Kriging-HDMR metamodeling technique for nonlinear problems

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.