Research On Global And Regional Sensitivity Analysis For Structures With Uncertainty

Uncertainties widely exist in aeronautics and astronautics aircraft design.According to whether they can be reduced by gathering more information,they can be classified into two categories:aleatory uncertainty and epistemic uncertainty.Generallly,the aleatory uncertainty can be described in probabilistic framework,while three models are suggested to describe the epistemic uncertainty,i.e.probabilistic model,fuzzy model,and non-probabilistic model.This work mainly investigates the sensitivity analysis in the presence of both aleatory uncertainties of input variables and epistemic uncertainties of distribution parameters,and proposes new sensitivity indices of inputs on output response.Besides,global and regional importance measure of distribution parameters on statistical characteristics of output response and their corresponding high efficient method are also constructed and testified.The contents are detailed as follows:(1)For structural systems with only aleatory uncertainties of input variables,we propose two kinds of global sensitivity indices are proposed in the probabilistic framework:i.e.a mixed sensitivity index based on the derivative of failure probability and a new Spearman correlation based moment independent sensitivity index.Then a high efficient method based on state dependent parameter(SDP)is proposed for estimating the mixed sensitivity index.To further improve the computational efficiency,SDP is combined with Importance Sampling(IS)and Truncated Importance Sampling(TIS).Besides,the idea of Unscented Transformation(UT)and High Order Unscented Transformation(HOUT)are introduced to estimate the latter sensitivity index.(2)When the structural system contains both aleatory uncertainties of input variables and epistemic uncertainties of distribution parameters,two importance measures:Correlation Coefficient and Correlation Ration are defined in the probabilistic framework in order to analyze the effect of distribution parameter on failure probability under the condition of fuzzy state.For reducing the computational cost,the two measures are simplified by introducing a proportional coefficient,and then a novel Moving Least Square(MLS)method is constructed to compute them.Besides,for the variance based sensitivity measure of distribution parameter,the M-DRM(multiplicative form of dimensional reduction method)idea is extended into the map from distribution parameters to failure probability function(FPF),the highly efficient approximation form is constructed for the variance-based sensitivity measure of the distribution parameter,then the Extended Monte Carlo(EMC)and Rejection Sampling(RS)to estimate the FPF.Thus only one set of samples of inputs are essential to compute the sensitivity index under two kinds of uncertainties.Since RS shows its advantage on calculating characteristics of output response,it is applied to parametric reliability optimization and parametric robust optimization,and its accuracy and high efficiency are proved again.(3)For situations where structural system contains both aleatory and epistemic uncertainties of input variables,the inputs are defined in the probabilistic and fuzzy framework simultaneously.Then an average fuzzy failure index is defined similar to the index in slope analysis.And importance measures are defined to quantify the influence of random and fuzzy inputs on the system failure.Besides,when the structural system contains both aleatory uncertainty of input variables in the probabilistic framework and the epistemic uncertainty of distribution parameter in the fuzzy framework,moment independent sensitivity indices are proposed to measure the effect of fuzzy parameters on the membership function of failure probability.For efficiently calculating the indices,a single loop method based on EMC is constructed.It is found that the proposed measures also have the property of transformation invariance,and they are an extension of existing moment independent sensitivity index.(4)For cases that aleatory uncertainties of input variables and epistemic uncertainties of distribution parameters are described in probabilistic framework,regional importance measures(RIMs)are proposed similar with CSM and CSV in order to measure the influence of distribution parameters on characteristics of output response.By taking the mean varying with the different region of the input into consideration,the proposed RIMs are revised.The analytical solutions of the revised RIMs for general form of quadratic polynomial output are also deduced.Since we care more about the failure probability of structural system,RIMs of distribution parameters on mean>variance and first order variance contribution of FPF are also proposed,and a method based on SDP is constructed to efficiently compute those RIMs.