分形插值在地球化学数据中的应用

 地球化学数据的正常值往往服从正态分布或对数正态分布,异常值往往具有分形分布,具有局部奇异性。文中分别采用分形分布数据、正态分布数据和西藏驱龙地区的实际数据比较3种具有代表性的插值方法：反距离加权法、克里格法和分形法。结果表明：服从正态分布的数据,三种插值方法应用效果相差甚微;服从分形分布的数据使用分形插值的效果优于反距离加权和克里格法;分形插值法适用于具有奇异性的数据。此研究有助于合理选择插值方法。     

Spatial Regression Models,Response Surfaces,and Process Optimization

Abstract

Spatial regression models are developed as a complementary alternative to second-order polynomial response surfaces in the context of process optimization. These models provide estimates of design variable effects and smooth, data-faithful approximations to the unknown response function over the design space. The predicted response surfaces are driven by the covariance structures of the models. Several structures, isotropic and anisotropic, are considered and connections with thin plate splines are reviewed. Estimation of covariance parameters is achieved via maximum likelihood and residual maximum likelihood. A feature of the spatial regression approach is the visually appealing graphical summaries that are produced. These allow rapid and intuitive identification of process windows on the design space for which the response achieves target performance. Relevant design issues are briefly discussed and spatial designs, such as the packing designs available in Gosset, are suggested as a suitable design complement. The spatial regression models also perform well with no global design, for example with data obtained from series of designs on the same space of design variables. The approach is illustrated with an example involving the optimization of components in a DNA amplification assay. A Monte Carlo comparison of the spatial models with both thin plate splines and second-order polynomial response surfaces for a scenario motivated by the example is also given. This shows superior performance of the spatial models to the second-order polynomials with respect to both prediction over the complete design space and for cross-validation prediction error in the region of the optimum. An anisotropic spatial regression model performs best for a high noise case and both this model and the thin plate spline for a low noise case. Spatial regression is recommended for construction of response surfaces in all process optimization applications.     

Kriging与响应面方法在气动优化设计中的应用

近似模型方法在工程优化设计中开始得到重视。本文分别应用Kriging方法和响应面方法进行了翼型气动优化设计。结果表明,Kriging方法的设计结果,升阻比较参考翼型提高了81%;在初始设计空间,响应面方法的结果很差,通过不断缩减设计空间,设计得到了有效的改善,升阻比提高了70%,但需要的计算量远远高于Kriging模型。     

Bayesian process optimization using failure amplification method

This work is motivated by a problem of optimizing printed circuit board manufacturing using design of experiments. The data are binary, which poses challenges in model fitting and optimization. We use the idea of failure amplification method to increase the information supplied by the data and then use a Bayesian approach for model fitting. The Bayesian approach is implemented using Gaussian process models on a latent variable representation. It is demonstrated that the failure amplification method coupled with a Bayesian approach is highly suitable for optimizing a process with binary data. Copyright © 2010 John Wiley & Sons, Ltd.     

Accuracy and tractability of a kriging model of intramolecular polarizable multipolar electrostatics and its application to histidine

We propose a generic method to model polarization in the context of high‐rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc‐1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds (“1, 4 and higher” interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom–atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol^?1. © 2013 Wiley Periodicals, Inc.     

城市土地价格的空间插值估计方法

随着城市的快速发展,准确的衡量城市土地价格,以及土地价格分布,对于城市建设规划具有非常重要的作用。首先,获取土地价格的实际数据,并对数据的空间特征和统计学特征进行分析。然后,在空间统计分析的基础上,设计出对克里金插值的半变异函数进行拟合的实验方案,并从中选出误差最小的估计模型。最后,得到土地价格估计模型后,以某城市为例进行土地价格估计,并对估计结果进行误差分析。分析结果与预测结果基本一致,估计得到的土地价格分布也与实际情况相符,准确的估计结果在所有结果中占90%以上,得到较好的估计精度。