Efficient Global Optimization of Multidisciplinary System using Variable Fidelity Analysis and Dynamic Sampling Method


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Virginia Tech


Work in this dissertation is motivated by reducing the design cost at the early design stage while maintaining high design accuracy throughout all design stages. It presents four key design methods to improve the performance of Efficient Global Optimization for multidisciplinary problems. First, a fidelity-calibration method is developed and applied to lower-fidelity samples. Function values analyzed by lower fidelity analysis methods are updated to have equivalent accuracy to that of the highest fidelity samples, and these calibrated data sets are used to construct a variable-fidelity Kriging model. For the design of experiment (DOE), a dynamic sampling method is developed and includes filtering and infilling data based on mathematical criteria on the model accuracy. In the sample infilling process, multi-objective optimization for exploitation and exploration of design space is carried out. To indicate the fidelity of function analysis for additional samples in the variable-fidelity Kriging model, a dynamic fidelity indicator with the overlapping coefficient is proposed. For the multidisciplinary design problems, where multiple physics are tightly coupled with different coupling strengths, multi-response Kriging model is introduced and utilizes the method of iterative Maximum Likelihood Estimation (iMLE). Through the iMLE process, a large number of hyper-parameters in multi-response Kriging can be calculated with great accuracy and improved numerical stability. The optimization methods developed in the study are validated with analytic functions and showed considerable performance improvement. Consequentially, three practical design optimization problems of NACA0012 airfoil, Multi-element NLR 7301 airfoil, and all-moving-wingtip control surface of tailless aircraft are performed, respectively. The results are compared with those of existing methods, and it is concluded that these methods guarantee the equivalent design accuracy at computational cost reduced significantly.



Efficient Global Optimization(EGO), Variable-Fidelity(VF) Analysis, Data mining, Gaussian Process Regression(GPR) modeling, Design of Experiment(DoE)