Hybrid Reliability Analysis And Optimization Under Random And Interval Uncertainties Based On Projection Outline Active Learning

Aleatory and epistemic uncertainties widely exist in design and optimization of engineering products.When engineering structures are influenced by hybrid uncertainties,their reliability can be assessed by hybrid reliability analysis(RA)methods.Based on hybrid RA,hybrid reliability-based design optimization(RBDO)can obtain structures that satisfy the prescribed reliability indexes.Traditional RA and RBDO methods require a lot of evaluations of performance functions.However,the evaluations of performance functions often involve time-consuming computing processes,which result in high computational cost during analysis and optimization.Thus,surrogate model-assisted approaches have got high attention,where the modelling accuracy and efficiency of crucial approximate region directly influence the performance of RA and RBDO methods.In this paper,probabilistic model and interval model are utilized to quantify aleatory uncertainties and epistemic uncertainties,respectively.Then,hybrid RA and RBDO methods under random and interval variables are researched in this paper.The main work of this paper includes:(1)This paper proposes a hybrid RA method under random and interval variables based on projection-outline-active-learning(POAL).For hybrid RA under random and interval variables,it is proved that projection outlines on the limit-state surface are the crucial approximate region.Then,a POAL mechanism is built,which can adaptively and sequentially approximate the projection outlines.Compared to limit-state surfaces,projection outlines are much smaller.Thus,for modelling,POAL mechanism is more efficient than existing methods that concentrate on limit-state surfaces.(2)An adaptive importance sampling(AIS)method is developed for the cases with small failure probabilities in hybrid RA with random and interval variables.Compared to Monte Carlo simulation,AIS has the effect of variance reduction,which can reduce the number of samples required by the assessment of failure probabilities.Then,to further reduce computational cost of hybrid RA in the cases with small failure probabilities and time-consuming performance functions,a hybrid RA method based on AIS and POAL mechanism is built.(3)In consideration of correlation between epistemic variables,a hybrid RA method based on convex model is proposed.The correlated epistemic variables are described by convex model,and the projection outlines under correlated variables are defined.Then,a new POAL mechanism is built to approximate the projection outlines.Simultaneously,the prediction uncertainties of surrogate models are quantified in the stopping condition of model update,which is utilized to ensure small influence of prediction uncertainties on the estimation of failure probabilities.(4)For multiple failure modes,a system hybrid RA method with random and interval variables is proposed.It is proved that the composite projection outlines on the composite limit-state surface are the crucial approximate region in system hybrid RA with random and interval variables.Then,system learning functions are defined to adaptively and sequentially approximate the composite projection outlines.Simultaneously,the prediction uncertainties of multiple models are quantified to ensure small influence of prediction uncertainties on the estimation of system failure probabilities.(5)A hybrid RBDO method with random and interval uncertainties is proposed.The failure probabilities of constraints are estimated by a sampling method,and stochastic sensitivity analysis is extended to calculate the sensitivity of the failure probabilities.A screening rule of active constraints is defined,and then the projection outlines of only active constraints are concentrated on during modelling process,which can reduce the number of training points and improve the computational efficiency of hybrid RBDO.