Extracting optimal datasets for metamodelling and perspectives for incremental samplings

Selecting the best input values for the purpose of fitting a metamodel to the response of a computer code presents several issues. Classical designs for physical experiments (DoE) have been developed to deal with noisy responses, while general space filling designs, though being usually effective for complete classes of problems, are not easily translated into adaptive incremental designs for specific problems. We discuss one-stage and incremental strategies for generating designs of experiments encountered in literature and present an extraction technique along with some benchmark on theoretical functions. We finally propose complexity indicators which could be considered for developing effective incremental samplings.     

基于非列线数据的泛克立格法在地下水位空间变异性研究中的应用

考虑研究区地下水位在流向和垂直流向方向有明显变化这一特点,选用正交多项式方法利用2002年9月到2006年9月地下水位的非列线观测数据确定了地下水位的二次漂移式,进而确定出地下水位剩余R(x)的变差函数γR(h),用泛克立格方法研究了月平均地下水位的空间变异规律。对变异程度的估值进行了统计检验。将其成果应用于流域地下水资源数值模拟评价中,收到满意的效果。     

Subset selection from large datasets for Kriging modeling

When building a Kriging model, the general intuition is that using more data will always result in a better model. However, we show that when we have a large non-uniform dataset, using a uniform subset can have several advantages. Reducing the time necessary to fit the model, avoiding numerical inaccuracies and improving the robustness with respect to errors in the output data are some aspects which can be improved by using a uniform subset. We furthermore describe several new and current methods for selecting a uniform subset. These methods are tested and compared on several artificial datasets and one real life dataset. The comparison shows how the selected subsets affect different aspects of the resulting Kriging model. As none of the subset selection methods performs best on all criteria, the best method to choose depends on how the different aspects are valued. The comparison made in this paper can be used to facilitate the user in making a good choice.     

DESIGN OF GROUNDWATER LEVEL MONITORING NETWORK WITH ORDINARY KRIGING

The primary network of groundwater level observation wells aims at realizing a regional groundwater management policy. It may give a regional picture of groundwater level with emphasis on the natural situation. Observation data from the primary network can be used to estimate the actual state of groundwater system. Since the cost of the installation and maintenance of a groundwater monitoring network is extremely high, the assessment of effectiveness of the network becomes very necessary. Groundwater level monitoring networks are the examples of discontinuous sampling on variables presenting spatial continuity and highly skewed frequency distributions. Anywhere in the aquifer, ordinary kriging provides estimates of the variable sampled and a standard error of the estimate. In this article, the average Kriging standard deviation was used as a criterion for the determination of network density,and the GIS-based approach was analysized. A case study of groundwater level network simulation in the Chaiwopu Basin, Xinjiang Uygur Autonomous Region, China, was presented. In the case study, the initial phreatic water observation wells were 18, a comparison of the three variogram parameters of the three defferent variogram models shows that the Gaussian model is the best. Finally, a network with 55 wells was constructed.     

稳健优化设计中代理模型不确定性的研究

代理模型的应用解决了稳健设计中计算量大的难题,但由于代理模型与真实模型间存在误差(代理模型的不确定性),而传统的稳健设计忽视了这种不确定性,必然会带来一定的设计误差。因此,针对稳健设计提出了一种基于蒙特卡洛抽样的代理模型不确定性的量化方法,在传统仅考虑参数不确定性的基础上,额外计入代理模型的不确定性对设计的影响。将提出的方法应用于一个数学算例和一个火箭弹卷弧翼气动稳健优化设计,所得优化结果较传统的未考虑代理模型不确定的稳健设计更为精确、合理,证实了提出方法的有效性。     

精细化矿体三维混构模型构建技术研究

为满足数字矿山建设对矿体三维模型越来越高的精度要求, 研究了精细化矿体混构模型的构建方法。利用分支轮廓线的中轴线构造过渡轮廓线, 建立无缝连接的矿体分支; 通过断层与矿体、矿体与矿体模型之间的布尔运算, 实现矿体和断层边界吻合的无缝模型; 使用外存八叉树技术构建小尺寸单元块的精细块段模型,提高块段模型边界与矿体表面模型边界的吻合; 分析矿石品位的空间变异性, 根据变异函数变程、勘探网度以及钻孔工程数量确定对应储量分级的样品搜索策略对矿石品位进行克里格方法估值。以某铜矿为实例对该方法进行验证, 结果表明本文提出的精细化模型构建技术能够满足资源分类评价、采矿设计、剖切后出工程图等较高的模型精度要求。     

基于滑动Kriging插值的无网格MLPG法求解结构动力问题

利用基于滑动Kriging插值的无网格局部Petrov-Galerkin (MLPG) 法来求解二维结构动力问题,Heaviside分段函数作为局部弱形式的权函数并采用精细积分法来离散时间域。基于滑动Kriging插值构造的形函数满足Kronecker Delta性质,因此可以直接施加本质边界条件。刚度矩阵形成过程中只涉及到边界积分,而没有涉及到区域积分和奇异积分。计算结果表明：基于滑动Kriging插值的MLPG法具有模拟简单、计算精度高等优点。     

激波针气动特性及外形参数优化研究

采用钝头体的飞行器在超声速特别是高超声速条件下,其前缘会形成头部弓形激波,进而带来较大的波阻,严重影响飞行器的气动性能。相关研究表明,在高超声速条件下,钝前缘安装激波针可以将激波推离物面,从而减小头部表面压力,是减小超声速钝体阻力的有效方法,但在超声速,特别是一些巡航速度不高（马赫数Ma=1.5左右）的导弹中,为满足射程等相关要求,对激波针减阻的使用价值还有待进行验证。为了研究激波针在Ma=1.5条件下对轴对称钝锥外形气动特性的影响,通过数值模拟方法对比了不同形状激波针在Ma=1.5条件下的减阻效果,分析了减阻机理及外形参数影响;通过基于Kriging和遗传算法相结合的优化方法对主要外形参数进行了优化设计,给出了减阻效果较好的激波针外形参数选取范围,对工程应用具有一定的借鉴意义。     

基于Kriging模型的武器站炮口扰动优化

炮口扰动是影响顶置武器站射击精度的重要因素。为研究抑制炮口扰动的技术途径,基于有限元理论建立顶置武器站刚柔耦合动力学模型,并通过射击精度试验验证了该模型的准确性。以炮口扰动综合函数为优化目标,构建顶置武器站炮口扰动优化设计模型,应用Kriging序列优化算法实现优化问题的求解。仿真结果表明,考虑部件柔性变形的有限元模型符合真实系统的振动特性,Kriging序列优化算法能够快速有效地用于武器站炮口扰动优化问题的求解。寻优得到的全局最优解,能使顶置武器站炮口扰动得到有效抑制。     

复合翼无人机机翼结构优化设计

针对轻小型复合翼无人机重量轻、刚度大的结构性能需求特点,对1种复合翼无人机机翼进行了结构布局优化设计。首先,根据设计指标与功能要求,对机翼内部承力结构进行了初始布局设计,并对4种梁、肋布置方案进行了静力学分析,通过对比选取最优结果。然后,考虑到翼梁位置参数对机翼刚度的影响较大,对机翼进行参数化建模,并采用基于Kriging模型的响应曲面法对其进行优化。最后,对样机进行了静力测试试验,验证仿真优化结果。优化后机翼的强度满足约束条件,翼梢变形下降了49.9%。结果表明,机翼的传力路线更合理,结构的效率更高。