and for the sub-regions (based on the local variograms). Second, a segmentation approach was used to divide a digital terrain model into separate segments. Segment-based variograms were predicted and fitted with models. Optimal sample spacings were then determined for the whole region and for the sub-regions. It was demonstrated that the global design was inadequate, grossly over-sampling some segments while under-sampling others.     

Ns-kriging based microstructural optimization applied to minimizing stochastic variation of homogenized elasticity of fiber reinforced composites

This paper describes an approximate microstructural optimization using the ns-kriging (noise-resistant smoothed kriging) method for minimizing the maximum stochastic variation of homogenized elastic properties of a composite material caused by microscopic uncertainties of component materials. Since evaluation of a stochastic characteristic of a homogenized material property such as expectation or variance will involve a high computational cost and its results include inaccuracy in using the Monte Carlo simulation, an approximation-based optimization technique is useful for solving the optimization problem considering the multiscale stochastic problem. Especially, the ns-kriging will work well in case of using inaccurate data for an unknown objective function. In order to investigate applicability and effectiveness of the proposed ns-kriging based approach to the optimization problem, it is applied to the cross-sectional shape optimization of fiber in a unidirectional FRP. From the numerical results, validity and effectiveness of the proposed approach are confirmed.     

克里格方法在大地电磁静校正中的应用

大地电磁测深中,静校正处理直接影响到视电阻率的真实性以及反演、解释结果的可靠性.考虑到地学断面的空间结构横向上存在着一定的相关性,引入地质统计学的克里格(Kriging)方法以校正畸变的视电阻率断面和相位断面.克里格方法是根据待估样点或待估块段有限领域内已测定的样点数据,在认真考虑了样点的形状,大小和空间相互位置关系,它们与待估样点空间相互位置关系,以及变异函数提供的结构信息之后,对该待估样点值进行的一种线性无偏最优估计.根据这一思路,编制了大地电磁测深数据校正软件,并且进行了理论模型试验和实际资料的处理,取得良好的效果.     

Kriging-based reliability analysis of the long-term stability of a deep drift constructed in the Callovo-Oxfordian claystone

Callovo-Oxfordian(COx) claystone has been considered as a potential host rock for geological radioactive waste disposal in France(Cigéo project). During the exploitation phase(100 years), the stability of drifts(e.g. galleries/alveoli) within the disposal is assured by the liner, which includes two layers: concrete arch segment and compressible material. The latter exhibits a significant deformation capacity(about 50%)under low stress(3 MPa). Although the response of these underground structures can be governed by complex thermo-hydro-mechanical coupling, the creep behavior of COx claystone has been considered as the main factor controlling the increase of stress state in the concrete liner and hence the long-term stability of drifts. Therefore, by focusing only on the purely mechanical behavior, this study aims at investigating the uncertainty effect of the COx claystone time-dependent properties on the stability of an alveolus of Cigéo during the exploitation period. To describe the creep behavior of COx claystone, we use Lemaitre's viscoplastic model with three parameters whose uncertainties are identified from laboratory creep tests. For the reliability analysis, an extension of a well-known Kriging metamodeling technique is proposed to assess the exceedance probability of acceptable stress in the concrete liner of the alveolus.The open-source code Code_Aster is chosen for the direct numerical evaluations of the performance function. The Kriging-based reliability analysis elucidates the effect of the uncertainty of COx claystone on the long-term stability of the concrete liner. Moreover, the role of the compressible material layer between the concrete liner and the host rock is also highlighted.     

基于Kriging代理模型的注塑件残余应力优化分析

以注塑成型制品中脱模后的最大Mises-Hencky残余应力为目标函数,运用基于Kriging代理模型及EI加点准则的序列优化方法,对聚碳酸酯材料制品进行了工艺参数(包括熔体温度、模具温度、注射速率、保压压力及保压时间)优化。算例结果表明,所提出方法可以有效地降低注塑件内的最大Mises-Hencky残余应力。在此基础上对充填阶段进行深入分析,用贝塞尔曲线控制方式代替常规的常速率充填控制方式,进一步降低了制件内的残余应力。     

分形理论在某钼矿特高品位识别与处理中的应用

针对参数选取缺乏合理性、平均品位下降等问题,提出了一种基于分形理论的特高品位识别与处理方法。该方法首先采用含量-总量法确定特高品位下限值,然后运用平均值替代法处理特高品位。将该方法应用于某露天钼矿的特高品位识别与处理,并通过克里金插值法进行品位估算。结果表明:该方法识别与处理特高品位后的插值效果明显优于3σ法和分布函数法,且能够较好地反映该钼矿的原始品位分布规律,验证了该方法的可行性和有效性。     

基于Kriging代理模型的气辅注射成型工艺优化

针对气辅成型工艺设定及控制的复杂性,使用Kriging代理模型近似拟合气辅成型工艺参数与气体穿透长度之间的非线性函数关系,建立起Kriging代理模型与APSO算法相结合的优化策略。应用所建立的优化方案,以气体的穿透深度为优化的目标,模拟了某汽车后视镜的气辅成型工艺优化过程。算例表明,基于Kriging代理模型与APSO算法耦合的优化策略可以在小样本情况下获取较高的求解精度和较快的收敛速度。     

Kriging插值模型在地下水位监测网优化中的应用

目前运行的地下水监测网存在着很多问题,很难适应现代社会对信息的需求,需要对地下水监测网进行优化。详细介绍了Kriging插值模型的建立及求解过程,并运用该模型对黄水河流域平原区进行了地下水水位监测网的优化,得到了备选方案,然后根据具体的优化目标选出最优方案,结果较为合理。Kriging插值模型充分考虑了水文地质条件的影响,是优化地下水监测网密度的有效方法。     

Holes in the ocean: Filling voids in bathymetric lidar data

The mapping of coral reefs may be efficiently accomplished by the use of airborne laser bathymetry. However, there are often data holes within the bathymetry data which must be filled in order to produce a complete representation of the coral habitat. This study presents a method to fill these data holes through data merging and interpolation. The method first merges ancillary digital sounding data with airborne laser bathymetry data in order to populate data points in all areas but particularly those of data holes. What follows is to generate an elevation surface by spatial interpolation based on the merged data points obtained in the first step. We conduct a case study of the Dry Tortugas National Park in Florida and produced an enhanced digital elevation model in the ocean with this method. Four interpolation techniques, including Kriging, natural neighbor, spline, and inverse distance weighted, are implemented and evaluated on their ability to accurately and realistically represent the shallow-water bathymetry of the study area. The natural neighbor technique is found to be the most effective. Finally, this enhanced digital elevation model is used in conjunction with Ikonos imagery to produce a complete, three-dimensional visualization of the study area.     

Optimal experimental design in stochastic structural dynamics

This paper provides a methodology for optimal prediction of the response of randomly vibrating structures using information from a limited number of measurements. The objective is to optimize the locations of sensors for the purpose of making the most accurate predictions of the response at unmeasured locations in structural systems. The kriging method is used to find the response predictions and the corresponding mean-square errors at unmeasured locations. The mean-square errors in the predictions depend on the locations of sensors and the correlation characteristics of the response evaluated from the model of dynamics and the characteristics of the excitation. The response predictions depend also on the information contained in measurements. The optimal sensor locations are selected to minimize the total mean-square error of the response predictions at unmeasured points. This leads to a complicated non-convex optimization problem in which multiple local and global optima may exist. A hybrid optimization method based on evolution strategies is used to determine a global minimum. The optimal experimental design method presented in the paper is illustrated by designing the optimal sensor locations for an elastic beam and a plate subjected to a class of random stationary loads.