On Non-probabilistic Uncertainty Quantization And Reliability Sensitivity Of Structures Considering Correlated Variables

Compared with the traditional probability model,the non-probabilistic convex model only needs the boundary or range of uncertainties in structure analysis and design,which is more suitable for mechanical structures with small samples,poor information and high reliability requirements.On the basis of considering the correlation of variables,this paper focuses on the non-probabilistic uncertainty quantification and reliability sensitivity of structural considering correlates variables.The main research contents are as follows:1.Comparative study on uncertainty quantification and propagation of the two convex models:point at the ellipsoid model and the multidimensional parallelepiped model for describing the related variables,the uncertainty quantification and propagation are compared under the same uncertainties sample information.The basic idea of the study is that convex models with smaller envelope volume and more compact structural response interval should be preferred.The study provides a criterion for selecting a reasonable convex model according to the experimental sample data.2.Approximate analytical method of reliability sensitivity based on multi-ellipsoid model:multi-ellipsoid model is used to describe the multi-source uncertainty of structure,and on this basis,a non-probabilistic reliability sensitivity calculation method for multi-source uncertain variables is proposed.Firstly,the non-probabilistic reliability index is used to measure the reliability of multi-source uncertain variables,and the non-probabilistic reliability index solutions of linear and nonlinear limit state functions are given respectively.Secondly,the non-probabilistic reliability sensitivity based on multi-ellipsoid model is defined as the partial derivative of the reliability index to the parameters of the variable,and the approximate analytical method of the non-probabilistic reliability sensitivity is given.Thirdly,the universality of multi-ellipsoid model reliability sensitivity analysis method compared with interval model and ellipsoid model reliability sensitivity analysis method is discussed.Three examples prove the feasibility and superiority of the proposed algorithm.3.Approximate analytical method of reliability sensitivity based on multidimensional parallel hexahedron model:multi-source uncertain variables are described in a unified framework by multidimensional parallel hexahedron model,and multidimensional parallel hexahedron model problem is transformed into interval model problem by model standardization.Based on the non-probabilistic reliability sensitivity calculation method of interval model,the analytical solution of linear limit state function and the approximate analytical solution of nonlinear limit state function are given respectively.The effectiveness and reliability of the proposed algorithm are verified by three examples.