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

Abstract

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.