Research On Methods Of Reliability And Sensitivity Analysis Based On Meta-models

Reliability is one of the most fundamental attributes of structure and mechanical products and also an important indicator for safety measure.With the increasing of the crucial and complicated designs,the methodology for assessing the reliability is essential for the uncertainties abound in load,geometry,material characteristic and processing,as well as for the quantification of uncertainty propagation within the system.On one hand,the evaluation for reliability not only provides initial tutorial in robust design,but also contributes to the research,tests and quality control for the purpose of improving system safety and performance.Especially,an accurate and equally effective method for reliability assessment and optimal design is critical for solving reliability problems of complex system.On the other hand,sensitivity analysis helps to identify the factors which have the most important impact to the performance of the output and determine how the parameters or the uncertainty of inputs influence the uncertainty of output quantitatively.Moreover,optimal design could be launched based on sensitivity results,which shed light on the theoretical guidance for researchers.Meta-modelling refers to the mathematical discipline that has interest in emulating the statistical relationship between some inputs and the output given a limited set of prior assumption.The motivation of meta-modeling in engineering field derives from the urgency of lessening the computational burden of expensive-to-evaluate model,such as finite element models,by replacing the authentic and yet complex model with easy-to-evaluate meta-models.Currently,meta-modeling has been widely used in the field of reliability and sensitivity analysis,and also has achieved the goal for accuracy and efficiency simultaneously in some extent.This thesis features the evaluation of failure probability and sensibility analysis in both local and global sense,in which Kriging model and polynomial chaos expansion are introduced into the modeling and analysis.There are two merits in this thesis:firstly,the incorporation of metamodels with traditional methods largely enhances the research tools,drastically reducing the the computational burden while maintaining the accuracy;meanwhile,the proposed methods are capable of measuring the errors resulted from the substitution of the authentic models;secondly,the implementation of sensitivity analysis extends from the local level to the global one,not only evaluating the influence of parameters(like mean or standard deviation)of input variables to the failure probability;but also effectively screening out the factors that have the most significant impact to the performance of the system.The specific work of this thesis includes:(1)The Kriging metamodeling for structural reliability analysis based on importance Sampling.In order to deal with the implicit reliability problems which are widely existed in practical engineering,an importance sampling-based Kriging metamodeling is proposed.This method inherits the advantage of active learning mechanism and Kriging model,and greatly increases the efficiency on the premise of that the calculating accuracy is guaranteed.The active learning mechanism makes full use of Kriging variance,and improves the fitting capability of Kriging model and the prediction accuracy for training samples.Kriging model itself decreases the amount of evaluation for authentic model and increases the calculation efficiency.Moreover,the replacement of probability classification function of indicator function considers both aleatory uncertainty and epistemic uncertainty,and allows the "correction" term to quantify the error from the substitution.(2)Reliability evaluation method based on PCE and bootstrap.Due to the fact that PCE model does not includes error term and thus scarcely be used in reliability analysis,a simulation method based on PCE model and bootstrap procedure is proposed.This method can characterize the prediction variance in PCE,and based on the variance derived by bootstrap procedure,an active learning function is proposed to update PCE model iteratively.Once the model becomes enough accurate,a general simulation method is used to calculate the failure probability.The proposed parallel enrichment criteria not only identifies the potential samples,but also considers the computational task for model updating.Furthermore,when the failure probability is extremely small,the combination of PCE-bootstrap and subset simulation can boost the convergence of the failure probability.(3)Sensitivity analysis based on Kriging model and importance sampling.Due to the lack of the gradient information in practical engineering problem,the reliability sensitivity analysis can't be implemented in an analytical manner.Therefore,a simulation-based sensitivity method is proposed.It is suggested to compute the failure probability by the importance sampling-based Kriging at first,and then the estimator of failure probability is differentiated through the score function approach.The stepwise uncertainty reduction criterion is used for model updating,which equips the Kriging model with the excellent approximation for highly nonlinear function,and by formulating the sensitivity results as the expectation of score function,the approach enables the estimation of the gradient of the failure probability without any additional evaluation to the limit state function.(4)PCE-based sensitivity analysis considering the linear correlation among random inputs.To overcome the computational burden for Sobol indices resulted from Monte Carlo simulation-based method and to consider the linear correlation among random inputs,a PCE-based method is proposed for global sensitivity analysis.The correlation and non-normality of inputs are dealt with by the suggested Nataf transformation,and then two criteria are recommended to determine the optimal number of sampling points and the optimal order of the polynomial.Once the optimal PCE model is built,the sensitivity indexes become the 'by-product' of the model coefficients.Considering the linear correlation,the proposed method identifies the most important factors to the output with limited computational cost.Finally,we also point out the limitation of this study and discuss some challenging topics which deserve further research in the future based on the above research results.