The Driect Gek Surrogate Model Method Based On Improved Experimental Selection

In the study of structural reliability,the ultimate state equation of a structure usually takes load-resistance as its calculation model.In many complex systems,there is a high-dimensional non-linear relationship between input and response.The surrogate model method,which uses interpolation regression technique to approximate implicit limit state functions,has been widely used in recent years.Kriging model is one of the typical examples.Based on the existing research,the gradient-enhanced Cokriging method is deeply studied in this paper.The main research contents are as follows:(1)The experimental design is a mathematical method for statistical analysis of experimental results by effectively screening test points according to the predetermined experimental objectives.Its theory originates from the construction of number argument sets.Based on the principle of uniform distribution,the similarities and differences between LHS and UD are analyzed,and an experimental site selection strategy based on number theory is proposed through comparison.(2)An improved uniform design method for point selection is proposed,and mathematical derivation is made.It is proved that the improved method does not reduce the deviation order of point set construction,and the validity of point selection is verified theoretically.At the same time,it is proved that the improved uniform design has the good properties of LHS global sampling under the condition of meeting the "uniformity" of the selected points.In practical problems,the improved point selection strategy is applied to Kriging model,and the applicability of this method is proved by an example analysis.Comparing with the common experimental design method,the calculation accuracy is obviously improved.(3)The Kriging theory is briefly introduced.By introducing gradient information of functions,the gradient-enhanced Kriging method(GEK)is proposed.In practical problems,the improved point selection strategy is applied to Kriging model,and the applicability of this method is proved by an example analysis.On the basis of Kriging's principle,the direct GEK method is deduced,the undetermined parameters are solved and the relevant program is established to realize the theoretical calculation.(4)For the direct GEK method and the indirect GEK method,combined with the improved experimental design selection strategy,the numerical examples are analyzed respectively,which proves that the direct GEK method tends to be accurate in theory,and for the high-dimensional problems,the calculation accuracyof the direct GEK method is higher than that of the indirect method.Comparing with the common experimental design method,the calculation accuracy is obviously improved.