Surrogate models have been widely studied for optimization tasks in the domain of engineering design. However, the expensive and time-consuming simulation cycles needed for complex products always result in limited simulation data, which brings a challenge for building high accuracy surrogate models because of the incomplete information contained in the limited simulation data. Therefore, a method that builds a surrogate model and conducts design optimization by integrating limited simulation data and engineering knowledge through Bayesian optimization (BO-DK4DO) is presented. In this method, the shape engineering knowledge is considered and used as derivative information which is integrated with the limited simulation data with a Gaussian process (GP). Then the GP is updated sequentially by sampling new simulation data and the optimal design solutions are found by maximizing the GP. The aim of BO-DK4DO is to significantly reduce the required number of computer simulations for finding optimal design solutions. The BO-DK4DO is verified by using benchmark functions and an engineering design problem: hot rod rolling. In all scenarios, the BO-DK4DO shows faster convergence rate than the general Bayesian optimization without integrating engineering knowledge, which means the required amount of data is decreased.

在工程设计领域，替代模型已被广泛研究用于优化任务。但是，复杂产品所需的昂贵且费时的仿真周期始终会导致有限的仿真数据，由于有限的仿真数据中包含的信息不完整，这给构建高精度的替代模型带来了挑战。因此，提出了一种通过贝叶斯优化（BO-DK4DO）集成有限的仿真数据和工程知识来构建替代模型并进行设计优化的方法。在这种方法中，考虑了形状工程知识并将其用作派生信息，该信息与具有高斯过程（GP）的有限模拟数据集成在一起。然后，通过采样新的仿真数据来顺序更新GP，并通过最大化GP来找到最佳设计解决方案。BO-DK4DO的目的是显着减少寻找最佳设计解决方案所需的计算机仿真次数。BO-DK4DO已通过使用基准功能和一个工程设计问题：热棒轧制进行了验证。在所有情况下，BO-DK4DO的收敛速度都比一般的贝叶斯优化快，而且没有集成工程知识，这意味着减少了所需的数据量。