Multi-fidelity (MF) surrogate model has been widely used in simulation-based engineering design processes to reduce the computational cost, with a focus on cases involving hierarchical low-fidelity (LF) data. However, accurately identifying and sorting the fidelity of LF models is challenging when dealing with non-hierarchical cases. In this paper, we propose a novel non-hierarchical MF surrogate framework called weighted multi-bi-fidelity (WMBF) to solve this problem. The proposed WMBF has both the advantage of two non-hierarchical frameworks, the weighted sum (WS) and parallel combination (PC) techniques, leveraging an entropy-based weight to include multiple-moments statistical information. It offers not only a weight with more information but also a more individualized scaling function within the weighted-sum framework, additionally a more individualized discrepancy function compared with existing methods. Moreover, it provides the idea of exploiting Kullback–Leibler (KL) divergence (an entropy-based metric) to characterize uncertainty for calculating weight within the WS framework. To validate the performance of the WMBF, we conduct evaluations using several numerical test functions and one engineering case. The result demonstrates that the WMBF achieves both accurate and robust predictions with minimal computational cost.

多保真度（MF）代理模型已广泛应用于基于仿真的工程设计过程中，以降低计算成本，重点关注涉及分层低保真度（LF）数据的情况。然而，在处理非分层情况时，准确识别和排序 LF 模型的保真度具有挑战性。在本文中，我们提出了一种新颖的非分层 MF 代理框架，称为加权多重双保真度（WMBF）来解决这个问题。所提出的 WMBF 兼具两种非分层框架的优点，即加权和（WS）和并行组合（PC）技术，利用基于熵的权重来包含多时刻统计信息。与现有方法相比，它不仅提供了具有更多信息的权重，而且在加权和框架内提供了更加个性化的缩放函数，此外还提供了更加个性化的差异函数。此外，它提供了利用 Kullback-Leibler (KL) 散度（一种基于熵的度量）来表征 WS 框架内计算权重的不确定性的想法。为了验证 WMBF 的性能，我们使用多个数值测试函数和一个工程案例进行评估。结果表明，WMBF 以最小的计算成本实现了准确且稳健的预测。