In numerical simulations, a high-fidelity (HF) simulation is generally more accurate than a low-fidelity (LF) simulation, while the latter is generally more computationally efficient than the former. To take advantages of both HF and LF simulations, a multi-fidelity surrogate (MFS) model based on moving least squares (MLS), termed as adaptive MFS-MLS, is proposed. The MFS-MLS calculates the LF scaling factors and the unknown coefficients of the discrepancy function simultaneously using an extended MLS model. In the proposed method, HF samples are not regarded as equally important in the process of constructing MFS-MLS models, and adaptive weightings are given to different HF samples. Moreover, both the size of the influence domain and the scaling factors can be determined adaptively according to the training samples. The MFS-MLS model is compared with three state-of-the-art MFS models and three single-fidelity surrogate models in terms of the prediction accuracy through multiple benchmark numerical cases and an engineering problem. In addition, the effects of key factors on the performance of the MFS-MLS model, such as the correlation between HF and LF models, the cost ratio of HF to LF samples, and the combination of HF and LF samples, are also investigated. The results show that MFS-MLS is able to provide competitive performance with high computational efficiency.

在数值模拟中，高保真 (HF) 模拟通常比低保真 (LF) 模拟更准确，而后者的计算效率通常高于前者。为了利用 HF 和 LF 模拟，提出了一种基于移动最小二乘法 (MLS) 的多保真代理 (MFS) 模型，称为自适应 MFS-MLS。MFS-MLS 使用扩展的 MLS 模型同时计算 LF 缩放因子和差异函数的未知系数。在所提出的方法中，在构建MFS-MLS模型的过程中，HF样本不被视为同等重要，并且对不同的HF样本给予自适应权重。此外，影响域的大小和缩放因子都可以根据训练样本自适应地确定。通过多个基准数值案例和一个工程问题，将 MFS-MLS 模型与三个最先进的 MFS 模型和三个单保真代理模型在预测精度方面进行了比较。此外，还研究了关键因素对 MFS-MLS 模型性能的影响，例如 HF 和 LF 模型之间的相关性、HF 与 LF 样本的成本比以及 HF 和 LF 样本的组合。结果表明，MFS-MLS 能够以高计算效率提供具有竞争力的性能。还研究了HF和LF模型之间的相关性，HF与LF样本的成本比以及HF和LF样本的组合。结果表明，MFS-MLS 能够以高计算效率提供具有竞争力的性能。还研究了HF和LF模型之间的相关性，HF与LF样本的成本比以及HF和LF样本的组合。结果表明，MFS-MLS 能够以高计算效率提供具有竞争力的性能。