To reduce the computational cost in engineering design, expensive high-fidelity simulation models are approximated by mathematical models, named as metamodels. Typical metamodeling methods assume that expensive simulation models are black-box functions. In this paper, in order to improve the accuracy of metamodels and reduce the cost of building metamodels, knowledge about engineering design problems is employed to help develop a novel metamodel, named as causal artificial neural network (causal-ANN). Cause–effect relations intrinsic to the design problem are employed to decompose an ANN into sub-networks and values of intermediate variables are utilized to train these sub-networks. By involving knowledge of the design problem, the accuracy of causal-ANN is higher than the traditional metamodeling methods that assume black-box functions. Additionally, one can identify attractive subspaces from the causal-ANN by leveraging the structure of the causal-ANN and the theory of Bayesian Networks. The impacts of fidelity of causal graphs and design variable correlations are also discussed in the paper. The engineering case studies demonstrate that the causal-ANN can be accurately constructed with a small number of expensive simulations, and attractive design subspaces can be identified directly from the causal-ANN.

为了减少工程设计中的计算成本，使用数学模型（称为元模型）来近似昂贵的高保真仿真模型。典型的元建模方法假定昂贵的仿真模型是黑盒函数。在本文中，为了提高元模型的准确性并降低构建元模型的成本，利用有关工程设计问题的知识来帮助开发一种新颖的元模型，称为因果人工神经网络（causal-ANN）。设计问题固有的因果关系用于将ANN分解为子网络，中间变量的值用于训练这些子网络。通过涉及设计问题的知识，因果ANN的准确性要高于假定黑盒功能的传统元建模方法。另外，通过利用因果ANN的结构和贝叶斯网络理论，可以从因果ANN识别有吸引力的子空间。本文还讨论了因果图保真度和设计变量相关性的影响。工程案例研究表明，可以通过少量昂贵的仿真来精确构建因果ANN，并且可以直接从因果ANN中识别出有吸引力的设计子空间。