Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency and efficiency in finding global optimal solutions, and is particularly useful for expensive systems.     

Kriging‐based optimization applied to flow control

The automatic optimization of flow control devices is a delicate issue because of the drastic computational time related to unsteady high‐fidelity flow analyses and the possible multimodality of the objective function. Thus, we experiment in this article the use of kriging‐based algorithms to optimize flow control parameters because these methods have shown their efficiency for global optimization at moderate cost. Navier–Stokes simulations, carried out for different control parameters, are used to build iteratively a kriging model. At each step, a statistical analysis is performed to enrich the model with new simulation results by exploring the most promising areas, until optimal flow control parameters are found. This approach is validated and demonstrated on two problems, including comparisons with similar studies: the control of the flow around an oscillatory rotating cylinder and the reduction of the intensity of a shock wave for a transonic airfoil by adding a bump to the airfoil profile. Copyright © 2011 John Wiley & Sons, Ltd.     

福建行洛坑钨矿变异函数模型的研究

以行洛坑细-网脉状钨矿为实例,对服从对数正态分布的区域化变量,分别用原始品位值和对数变换值建立变异函数模型。通过交叉验证等方法研究表明,对原始数据进行对数变换所得到的模型能更好地揭示区域化变量的空间变化规律,而且,对数线性克立格估值也比线性克立格估值更佳。     

Toward amino acid typing for proteins in FFLUX

Continuing the development of the FFLUX, a multipolar polarizable force field driven by machine learning, we present a modern approach to atom‐typing and building transferable models for predicting atomic properties in proteins. Amino acid atomic charges in a peptide chain respond to the substitution of a neighboring residue and this response can be categorized in a manner similar to atom‐typing. Using a machine learning method called kriging, we are able to build predictive models for an atom that is defined, not only by its local environment, but also by its neighboring residues, for a minimal additional computational cost. We found that prediction errors were up to 11 times lower when using a model specific to the correct group of neighboring residues, with a mean prediction of ∼0.0015 au. This finding suggests that atoms in a force field should be defined by more than just their immediate atomic neighbors. When comparing an atom in a single alanine to an analogous atom in a deca‐alanine helix, the mean difference in charge is 0.026 au. Meanwhile, the same difference between a trialanine and a deca‐alanine helix is only 0.012 au. When compared to deca‐alanine models, the transferable models are up to 20 times faster to train, and require significantly less ab initio calculation, providing a practical route to modeling large biological systems. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

利用Kriging方法进行结构模型修改

结构模型修改已经演化为一个多学科的研究课题，本文将该问题处理为确定从模态参数到模型参数之间的映射问题，并利用起源于地质统计学的Kriging技术实现该映射。对于一实际钢结构，通过实验测量得到了全部摸态数据，利用部分测量得到的模态数据进行了模型修改的实验研究，实验结果表明，利用修改后模型计算得到的全部摸态数据与测量结果吻合良好，表明该模型修改方法是可行的；同时该方法表现出了与基于神经网络的修改方法的互补特性。     

Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.     

溢流阀环形槽抗气穴性能分析及优化设计

采用RNG k ε湍流模型数值模拟溢流阀环形槽口的气穴流动现象,并分析环形槽各结构参数对阀腔内气穴流场的影响。结果表明,结构参数θ越大,参数R1和R2取值最优时,抗气穴性能更明显。根据环形槽结构参数的数值模拟数据,利用kriging模型方法得出代理函数,即以阀腔内最大气体体积分数为目标函数,以Gauss函数为相关函数,采用常数回归模型的似然函数。利用改进PSO算法对代理函数进行优化计算,经对比得出优化参数的抗气穴性能显著。     

A generalization of inverse distance weighting and an equivalence relationship to noise-free Gaussian process interpolation via Riesz representation theorem

In this paper, we show the relationship between two seemingly unrelated approximation techniques. On the one hand, a certain class of Gaussian process-based interpolation methods, and on the other hand inverse distance weighting, which has been developed in the context of spatial analysis where there is often a need for interpolating from irregularly spaced data to produce a continuous surface. We develop a generalization of inverse distance weighting and show that it is equivalent to the approximation provided by the class of Gaussian process-based interpolation methods. The equivalence is established via an elegant application of Riesz representation theorem concerning the dual of a Hilbert space. It is thus demonstrated how a classical theorem in linear algebra connects two disparate domains.