Structural Reliability Analysis Method Based On Kriging Model

The uncertainty in engineering has a significant effect on structural failure,to avoid accidents,it is important to analyze the reliability and evaluate failure probability of mechanical structures.The structural reliability analysis methods based on surrogate model can not only provide accurate evaluation result,but also effectively reduce the computational burden.Although the methods have made some progress,the evaluation accuracy and calculation efficiency of the analysis methods need to be further improved.Therefore,some methods for the structural reliability analysis are constructed based on Kriging model.The research results are as follows:(1)Aiming at the time-independent reliability problems in engineering,a new reliability analysis method is established to improve the evaluation accuracy and computational efficiency of AK-MCS method.Firstly,an efficient active learning function is established based on the sign prediction error of Kriging model.Secondly,a new stopping criterion is proposed based on estimation result error of Kriging model.The new learning function and stopping criterion are nested in the AK-MCS method,which effectively improves the evaluation accuracy and calculation efficiency of the timeindependent reliability analysis method.(2)For the problems of time-independent small failure probability in engineering,a small failure probability analysis method based on Gibbs importance sampling is established to solve the inefficiency of M-H algorithm in dealing with high-dimensional reliability problems.Firstly,based on the importance sampling density function,a conditional importance sampling density function suitable for importance sampling is derived.Secondly,a Gibbs importance sampling algorithm suitable for small failure probability problems is proposed by combining Gibbs sampling algorithm and M-H algorithm.The time-independent small failure probability analysis method based on Gibbs importance sampling method solves the problem of the inefficiency of M-H algorithm in dealing with high-dimensional reliability problems.(3)To improve the calculation accuracy and efficiency of the inner optimization loop and improve the evaluation accuracy of the outer loop of the Kriging model for the timedependent reliability problems,an improved Mixed-EGO method based on active learning is established.Firstly,the time variable is discretized to establish the inner optimization loop candidate sample pool.Secondly,the inner optimization loop is realized by active learning process.Finally,the efficiency of the method is further improved by combining the efficient active learning function and the stopping criterion proposed.The cases show that the improved Mixed-EGO method significantly improves the computational efficiency.