Extension Of Kriging Model In Structural Reliability Analysis And Optimization

The proxy model is a method that can efficiently solve practical engineering problems.In structural reliability analysis and optimization design,problems with finite element analysis are often encountered,which places higher requirements on reliability analysis and design methods.The proxy model method is one of the most promising processing methods,which can greatly improve the analysis and calculation efficiency of complex problems.As a classic proxy model research method,Kriging has received extensive attention and become one of the hot topics.In this paper,the extended research of Kriging model and its application on structural reliability analysis and structural optimization design are carried out,It has been proved to have certain guiding significance for solving practical engineering problems.The main work of this article is as follows:(1)The theory and framework of the Kriging method are introduced in detail.The selection of the regression function and related functions in the Kriging model is analyzed.The problem of model building errors due to repeated samples in the Kriging model construction process is analyzed.(2)In order to make full use of the existing model information in the model prediction and improve the interpretation accuracy of the model to the real physical system,a research of analysis method is proposed to integrate the existing model information into the Kriging model.The proposed method integrates the information of alternative models into the Kriging model in order to improve the prediction accuracy.Compared with the conventional Kriging model and the multi-model combination prediction method,the proposed method has better prediction ability and higher accuracy.(3)In the reliability analysis of structure,improving the first order and second moment is a classical reliability analysis method,but it is difficult to solve the implicit limit state function.However,difficulty remains in solving the implicit limit state function,this paper proposes a fused Kriging and improved a first order and second moment reliability analysis methods.The method makes use of the gradient information provided by Kriging model and the iteration points provided in the process of improving the reliability of the first-order second moment,which not only solves the problem of solving the implicit limit state function by improving the first-order second moment,but also greatly improves the computational efficiency of the reliability analysis.(4)For the reliability optimization design problem of the structure,it is proposed to apply the Bayesian optimization method to solve the reliability optimization problem that reliability analysis as the goal,deal with the uncertainty of the objective function value,and find the global optimal value.For the optimization problem with reliability analysis as a constraint,a Bayesian optimization method with coupled constrained objectives is used to effectively solve the problem of large calculation amount of reliability optimization.(5)Structural reliability optimization design often encounters problems of local optimality and high computational cost,especially in optimization problems with implicit small failure probability and including finite element analysis.In this regard,it is proposed to use Bayesian optimization method as a global optimization,and at the same time use the Kriging method to deal with reliability analysis problems.Combining the two methods together can effectively solve the reliability optimization problem of complex structures.