2014 年 80 巻 818 号 p. TRANS0285
In this research, a Gradient-Vector Product (GVP) enhanced Kriging response surface model approach has been developed in which the GVP is defined by the gradient vector of objective function with respect to design variables as well as an arbitral unit directional vector in design variable space. When two sample points are given closely in design variable space, the correlation matrix in the Kriging formulation becomes ill-conditioned, which results in the inaccuracy of the constructed response surface model. In this research, therefore, we try to treat the two functional data as one functional datum with one GVP datum in the Kriging formulation. The conventional Kriging formulation is extended to make use of the GVP information, and then a global design optimization system is proposed with the developed GVP-enhanced Kriging model approach. The validity of the developed approach is investigated in analytical function fitting/minimization problems as well as a 2D airfoil shape optimization problem. The performance of the developed GVP-enhanced model approach overcomes that of the conventional Kriging model approach when additional sample points are given closely to existing samples. The effectiveness and robustness of the developed response surface model approach are clearly demonstrated in this paper.
