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.

中文翻译：

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一种用于结构工程优化的自适应增广径向基函数-高维模型表示方法

开发和研究了一种使用自适应元建模方法的新工程优化方法。自适应元模型基于高维模型表示框架，高维模型表示组件函数是使用径向基函数或增强径向基函数创建的。在应用数值优化算法之前，所提出的优化方法从显式一阶增强径向基函数-高维模型表示元模型开始。在随后的每次迭代中，都会找到一个额外的样本点，并创建一个高阶高维模型表示组件函数，并将其添加到一阶增广径向基函数-高维模型表示元模型中。以自适应方式提高了增强径向基函数-高维模型表示元模型的准确性，尤其是在最佳设计点附近。解决了几个数值例子来证明该方法，包括一个实用的三维钢筋混凝土高层建筑结构。所提出的方法运行良好，并且在几次自适应迭代内获得每个示例的最优解的收敛。