Multi-fidelity (MF) surrogate models have been widely used in engineering optimization problems to reduce the design cost by replacing computat ional expensive simulations. Ignoring the prediction uncertainty of the MF model that is caused by a limited number of samples may result in infeasible solutions. Conservative MF surrogate model, which can effectively improve the feasibility of the constraints, has been a promising way to address this issue. In this paper, an ensemble weighted average (EWA) conservative multi-fidelity modeling method that integrates the performance of different error metrics is proposed. In the proposed method, the bootstrap method and mean-square-error method are reasonably weighted to calculate the safety margin of the MF surrogate model. The weights for the two metrics are determined through an optimization problem, which considers the performance of the two metrics in different subsets of the sample points. The effectiveness of the proposed method is illustrated through several numerical examples and a pressure vessel design problem. Results show that the proposed method constructs a more accurate conservative MF surrogate model than other methods in different problems. Furthermore, applying the constructed conservative MF surrogate model into optimization problems obtains more accurate optimal solutions while ensuring the feasibility of it.

中文翻译：

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一种用于工程优化的集成加权平均保守多保真代理建模方法

多保真 (MF) 代理模型已广泛用于工程优化问题，以通过替代昂贵的计算模拟来降低设计成本。忽略由有限数量的样本引起的 MF 模型的预测不确定性可能会导致不可行的解决方案。保守的MF代理模型可以有效地提高约束的可行性，是解决这个问题的一种很有前途的方法。在本文中，提出了一种集成不同误差度量的性能的集成加权平均（EWA）保守多保真建模方法。该方法通过合理加权自举法和均方误差法来计算MF代理模型的安全裕度。这两个指标的权重是通过优化问题确定的，它考虑了两个指标在样本点的不同子集中的性能。通过几个数值例子和压力容器设计问题说明了所提出方法的有效性。结果表明，所提出的方法在不同问题上构建了比其他方法更准确的保守MF代理模型。此外，将构建的保守MF代理模型应用于优化问题，在保证其可行性的同时，可以获得更准确的最优解。结果表明，所提出的方法在不同问题上构建了比其他方法更准确的保守MF代理模型。此外，将构建的保守MF代理模型应用于优化问题，在保证其可行性的同时，可以获得更准确的最优解。结果表明，所提出的方法在不同问题上构建了比其他方法更准确的保守MF代理模型。此外，将构建的保守MF代理模型应用于优化问题，在保证其可行性的同时，可以获得更准确的最优解。