Optimization method using nodal aberration theory for coaxial imaging systems with radial basis functions based on surface slope

2021 ◽  
Vol 60 (9) ◽  
pp. 2722
Author(s):  
Shuai Zhang ◽  
Liuchang Xiao ◽  
Xing Zhao ◽  
Lipei Song ◽  
Yongji Liu ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Optimization Method ◽  
Basis Functions ◽  
Imaging Systems ◽  
Surface Slope ◽  
Radial Basis ◽  
Aberration Theory

scholarly journals Applying models of spatial interpolation for the approximation of responses in the refinement of parameters of finite element models

2018 ◽  
Vol 212 ◽  
pp. 01021
Author(s):  
Anatoly Pikhalov ◽  
Anton Zabelin
Keyword(s):  
Finite Element ◽  
Radial Basis Functions ◽  
Element Model ◽  
Optimization Method ◽  
Latin Squares ◽  
Basis Functions ◽  
Finite Element Models ◽  
Radial Basis ◽  
High Level ◽  
Parameter Values

The numerical experiment on refining the parameters of the finite element model of the beam by the method of approximating the responses is presented in the article. As mathematical models of joint-stock companies are used: linear combinations of radial-basis functions, and Kriging-models. These models are generated in the work on the basis of Latin squares and depend on the parameters to be refined (the moduli of elasticity of finite element groups of the beam). To obtain optimal values of the parameters, a genetic optimization method was used. The results of solving the optimization problem showed a high level of coincidence of the parameter values with a combination of response models obtained from dynamic and static types of calculations. It was also shown that when solving the problems of finite element models, it is sufficient to use models constructed only on the basis of radial-basis functions.

scholarly journals Model of radial basis functions based on surface slope for optical freeform surfaces

2018 ◽  
Vol 26 (11) ◽  
pp. 14010 ◽  
Author(s):  
Kainian Tong ◽  
Yi Zheng ◽  
Zan Zhang ◽  
Xing Zhao ◽  
Bo Zhang ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Surface Slope ◽  
Freeform Surfaces ◽  
Radial Basis ◽  
Optical Freeform Surfaces

scholarly journals Hypersonic Vehicle Aerodynamic Optimization Using Field Metamodel-Enhanced Sequential Approximate Optimization

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wenjie Wang ◽  
Zeping Wu ◽  
Donghui Wang ◽  
Jiawei Yang ◽  
Pengyu Wang ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Optimization Design ◽  
Optimization Method ◽  
Hypersonic Vehicle ◽  
Basis Functions ◽  
Sequential Approximate Optimization ◽  
Sequential Optimization ◽  
Aerodynamic Optimization ◽  
Approximate Optimization ◽  
Radial Basis

Hypersonic vehicle has gained increasing attention due to its high cruise speed and long voyage. In this paper, an enhanced Sequential Approximate Optimization method is proposed for aerodynamic optimization of a hypersonic vehicle. In this method, a constrained design of experiment method is adopted to generate the initial sampling set with adequate number of feasible points. A field metamodel is proposed to surrogate the aerodynamic parameters distributions in the flow field obtained by the aerodynamic simulation. A hybrid metamodel combing radial basis functions and polynomial chaos expansion is applied to construct the field metamodel with good approximate performance. A robust mesh morphing scheme based on radial basis functions is developed to generate high-quality meshes for the sequential optimization scheme. The hypersonic vehicle aerodynamic optimization problem is performed using the proposed optimization framework and satisfactory results are obtained with limited computational budgets. Results show that the proposed field metamodel-enhanced Sequential Approximate Optimization method possesses powerful optimization performance and promising prospects in the field of hypersonic vehicle optimization design.

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