A Research Of Surrogate-based Model For Structural Reliability Method Under Aleatory And Epistemic Uncertainties

Theory and method of structural reliability are powerful tools to guarantee the safe and reliable operation of structural systems,which have attracted enormous attention from research communities and industries,and are a research hot in the field of reliability engi-neering.Various uncertainties arising from the development,design and manufacture of equipment products are key factors affecting structural reliability.The theory and method of structural reliability are precisely quantitative analysis of the safety degree and perfor-mance of the system structure based on the full consideration of various uncertainties.In order to quantify the effects of the two kinds of uncertainties on the reliability of struc-tural systems,the theory and method of structural reliability under aleatory and epistemic uncertainties have received tremendous attention from scholars at home and abroad,and fruitful results have been generated.However,if the performance function of the system is implicit,large-scale numerical simulations are required to perform structural reliability analysis,whose computational burden is unimaginable in engineering.The existing meth-ods still have multiple problems to be solved on how to balance accuracy and efficiency.Therefore,efficient structural reliability analysis under aleatory and epistemic uncertain-ties is still a challenging problem.In view of this,using the surrogate model as a tool,the issues of efficient structural reliability analysis under aleatory uncertainty with single failure mode?reliability analysis under aleatory uncertainty with small failure probability?structural reliability analysis under hybrid uncertainties?and system reliability analysis under multiple failure modes are investigated in this dissertation.The main work and innovations are summarized as follows:(1)A structural reliability analysis method combining probability density func-tion and adaptive Kriging model under aleatory uncertainty is proposed.The core of the structural reliability analysis method based on adaptive surrogate model under aleatory uncertainty lies in how to select the best sample point during each it-eration step.Under this topic,an efficient learning function,i.e.,U~*function,is developed in this dissertation.The learning function consists of two parts:the A part is the existing U learning function,which serves to make the selected sample points have the character-istics of small absolute value of performance function and large prediction variance?the B part integrates the U function and the probability density function of variables,which can effectively avoid selecting sample points with small contribution to failure probability and improve the computing efficiency.The proposed learning function introduces weight coefficients,which organically integrates the advantages of A part and B part,and can avoid invalid calls to the performance function as much as possible.The research results demonstrate the effectiveness of the proposed method.(2)A structural reliability analysis method based on improved sampling strategy and convergence criterion for problems with small failure probability under aleatory uncertainty is proposed.Two important factors,affecting Kriging modeling in the structural reliability anal-ysis method based on surrogate model,are learning function and convergence criterion.In this dissertation,a structural reliability analysis method based on improved sampling strategy and convergence criterion under aleatory uncertainty is proposed.The research on the selection of the target area of the best sample point and the determination of the best sample point in constructing the surrogate model are systematically carried out.By using the idea of Importance Sampling to determine the target sampling area and the di-chotomous optimization strategy to determine the best sample point,and the improved convergence criterion to accelerate the convergence of the model,the efficient selection of the best sample point is effectively achieved,also the disadvantage of the slow con-vergence of the existing reliability methods is overcome.Then,the structural reliability analysis model based on the improved sampling strategy and convergence criterion under aleatory uncertainty is constructed.Meanwhile,on the basis of the above structural reli-ability theory,this dissertation further investigates the small failure probability structural reliability theory in-depth and takes advantage of the Subset Simulation,and proposes an optimization strategy for updating the surrogate model based on Subset Simulation,which provides theoretical guidance for solving the structural reliability problem with small fail-ure probability.(3)A hybrid-variable reliability analysis method based on Kriging model and DIRECT function under aleatory and epistemic uncertainties is proposed.For the structural reliability problem of the system with both random and interval variables,this dissertation proposes a reliability analysis method based on Kriging model and DIRECT function for hybrid variables under aleatory and epistemic uncertainty.This dissertation takes the relationship between the interval of sample response and the limit state function under the random and interval variables as the starting point,then proposes a sampling method for the best sample point under the hybrid variables,and evaluates the uncertainty of sample by the mean value of the learning function to compensate for the defect of relying on a single learning function value to determine the best sample point.Also,this dissertation proposes a more efficient sample point traversal strategy for solving the failure probability,which overcomes the shortcomings of existing methods.(4)A reliability analysis method based on Kriging model for multi-failure modes systems under aleatory uncertainty is proposed.The reliability analysis method based on the Kriging model is proposed for the prob-lem of structural reliability of the systems containing multi-failure modes.Taking the series-parallel relationship between failure modes in the system as the starting point,this dissertation systematically carries out the research on the determination of the selection area of the best sample point in series and parallel modes.By establishing the mapping re-lationship between the series-parallel connection of the system and the safety domain and the failure domain,the efficient selection of the best sample point is effectively achieved,and the limitation of the existing method of over-sampling in the region with small con-tribution from the variable space is overcome.Meanwhile,through proposing an interpo-lation optimization method,the best sample points are made to further approximate the limit state function.The research results show that the method substantially improves the efficiency of reliability analysis.