An Improved Gradient Enhanced Kriging Of Surrogate Model Methods For Structural Reliability

As a kind of important analytical method in structural reliability theory, surrogate model methods are widely used to alleviate the computational burden of engineering analysis at present. Kriging has received extensive attention as a typical representative of the surrogate model, although it is developed relatively late in the field of reliability. Based on the existing research work, this study makes a deep research on the Gradient-enhanced Kriging method, and provides theoretical guidance for the follow-up research work. The main work of this study is as follows:(1) The structural reliability analysis method of the direct Cokriging model is proposed, and the process of the Cokriging model is derived by using the sample set.(2) The experiment design methods in applied statistics are carried on a more thorough research. Suggestions for the selection of experiment design methods in the direct Cokriging method are provided through the comparison of some experiment design methods for the direct Cokriging model fitting in structural reliability analysis.(3) For Cokriging modeling process by adding the gradient information of the two methods, direct method and indirect method, carries on the contrast analysis of the influence on the calculation results in structural reliability analysis. Through the example results indicate that the direct Cokriging method is better than indirect Cokriging method in accuracy and efficiency. For considering several different nonlinear degree examples, the effect of several different correlation function models of Cokriging method in reliability calculation is investigated.(4) Cokriging model is improved to the Kriging by adding the first order derivative information of the sample points to improve the accuracy of the surrogate model. Second-order derivative information also can used to improve the accuracy of the surrogate model. Therefore this study puts forward the Hessian-enhanced Kriging model, and apply it in structural reliability analysis, and illustrate the effectiveness of reliability analysis through the examples.