Research On The Variance Based Sensitivity Analysis For The Random And Fuzzy Structure Systems

There are various uncertainties in structural design and system analysis.Studying the effects of these uncertainties on the output performance of the structure and system is of great significance for the prediction of their behaviors and developing reasonable risk evaluation.This paper focus on the sensitivity analysis of the uncertainty effects of random and fuzzy inputs on the structure and system output.The detailed contents are listed as follows:1 For the variance based global sensitivity analysis of models with correlated inputs,basing on the input-output relationship represented by tensor product basis functions and the orthogonal decorrelation of the correlated variables,using subset decomposition a new analytical variance based global sensitivity analysis method is derived.Since tensor product basis function based simulator is widely used in complicated structure systems,the analytical method of the variance based global sensitivity analysis is especially applicable to engineering practice problems.Metamodels commonly used in engineering,such as polynomial regression model,Kriging model,Gaussian radial basis model,MARS model etc.,all can be translated into the form expressed by the tensor product basis functions.The analytical method is used to carry out the variance based global sensitivity analysis of the riveting and two dimension fracture problem.In addition,the polynomial regression model is employed as an example to derive the analytical global sensitivity analysis in detail,and the analytical solutions of Kriging model,Gaussian radial basis model and MARS model are presented.2 The physical meanings of sensitivity indices obtained by variance based global sensitivity analysis for models with correlated inputs are deeply analyzed and some existing problems are researched and discussed.The function of high dimension model representation in variance based global sensitivity analysis is discussed and the computation of conditional expectation is accounted as the reason of the physical meaning complexity of sensitivity indices,which also causes the additional variance contribution.With these knowledge,a new global sensitivity analysis method based on model uncorrelated decomposition is proposed,which can well deal with the variance based global sensitivity analysis for models with correlated inputs,and it is applied to roof truss and gas pipeline model.3 Deep researching on the physical meanings of sensitivity indices of Sobol variance based global sensitivity analysis,the problem is observed that it cannot distinctly differentiate the variance contributions of inputs to the variance of model output in some cases.Variance based semi-global sensitivity analysis is proposed,with which the impact of inputs on the variance of output can be identified more clearly.It greatly simplifies the variance based sensitivity analysis for it avoids the computation of conditional expectation,making the variance based sensitivity analysis more efficient and more applicable for engineering practice.In this work,the variance based semi-global sensitivity analysis is applied to thin plate with hole model,cantilever beam and gas pipeline model.Variance based semi-global sensitivity analysis is suitable for both uncorrelated and correlated inputs and it can be extended more conveniently than Sobol's method.4 For the existing problem in the global sensitivity analysis of multivariate output model,basing on the proper variance quantification of multivariate random variable's uncertainty,a new global sensitivity analysis method for multivariate output model is proposed,and it is also extended to the global sensitivity analysis of time-varying model.This new method divides the output uncertainty of multivariate output model and time-varying model into two parts: the uncertainty caused by the inputs uncertainty and the uncertainty caused by model mode difference.5 For the sensitivity analysis of fuzzy input model,basing on the credibility theory the credibility variance based global sensitivity analysis is proposed to research the effect of fuzzy input uncertainty on the model output uncertainty.For the sensitivity analysis of fuzzy and random input model,basing on the chance theory the hybrid variance based global sensitivity analysis is proposed to research the effect of fuzzy and random input uncertainty on the model output uncertainty.For the sensitivity analysis of model's input uncertainty described by cloud model,cloud variable's entropy based semi-global sensitivity analysis is proposed to research the effect of cloud input uncertainty on the model output uncertainty.