Hierarchical Kriging Model for Variable-Fidelity Surrogate Modeling
Hierarchical Kriging Model for Variable-Fidelity Surrogate Modeling
复制标题
用于可变保真度代理建模的分层克里金模型
DOI：
10.2514/1.j051354
复制
发表时间：
2012-09-01
期刊：
影响因子：
2.5
通讯作者：
Goertz, Stefan
中科院分区：
文献类型：
--
作者：
Han, Zhong-Hua;Goertz, Stefan
通过可变保真度的代理建模技术，可以显著提高为计算机代码的输出构建代理模型的效率。本文提出了一种分层克立格模型，并将其用于可变保真度代理建模问题。这里，分层克里格法是指使用采样的低保真函数的克里格法模型作为模型趋势的高保真函数的代理模型。结果，将低保真数据中的变化映射到高保真数据，并获得更准确的高保真函数的代理模型。给出了分层克立格模型的一个完整的推导。文中给出了一个算例，并对RAE2822翼型和工业运输机外形的气动数据进行了建模。数值算例表明，该方法具有较高的计算效率、精度和鲁棒性。我们还观察到，分层克立格法比传统的协克立格法提供了更合理的均方误差估计。它可以应用于飞机的高效气动分析和外形优化，或任何其他使用变保真度计算机代码的研究领域。
The efficiency of building a surrogate model for the output of a computer code can be dramatically improved via variable-fidelity surrogate modeling techniques. In this article, a hierarchical kriging model is proposed and used for variable-fidelity surrogate modeling problems. Here, hierarchical kriging refers to a surrogate model of a highfidelity function that uses a kriging model of a sampled lower-fidelity function as a model trend. As a consequence, the variation in the lower-fidelity data is mapped to the high-fidelity data, and a more accurate surrogate model for the high-fidelity function is obtained. A self-contained derivation of the hierarchical kriging model is presented. The proposed method is demonstrated with an analytical example and used for modeling the aerodynamic data of an RAE 2822 airfoil and an industrial transport aircraft configuration. The numerical examples show that it is efficient, accurate, and robust. It is also observed that hierarchical kriging provides a more reasonable mean-squared-error estimation than traditional cokriging. It can be applied to the efficient aerodynamic analysis and shape optimization of aircraft or any other research areas where computer codes of varying fidelity are in use.