Alternative Cokriging Method for Variable-Fidelity Surrogate Modeling
Alternative Cokriging Method for Variable-Fidelity Surrogate Modeling
复制标题
DOI：
10.2514/1.j051243
复制
发表时间：
2012-08
期刊：
影响因子：
2.5
通讯作者：
Zhonghua Han;Ralf Zimmerman;S. Görtz
中科院分区：
文献类型：
--
作者：
Zhonghua Han;Ralf Zimmerman;S. Görtz
代理建模在航空航天工程的不同领域发挥着越来越重要的作用，例如飞机或航天器的空气动力学形状优化、空气动力学数据生产、结构设计以及多学科设计优化。协同克里金法为传统克里金法提供了一种有吸引力的替代方法，以提高构建替代模型的效率。它最初是在地质统计学界提出并应用的，目的是在密集采样的辅助变量的帮助下，增强对不太密集采样的主要感兴趣变量的预测。由于协同克里金法的基础理论是双变量或多变量克里金法，因此它可以被视为（单变量）克里金法对辅助变量或二级信息辅助的模型的一般扩展。为了将协同克里金法应用于与确定性计算机实验相关的代理建模问题，本文的动机是开发另一种协同克里金法，以解决与构建协同克里金法协方差矩阵相关的挑战[7]。其他作者与本研究相关的早期工作可以在统计界找到。例如，Kennedy 和 O’Hagan (KOH) 提出了一种自回归模型来计算协方差矩阵中的协方差和互协方差，并开发了一种贝叶斯方法来在低保真度模拟代码的帮助下预测昂贵的高保真模拟代码的输出。这种贝叶斯方法与适用于计算机实验的协同克里金法形式相同。后来，Qian和Wu提出了类似的方法，用随机函数（高斯过程模型）代替KOH方法中的常数乘因子来解释非线性尺度变化。 Forrester 等人将 KOH 的方法应用于航空航天工程背景下的多保真度分析和设计优化。和 Kuya 等人。最近，Zimmerman 和 Han 提出了一种具有简化互相关估计的协同克里金方法。在本文中，我们提出了一种构建协同克里金协方差矩阵的替代方法，并在基于代理的分析和优化的背景下开发了更实用的协同克里金方法。所开发的协同克里金方法针对分析问题进行了验证，并应用于构建 RAE 2822 翼型的空气动力系数和阻力极的全局近似模型。
Surrogate modeling plays an increasingly important role in different areas of aerospace engineering, such as erodynamic shape optimization, aerodynamic data production, structural design, and multidisciplinary design optimization of aircraft or spacecraft. Cokriging provides an attractive alternative approach to conventional kriging to improve the efficiency of building a surrogate model. It was initially proposed and applied in the geostatistics community for the enhanced prediction of less intensively sampled primary variables of interest with the assistance of intensively sampled auxiliary variables. As the underlying theory of cokriging is that of two-variable or multivariable kriging, it can be regarded as a general extension of (one-variable) kriging to a model that is assisted by auxiliary variables or secondary information. In an attempt to apply cokriging to the surrogate modeling problems associated with deterministic computer experiments, this article is motivated by the development of an alternative cokriging method to address the challenge related to the construction of the covariance matrix of cokriging [7]. Earlier work done by other authors related to this study can be found in the statistical community. For example, Kennedy and O’Hagan (KOH) proposed an autoregressive model to calculate the covariances and crosscovariances in the covariance matrix and developed a Bayesian approach to predict the output from an expensive high-fidelity simulation code with the assistance of lower-fidelity simulation codes. This Bayesian approach is identical to a form of cokriging suitable for computer experiments. Later, Qian andWu proposed a similar method, in which a random function (Gaussian process model) was used to replace the constant multiplicative factor of KOH’s method to account for the nonlinear scale change. KOH’s method was applied to multifidelity analysis and design optimization in the context of aerospace engineering by Forrester et al. and Kuya et al. More recently, Zimmerman and Han proposed a cokriging method with simplified cross-correlation estimation. In this article, we propose an alternative approach for the construction of the cokriging covariance matrix and develop a more practical cokriging method in the context of surrogate-based analysis and optimization. The developed cokriging method is validated against an analytical problem and applied to construct global approximation models of the aerodynamic coefficients as well as the drag polar of an RAE 2822 airfoil.