Kriging-HDMR非线性近似模型方法

摘要

Some large-scale structural engineering problems need to be solved by metamodels.With the increasing of complexity and dimensionality,metamodeling techniques confront two major challenges.First, the size of sample points should be increase exponentially as the number of design variables increases.Second, it is difficult to give the explicit correlation relationships amongst design variables by popular metamodeling techniques.Therefore,a new high-dimension model representation（HDMR） based on the Kriging interpolation, Kriging-HDMR,is suggested in this paper.The most remarkable advantage of this method is its capacity to exploit relationships among variables of the underlying function.Furthermore,Kriging-HDMR can reduce the corresponding computational cost from exponential growth to polynomial level.Thus,the essence of the assigned problem could be presented efficiently.To prove the feasibility of this method,several high dimensional and nonlinear functions are tested.The algorithm is also applied to a simple engineering problem.Compared with the classical metamodeling techniques,the efficiency and accuracy are improved.%提出基于克里金（Kriging）插值的高维模型表示（high dimensional model representation,HDMR）方法,即Kriging-HDMR方法.Kriging-HDMR方法的最大优势在于：能够明确输入参数的耦合特性,将构造模型复杂度由指数级增长降阶为多项式级增长,进而用有限样本确定待求问题的物理实质.为了验证算法的建模性能,采用高维非线性函数成功地验证了该算法的可行性,并将该算法初步应用于简单的非线性工程问题,同传统算法相比,其精度和效率都得到了明显提升.