Hybrid Reliability Analysis Method Under Epistemic Uncertainty For Complex Product

In complex products,the lack of experience,tests,and data is common and causes uncertainty information scarce.Due to scarce uncertainty information,probability distributions of some uncertainty variables cannot be precisely modelled and epistemic uncertainty exists.Meanwhile,many types of uncertainty variables exist in complex products,such as random variables,interval variables,dependent interval variables and interval variables with different confidence intervals.This makes the traditional reliability analysis methods,which only deal with random variables,inappropriate or lowly efficient.Focusing on the coexistence of aleatory uncertainty and epistemic uncertainty,this paper studies reliability analysis under various uncertainties for complex products,develops the hybrid reliability analysis models,and proposes efficient hybrid reliability analysis algorithms.The main work and achievement are as follows:(1)The hybrid reliability analysis model with random and interval variables is set up.To improve the efficiency,the coupled double loops is decomposed into sequential two separate ones,and an efficient algorithm is proposed.A robust iterative algorithm is employed in probability analysis(PA)loop,and a new efficient interval analysis(IA)method consisting of two stages is developed based on the gradient projection method.The first stage is for monotonic limit-state functions.In the second stage,the limit-state function is sequentially approximated with a second order form,and the gradient projection method is applied to deal with non-monotonic cases.The decomposed loops and the proposed IA algorithm improve the efficiency of the hybrid reliability analysis with random and interval variables.(2)The hybrid reliability analysis model with dependent interval variables and random variables is set up based on multi-ellipsoid model,and an efficient hybrid reliability analysis method is proposed by using the High Dimensional Model Representations(HDMR)method.In HDMR,the reference point is found by the most probable point(MPP)algorithm based on the first order reliability method(FORM).The quadratic polynomial is applied to get the sub-model,and a sampling strategy is proposed.Based on the sub-model,the extreme responses of the limit-state function in the feasible multi-ellipsoid region are efficiently identified and then Monte Carlo simulation(MCS)is used to solve the bound of probability of failure.The proposed method can solve the bound of probability of failure with a small number of the original limit-state function calls,and improve the efficiency of the hybrid reliability analysis.(3)The hybrid reliability analysis model under interval variables with different confidence intervals,second order uncertainty variables and random variables is set up based on evidence theory.For computational efficiency,the two coupled loops are combined into a single loop by treating the KKT optimal conditions of the interval analysis as constraints.To solve the instability and non-convergence caused by KKT optimal conditions,a smooth function is used.The single loop optimization method simplified the hybrid reliability analysis model and decomposes the two coupled loops,and hence the efficiency of the hybrid reliability analysis is improved.(4)The accuracy and efficiency of the proposed hybrid reliability analysis method in the paper is verified by the application research in three main components,the engaged wheel,the bed and the cutting component,of the complex product metal cutting band saw.According to the mixture of epistemic and aleatory variables in the three main components,the proposed hybrid reliability analysis method with interval and random variables,the hybrid reliability analysis method with dependent interval and random variables,and the hybrid reliability analysis method under interval variables with different confidence intervals and random variables are applied,respectively.Compared with the number of the limit-state function call by existed hybrid reliability analysis methods,the proposed hybrid reliability analysis methods have better efficiency.With the reference of the MCS solutions,the proposed hybrid reliability analysis methods have good accuracy.