Research On The Method Of Global Sensitivity Analysis For Structures Considering Correlation And Multivariate Output

Sensitivity analysis is an important aspect of structural uncertainty research,and it can be uesd to study the influence of input variables on statistical characteristics of the model output performance.Sensitivity analysis can effectively identify the variables that have significant influences on the model responses,which can help reduce uncertainty of the model responses at a small cost,so as to improve the robustness and reliability of the model.In view of the prediction and diagnosis performance of sensitivity analysis,it is regarded as the precondition of modeling,model simplification and optimization design in many fields.In practical engineering applications,global sensitivity analysis is usually involved in a series of high-dimensional and high-order integrals which are generally difficult to solve directly,and the traditional method is usually approximately solved through Monte Carlo simulation.The accuracy and stability of the sensitivity results depends heavily on the samples.In addition,many sensitivity analysis methods assume that the input variables are independent of each other and the model is scalar output.However,the correlated variables or the multivariate outputs often exist in the practical engineerings.This thesis conducts some research on several issues of sensitivity analysis.The main research contents are as follows:(1)Based on the response surface and the dimension reduction integration method,an efficient global sensitivity analysis method is developed.The complex model in the practical engineering problems is replaced by the polynomial response surface of convenient analysis which is established on the basis of design of experiment.The model response function is transformed into the combination form of single random variable submodels through the improved dimension reduction method.The high-dimensional and high-order integrals which are generally difficult to be solved directly are transformed to the low dimensional integrals for easy solution.It is easy to use Gauss integration to solve the total variance of model response function and the partial variance of each function subterm.To get high accuracy,only a small number of integral nodes required.The method has the advantages of high computation efficiency and accurate solution,and has a good adaptability to global sensitivity analysis of the complex models.(2)As the widely used variance-based global sensitivity indices can not be directly used to correctly describe the influences of correlated variables on the model output responses,a practical method that can evaluate sensitivity of the correlated variables is investigated.Based on the idea of variance decomposition,the total variance of the model output responses is decomposed,and the effects of each function subitem on the model output responses are divided into correlated contribution and uncorrelated contribution.The proposed method can quantitatively analyze the effects of the correlated parts and the uncorrelated parts of correlated input variable on the model output responses,and can calculate the first order sensitivity index,the total sensitivity index and the high order sensitivity index of the correlated input variables.The method can also be applied to the global sensitivity of the independent variables.(3)Considering the multivariate output model widely existed in practical engineering problems,principal component analysis is applied to structural global sensitivity analysis.On the basis of covariance decomposition,principal component analysis method is used for orthogonal decomposition of model output response.The original variable system is transformed into a new orthogonal system by extracting the eigenvectors,and the former components which can contain most of information of the multivariate output model are extracted,and the principal components are uncorrelated each other.For a high-dimensional complex model,only a few former principal components should be considered,which can not only explain the main information of the original model,but also handle the correlation of variables.It can improve analysis efficiency.The generalized sensitivity index are defined.The proposed method can quantitatively analyze the influences of input variables on each principal component and the comprehensive influence of input variables on multivariate output.(4)In view of the high-dimensional nonlinear complex structure and the unknown model of input-output relationship existing in practical engineering problems,it is sometimes restricted by the factors such as the test technology,the test cost or the environment,and it is difficult to obtain enough samples to construct the surrogate model.However,the small samples often has multiple correlation.It is difficult to ensure the accuracy and reliability of the regression model if ordinary least square is applid to construct regression model,and the regression model is very complex in the case of more input variables and higher fitting order.To solve these problems,a global sensitivity analysis method based on partial least squares method is developed.Combined with polynomial structure-selection technique,partial least squares methodis used to construct the nonlinear polynomial model with simple structure.Then the global sensitivity analysis of the parameters of the multivariate output model can be conveniently carried out.