Structural Statistical Sensitivity Analysis And Reliability Assessment Considering Metamodeling Uncertainty

With the continuous progress of science and technology and the rapid development of modern industry,the duration of complex structures or products design becomes even shorter.As the computer simulation can improve the efficiency of design,it has widespread application in industry.However,it is also found that the computational load is extremely unaffordable in simulation-based design optimization.To overcome this issue,metamodels are oftentimes used in lieu of the computer simulation model in design optimization.In general,uncertainty is inevitable in complex structural design optimization,sensitivity analysis and reliability analysis are two effective tools to handle the uncertainty in structural design optimization.The former is used to identify the importance of design parameters,so as to facilitate dimension reduction and resources allocation,whereas the latter is to assess the failure probability of structures,identify the optimal design scheme,and improve the reliability of structures.By properly treating the uncertainties in structural design optimization,the reliability and robustness of structures can be greatly enhanced.Although the metamodel can reduce the computation burden of the computer simulation model and improve the computational efficiency of analysis,it also introduces metamodeling uncertainty which can be viewed as the deviation between a metamodel and the corresponding computer simulation model at non-sampling sites of the metamodel.In recent years,the structural uncertainty analysis methods based on metamodel have received considerable attentions all around the world.Nevertheless,to date,the metamodeling uncertainty has not been sufficiently considered in the structural uncertainty analysis.Ignoring such uncertainty may introduce a potential risk to the results of uncertainty analysis,leading to an unreliable design scheme.To address the aforementioned issues,this thesis devotes to study the statistical sensitivity analysis and structural reliability analysis methods with considering the metamodeling uncertainty.The specific research contributions of this thesis are summarized as follows:(1)Proposing a unified approach to statistical sensitivity analysis for model input uncertainty and metamodeling uncertainty.The statistical sensitivity analysis method is an important tool to study the contributions of model input uncertainty to the model output uncertainty.The existing methods usually use the predicted mean values of the metamodel,instead of the computer simulation models,to evaluate the statistical sensitivity indices and ignore the influence of metamodeling uncertainty.To take account of the impact of metamodeling uncertainty on statistical sensitivity analysis,a unified approach to statistical sensitivity analysis for model input uncertainty and metamodeling uncertainty is developed.By using the Karhunen-Loeve expansion,the metamodeling uncertainty can be converted into parametric uncertainty which can be further quantified by the statistical sensitivity analysis.By this way,the statistical sensitivity of metamodeling uncertainty and model input uncertainty can be analyzed in a unified manner.(2)Developing a structural reliability analysis method considering the metamodeling uncertainty.The sequential sampling methods are used in metamodel-based structural reliability analysis to improve the approximation between metamodels and computer simulation models.However,the new sample sites identified by the existing sequential sampling methods may not be the sites which can maximally reduce the uncertainty of the estimated failure probability.A new sequential sampling method is proposed with the aim of reducing the failure probability uncertainty as much as possible.By comparing to the existing sequential sampling methods,the proposed method can effectively screen out and eliminate the sites where are useless for reducing the uncertainty of estimated failure probability.Additionally,the new method can construct an accurate metamodel with a less number of sampling sites.(3)Investigating numerical integration methods for statistical sensitivity analysis and structural reliability analysis based on metamodels.The Monte Carlo-based integration method is extremely computationall unafforable to conduct statistical sensitivity analysis and structural reliability analysis based on metamodel for large dimensional problems.A set of three numerical integrations is implemented,instead of the Monte Carlo-based integration method,to alleviate the computational burden of the high dimensional integration.By comparing the accuracy and computational efficiency of the three numerical integration methods,an appropriate numerical integration method can be chosen for structural uncertainty analysis to better balance the result accuracy and computational efficiency.