Knowledge assisted metamodeling and optimization method for large-scale engineering design

Simulation-based design optimization methods commonly treat simulation as a black-box function. An approximation model of the simulation, called metamodel, is often built and used in optimization. However, modeling and searching in an unknown design space lead to high computational cost. To further improve the efficiency of optimization, knowledge of design problems needs to be involved in assisting metamodeling and optimization. This work endeavors to systematically incorporating knowledge for this purpose. After extensive review, two types of knowledge, sensitivity information and causal relations, are employed in solving large scale engineering design problems. Instead of constructing a complete metamodel, a Partial Metamodel-based Optimization (PMO) method is developed to reduce the number of samples for optimizing large-scale problems, using Radial Basis Function-High Dimensional Model Representation (RBF-HDMR) along with a moving cut-center strategy. Sensitivity information is used to selectively model component functions in a partial metamodel. The cut center of a HDMR model moves to the current optimum at each iteration to pursue the optimum. Numerical tests and an airfoil design case show that the PMO method can lead to better optimal results when the samples are scarce. Causal graphs capture relational knowledge among design variables and outcomes. By constructing and performing qualitative analysis on a causal graph, variables without contradiction can be found, whose values can be determined without resorting to optimization. The design problem can thus be divided into two sub-problems based on impact of variables. This dimension reduction and decomposition strategy is applied to a power converter design and an aircraft concept design problem with significantly improved efficiency. Combing the structure of Artificial Neural Networks (ANNs) with causal graphs, a causal-ANN is developed to improve the accuracy of metamodels by involving knowledge. The structure of causal graphs is employed to decompose an ANN into sub-networks. Additionally, leveraging the structure of causal-ANN and theory of Bayesian Networks, the attractive variable subspaces can be identified without additional simulation. Finally, the causal-ANN is applied in a residential energy consumption forecasting problem and both the modeling accuracy and efficiency are improved. This work systematically and methodically models and captures knowledge and brings knowledge in metamodeling and optimization. Sensitivities and causal relations have been incorporated in optimization strategies that have been successfully applied to various engineering design problems. Further research can be extended to studies on how to incorporate other types of knowledge to assist metamodeling and optimization.