Research On Reliability Analysis Method Of Mechanical Structure Based On Active Learning Kriging Model

In recent years,the structural reliability analysis method based on active learning Kriging model(ALK)has attracted extensive attention because it can evaluate the complex structural reliability problems within an affordable computational cost.As a result,a large number of high-quality literatures have emerged.Among them,the most representative ones are the efficient global reliability analysis(EGRA)and the active learning reliability method combining Kriging and Monte Carlo simulation(AK-MCS),which have become two important cornerstones in the field of ALK model.Many other reliability analysis methods based on ALK model are developed from these two methods.Although some scholars have done a lot of research,there are still some problems to be solved in the field of reliability analysis based on ALK model,and this paper also does some work around some of these problems.Firstly,aiming at the problem of multimodal distribution involved in structural reliability analysis,a new method named asλMM-AK-MCS is proposed in this paper.By introducingλMixed model(λMM),λMM-AK-MCS expands the application scope of the original AK-MCS method and make it can effectively deal with the structural reliability analysis problems including arbitrary distribution or multimodal distribution.The process of implementingλMM-AK-MCS mainly includes two stages,namely representing the random variables of multimodal distribution byλMM and classifying the random samples of AK-MCS.The bridge connecting these two stages is rejection sampling.Through the test of several examples,λMM-AK-MCS can well characterize the multimodal distribution of random variables and the fittedλMM is highly consistent with the probability distribution of observed data at a variable trend.At the same time,the accuracy of the evaluated failure probability is also very high,and the number of functional functions called is less.Secondly,aiming at the problem of small failure probability in structural reliability analysis,this paper first proposes a method combining ALK model and subset simulation(ALK-SS~2).This method uses two stages to approximate the limit state function.The main advantage of this phased approximation is that the larger candidate pool size and stricter convergence criteria required by the original single-stage approximation can be divided into two stages.In this way,the former stage can improve the efficiency with a smaller sample size,and the latter stage can ensure the accuracy with a larger sample size.However,the ALK-SS~2uses MCMC in sampling,which will lead to a certain correlation in the generated samples.In order to ensure the unbiased failure probability,ALK-SS~2 will still need to use a large sample size.To this end,on the basis of ALK-SS~2,this article proposes another method of combining ALK models and improved cross-entropy importance sampling(ALK-ICE)to ensure that the small failure probability can be solved accurately.In addition,considering that the learning function of traditional AK-MCS is too strict and conservative and may not be suitable for the two stages of ALK-SS~2 and ALK-i CE methods,a more efficient convergence standard based on the accuracy of failure probability is proposed to ensure that the Kriging model automatically stops the learning process after meeting the accuracy requirements of the two stages.Several actual test examples show that the ALK-SS~2 and ALK-i CE methods proposed in this paper are agent model methods with excellent accuracy and efficiency.Due to the use of more advanced sampling methods,these two methods are also very suitable for the evaluation of small failure probability problems.From the comparison between ALK-SS~2 and ALK-i CE,their efficiency is similar,but the accuracy of ALK-i CE method is better,and the calculated failure probability variance is smaller.