TY - JOUR
T1 - Optimized Generative Topographic Mapping Method for Aerodynamic Design Optimization
AU - Zhang, Wei
AU - Zhao, Ke
AU - Shi, Longlong
AU - Xia, Lu
AU - Gao, Zhenghong
N1 - Publisher Copyright:
© 2024 American Society of Civil Engineers.
PY - 2024/11/1
Y1 - 2024/11/1
N2 - This paper proposes a nonlinear space dimension reduction method named Optimized Generative Topographic Mapping (OGTM). The Generative Topographic Mapping (GTM) method relies on the training sample set to capture the manifold of objective functions, and the generation of the training sample set causes an enormous computational burden. The choice of GTM hyperparameters has a significant influence on the design results. Traditional research has generally adopted the "cut-and-try"method to determine the corresponding hyperparameters and the best design, leading to wasted computational cost. The proposed OGTM overcomes this issue by minimizing the fitting error between the low-dimensional and high-dimensional samples, and the suitable hyperparameters are directly obtained by minimizing the fitting. In addition, the paper adopts a variable-fidelity sample filtration method to extract the promising regions with fewer sample points. To test and verify the effectiveness of the proposed method, it was then compared with the PCA and EGO methods in RAE2822 airfoil and ONERA M6 wing aerodynamic designs. The results demonstrate that the proposed method could capture the effective design space and generally take less computational cost to find the ideal results in all design optimizations.
AB - This paper proposes a nonlinear space dimension reduction method named Optimized Generative Topographic Mapping (OGTM). The Generative Topographic Mapping (GTM) method relies on the training sample set to capture the manifold of objective functions, and the generation of the training sample set causes an enormous computational burden. The choice of GTM hyperparameters has a significant influence on the design results. Traditional research has generally adopted the "cut-and-try"method to determine the corresponding hyperparameters and the best design, leading to wasted computational cost. The proposed OGTM overcomes this issue by minimizing the fitting error between the low-dimensional and high-dimensional samples, and the suitable hyperparameters are directly obtained by minimizing the fitting. In addition, the paper adopts a variable-fidelity sample filtration method to extract the promising regions with fewer sample points. To test and verify the effectiveness of the proposed method, it was then compared with the PCA and EGO methods in RAE2822 airfoil and ONERA M6 wing aerodynamic designs. The results demonstrate that the proposed method could capture the effective design space and generally take less computational cost to find the ideal results in all design optimizations.
KW - Aerodynamic optimization
KW - Generative topographic mapping (GTM)
KW - High-dimensional design space
KW - Nonlinear dimension reduction
KW - Variable fidelity sample generation
UR - http://www.scopus.com/inward/record.url?scp=85202447214&partnerID=8YFLogxK
U2 - 10.1061/JAEEEZ.ASENG-5518
DO - 10.1061/JAEEEZ.ASENG-5518
M3 - 文章
AN - SCOPUS:85202447214
SN - 0893-1321
VL - 37
JO - Journal of Aerospace Engineering
JF - Journal of Aerospace Engineering
IS - 6
M1 - 04024085
ER -