A general multi-fidelity metamodeling framework for models with various output correlation
A general multi-fidelity metamodeling framework for models with various output correlation
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DOI：
10.1007/s00158-023-03537-5
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发表时间：
2023-04
影响因子：
3.9
通讯作者：
Yue Zhao;Jie Liu-;Zhelong He
中科院分区：
文献类型：
--
作者：
Yue Zhao;Jie Liu-;Zhelong He
多保真度元建模方法已被广泛应用于复杂工程设计领域，以权衡建模效率和模型精度。为了更好地集成具有各种相关性的多保真度模型的信息，进一步增强复杂设计问题多保真度建模的通用性，提出了一种通用的多保真度元建模框架--输出缩放多保真度（OS-MF）方法. OS-MF元建模框架首先分别通过最优和继承的拉丁超立方体采样方法生成高保真和低保真样本，以尽可能均匀地填充参数空间。随后，根据Kriging方法构建低保真元模型。为了逼近低保真输出和高保真输出之间的关系，引入支持向量回归，方便地生成一维输出映射模型。最后，通过优化Kriging极大似然方程，确定了两个子元模型的权因子和尺度函数的超参数。通过6个不同输出相关性的数值算例和2个工程算例验证了OS-MF方法的通用性和有效性。该方法提供了一个有效的工具，多保真度建模下的各种相关性之间的低保真度和高保真度的输出。
Multi-fidelity metamodeling methods have been widely utilized in the field of complex engineering design to trade off modeling efficiency against model accuracy. To better integrate the information from multi-fidelity models with various correlation and further enhance the universality of multi-fidelity modeling for complex design problems, a general multi-fidelity metamodeling framework namely output scaling multi-fidelity (OS-MF) method is proposed in this paper. The OS-MF metamodeling framework starts with generating high-fidelity and low-fidelity samples by optimal and inherited Latin hypercube sampling methods respectively to fill the parameter space as uniformly as possible. Subsequently, the low-fidelity metamodel is constructed according to Kriging method. For the purpose of approximating the relation between the low-fidelity and high-fidelity outputs, support vector regression is introduced to conveniently generate a single-dimensional output mapping model. Finally, the weighting factors of the above two sub-metamodels and hyperparameters of scaling function are evaluated through the optimization of Kriging maximum likelihood equation. Six numerical examples with different output correlation and two engineering examples are adopted to demonstrate the universality and effectiveness of the OS-MF approach. The proposed method provides an efficient tool for multi-fidelity modeling under various correlation between low-fidelity and high-fidelity outputs.