Efficient Structural Reliability Algorithms With The Active-learning Based Kriging Model

The mechanical structure is affected by uncertain factors such as machining tolerance,assembling clearance and load conditions of environment.The model parameters of a system and structural response cannot be characterized completely and accurately.However,the structural material properties also have random uncertainties in spatial position,which needs complex statistical models such as random field to describe these properties.These factors make the structural reliability analysis model more complicated,especially in the case of small failure probability,which lead to lots of model reanalysis and higher computing resource consumption.Therefore,based on the summary of traditional mechanical structure reliability analysis methods,this paper proposed an active learning Kriging surrogate model for efficient estimation of small failure probability of structures.Research on structural reliability and efficient estimation is carried out from the aspect of simulation space truncation,hybrid active learning implementation,and probability-interval coupling uncertainty.The main research contents are as follows:(1)By combing the typical active learning Kriging algorithms in the existing literatures,the comparative analysis of different learning function types,methods of selecting training samples and simulation space truncation is carried out.Based on the deficiency of the original active learning algorithms in the truncation of simulation space and combined with a reliability index calculation method,this paper proposed the criterion of adaptive simulation space truncation.The convergence efficiency of active learning algorithm is studied by combining global optimization algorithm and objective learning function type.Meanwhile,the validity and accuracy of the proposed algorithm are verified by some classical numerical examples.(2)The influence of the combination of U and REIF2 learning functions on the modeling precision of Kriging model is researched.For the non-normal random variable simulation problem,the quasi-FORM method of simulation space truncation is proposed,and its computational efficiency is much better than the literature algorithm.Taking the stochastic finite element model of aero-engine turbine disk as an example,the improved AL-Kriging algorithm proposed in this paper has high precision and good convergence.(3)Considering the mechanical reliability analysis problem under the action of probability-interval hybrid variables,the gradient information distribution of the samples corresponding to the extremum of the functional function is studied.From the condition of relaxed Karush-Kuhn-Tucker condition,the numerical method for efficient extraction of alternative samples is realized.Based on the truncation method and hybrid learning algorithm of hybrid random variables,the AL-Kriging surrogate model is applied to the structural reliability analysis successfully.The Monte Carlo simulation is executed to verify the performance of the proposed algorithm,which demonstrated the modeling efficiency and accuracy have certain advantages over other literature methods.