High Dimensional Model Representation Approximation of an Evolution Operator with a First Order Partial Differential Operator Argument

2004 ◽  
Vol 1 (1) ◽  
pp. 280-289 ◽  
Author(s):  
İrem Yaman ◽  
Metin Demiralp
Keyword(s):  
Differential Operator ◽  
Evolution Operator ◽  
Partial Differential Operator ◽  
Model Representation ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Dimensional Model ◽  
Partial Differential ◽  
First Order ◽  
Operator Argument

An adaptive augmented radial basis function–high-dimensional model representation method for structural engineering optimization

2020 ◽  
Vol 23 (15) ◽  
pp. 3278-3294
Author(s):  
Qian Wang ◽  
Yongwook Kim ◽  
Joseph Nafash ◽  
Javier Catala
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Model Representation ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Optimization Approach ◽  
Engineering Optimization ◽  
Dimensional Model ◽  
First Order ◽  
Radial Basis

A new engineering optimization approach using an adaptive metamodeling method is developed and studied. The adaptive metamodels are based on a high-dimensional model representation framework, and the high-dimensional model representation component functions are created using radial basis functions or augmented radial basis functions. The proposed optimization approach starts with an explicit first-order augmented radial basis function–high-dimensional model representation metamodel, before a numerical optimization algorithm is applied. In each subsequent iteration, an additional sample point is found, and a high-order high-dimensional model representation component function is created and added to the first-order augmented radial basis function–high-dimensional model representation metamodel. The accuracy of the augmented radial basis function–high-dimensional model representation metamodel is improved in an adaptive manner, especially in the neighborhood of the optimal design point. Several numerical examples are solved to demonstrate the method, including a practical three-dimensional reinforced concrete high-rise building structure. The proposed approach works well, and the convergence of the optimal solutions for each of the examples is obtained within a few adaptive iterations.

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