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 引用本文: 汤龙 王琥 李光耀. Kriging-HDMR非线性近似模型方法[J]. 力学学报, 2011, 43(4): 780-784.
Tang Long Wang Hu Li Guangyao. Kriging-HDMR metamodeling technique for nonlinear problems[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 780-784.
 Citation: Tang Long Wang Hu Li Guangyao. Kriging-HDMR metamodeling technique for nonlinear problems[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 780-784.

## Kriging-HDMR metamodeling technique for nonlinear problems

• 摘要: 提出基于克里金(Kriging)插值的高维模型表示(highdimensional 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.

Abstract: Some large-scale structural engineering problems need tobe solved by metamodels. With the increasing of complexity anddimensionality, metamodeling techniques confront two major challenges.First, the size of sample points should be increase exponentially as thenumber of design variables increases. Second, it is difficult to give theexplicit correlation relationships amongst design variables by popularmetamodeling techniques. Therefore, a new high-dimension modelrepresentation (HDMR) based on the Kriging interpolation, Kriging-HDMR, issuggested in this paper. The most remarkable advantage of this method is itscapacity to exploit relationships among variables of the underlyingfunction. Furthermore, Kriging-HDMR can reduce the correspondingcomputational cost from exponential growth to polynomial level. Thus, theessence of the assigned problem could be presented efficiently. To prove thefeasibility of this method, several high dimensional and nonlinear functionsare tested. The algorithm is also applied to a simple engineering problem.Compared with the classical metamodeling techniques, the efficiency andaccuracy are improved.

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