IDIRECT-HDMR高维近似模型方法及工程应用

IDIRECT-HDMR Approximation Model for High Dimensional Problems and Engineering Application

元建模常用于近似求解输入与输出间的映射关系。随着维度的增加,其计算成本将呈指数增长,使得常用的回归方法难以获得高精度的近似模型。提出一种基于改进分割矩形IDIRECT(improved dividing rectangles)采样的高维模型表示HDMR(high-dimensional model representation)方法,称为IDIRECT-HDMR。该方法将高维问题转化为一系列低维问题求和,从而用较少的样本点获得较高精度的近似模型。采用多维度的数值算例验证IDIRECT-HDMR的可行性并将其应用于工程实例。

Metamodeling is often used for approximate mapping between the input and output variables. Popular regression methodologies are inapplicable to the accurate metamodels for high dimensional practical problems since the computational time increases exponentially as the number of dimensions rises. This paper proposes a new form of high-dimensional model representation （ HD- MR） by integrating an intelligent sampling strategy, namely, Improved Dividing Rectangles （IDIRECT）, termed IDIRECT-HDMR. In this method, few sample points are used to obtain accurate metamodels by transforming a high dimensional problem into a series of low dimensional problems. Some mathematical test functions with a wide scope of dimensionalities are used to demonstrate the performance of IDIRECT-HDMR, and this method is applied to the practical application example.