Chinese Journal of Theoretical and Applied Mechani ›› 2011, Vol. 43 ›› Issue (4): 780-784.DOI: 10.6052/0459-1879-2011-4-lxxb2010-494

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Kriging-HDMR metamodeling technique for nonlinear problems

Tang Long,Wang Hu,Li Guangyao   

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body of Hunan University, Changsha 410082, China
  • Received:2010-08-02 Revised:2010-12-09 Online:2011-07-25 Published:2011-07-27
  • Contact: Tang Long

Abstract: 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.

Key words: nonlinearity

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