A non‐stationary covariance‐based Kriging method for metamodelling in engineering design
A non‐stationary covariance‐based Kriging method for metamodelling in engineering design
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DOI：
10.1002/nme.1969
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发表时间：
2007-08
影响因子：
2.9
通讯作者：
Ying Xiong;Wei Chen;D. Apley;Xuru Ding
中科院分区：
文献类型：
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作者：
Ying Xiong;Wei Chen;D. Apley;Xuru Ding
元模型被广泛用于促进涉及计算昂贵的模拟的工程系统的分析和优化。克里格法是一种元建模技术，以其构建具有非线性行为的响应的代理模型的能力而闻名。但是，在响应的平滑程度变化显著的情况下，克里格法所基于的平稳协方差结构的假设不成立。虽然非平稳高斯过程模型在统计学和地质统计学领域已经研究了多年，但这主要是针对相对低维的物理实验数据。在本文中，非平稳协方差结构被纳入克里格模型的计算机模拟。为了表示非平稳协方差结构，我们采用基于参数化密度函数的非线性映射方法。为了避免工程设计中典型的高维问题的过度参数化，我们提出了一种非线性映射方法的修改版本，具有更稀疏但更灵活的参数化。通过数学和工程实例证明了该方法的有效性。通过在各种采样设置下测试多个函数，验证了该方法的鲁棒性。我们还表明，我们的方法是有效的量化预测的不确定性与使用元模型。版权所有© 2006约翰威利父子有限公司。
Metamodels are widely used to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. Kriging is a metamodelling technique that is well known for its ability to build surrogate models of responses with non‐linear behaviour. However, the assumption of a stationary covariance structure underlying Kriging does not hold in situations where the level of smoothness of a response varies significantly. Although non‐stationary Gaussian process models have been studied for years in statistics and geostatistics communities, this has largely been for physical experimental data in relatively low dimensions. In this paper, the non‐stationary covariance structure is incorporated into Kriging modelling for computer simulations. To represent the non‐stationary covariance structure, we adopt a non‐linear mapping approach based on parameterized density functions. To avoid over‐parameterizing for the high dimension problems typical of engineering design, we propose a modified version of the non‐linear map approach, with a sparser, yet flexible, parameterization. The effectiveness of the proposed method is demonstrated through both mathematical and engineering examples. The robustness of the method is verified by testing multiple functions under various sampling settings. We also demonstrate that our method is effective in quantifying prediction uncertainty associated with the use of metamodels. Copyright © 2006 John Wiley & Sons, Ltd.