Surrogate models are widely used in simulation-based engineering design. The distribution of samples directly determines the quality and efficiency of surrogate models, which has a significant influence on follow-up work. This paper proposes a multipeak parallel adaptive infilling (MPEI) strategy based on expected improvement (EI), which can be divided into two stages: the construction of candidate peak areas and the selection of appropriate candidates at the candidate peak areas. In the first stage, the candidates are divided into the corresponding subspaces in sequence according to the value of EI and the position of each candidate to construct the candidate peak areas. In the second stage, the Gaussian function is used to extract the uncorrelated parent point and the corresponding offspring points in each candidate peak area. Based on these stages, the MPEI strategy selects multiple new samples in spaces with both local optima and areas of large uncertainty interest, which can fully balance global exploration and local exploitation. In addition, the samples selected in each candidate peak area are concise and locally uniform, which can effectively reduce the computational cost. Seven benchmark cases and one engineering problem are used to validate the performance of the MPEI strategy. The results show that the MPEI strategy can efficiently obtain the desired prediction accuracy of surrogate models at a small price of a few samples and confirm the feasibility and robustness of the presented methodology.

代理模型广泛用于基于仿真的工程设计。样本的分布直接决定了代理模型的质量和效率，这对后续工作有重要影响。本文提出了一种基于期望改进（EI）的多峰并行自适应填充（MPEI）策略，该策略可分为两个阶段：候选峰面积的构建和在候选峰面积处选择合适的候选物。在第一阶段，根据EI的值和每个候选的位置，将候选依次划分到相应的子空间中，构建候选峰区域。在第二阶段，利用高斯函数提取每个候选峰区域中不相关的父点和对应的后代点。基于这些阶段，MPEI 策略在具有局部最优和较大不确定性兴趣的空间中选择多个新样本，可以充分平衡全局探索和局部开发。此外，每个候选峰区域选择的样本简洁且局部均匀，可以有效降低计算成本。七个基准案例和一个工程问题用于验证 MPEI 策略的性能。结果表明，MPEI 策略可以以少量样本的小价格有效地获得代理模型所需的预测精度，并证实了所提出方法的可行性和稳健性。可以充分平衡全局探索和局部开发。此外，每个候选峰区域选择的样本简洁且局部均匀，可以有效降低计算成本。七个基准案例和一个工程问题用于验证 MPEI 策略的性能。结果表明，MPEI 策略可以以少量样本的小价格有效地获得代理模型所需的预测精度，并证实了所提出方法的可行性和稳健性。可以充分平衡全局探索和局部开发。此外，每个候选峰区域选择的样本简洁且局部均匀，可以有效降低计算成本。七个基准案例和一个工程问题用于验证 MPEI 策略的性能。结果表明，MPEI 策略可以以少量样本的小价格有效地获得代理模型所需的预测精度，并证实了所提出方法的可行性和稳健性。