Global And Regional Sensitivity Analysis For Uncertainties In Structure System

The uncertainties existed in aeronautical structural systems greatly affect its performance,thus,investigating how those uncertainties affect system performance is significant for improving the quality of aeronautical product,model simplification and reducing the probabilities of making wrong decisions.Focusing on global and regional sensitivity analysis,this thesis contains the following contributions:1.For choosing the most appropriate analysis methods to meet different requirements,the importance indices in case of correlated inputs,including the total,the structural and the correlative contributions,derived from the covariance decomposition,are firstly derived for the quadratic polynomial without interaction terms and the one with interaction terms.Then,based on these derived analytical solutions,the relation between the traditional variance based method and the newly covariance based method is explored.The conclusions derived from the quadratic polynomials are then extended to general cases,and validated from the high dimensional model representation.Three examples are introduced for investigating the relation between the two groups of importance indices,and relative merits of each.The conclusions are instructive and meaningful to importance analysis and engineering design when the model inputs are correlated.2.Based on the classical variance-based indices and global reliability sensitivity analysis(GRSA)indices,we develop the corresponding sensitivity indices for the p-box type of uncertainty so as to measure the relative importance of each input,and propose an efficient computational procedure,called extended Monte Carlo simulation(EMCS),to compute the developed sensitivity indices.The developed sensitivity indices are well interpreted,and the EMCS procedure is efficient as the computational cost is the same with the classical Monte Carlo estimators for Sobol's indices.Two numerical test examples and two engineering applications are introduced for illustrating the developed sensitivity indices and demonstrating the efficiency and effectiveness of the EMCS procedure.3.The permutation variable importance measure(PVIM)based on random forest(RF)has been regarded as a standard technique for learning the relative importance of model inputs.The aim of this work is to extend the PVIM to quantify the total contributions of the subranges of each input variable and to measure the residual PVIM of each input variable when its distribution range is reduced.For this purpose,the PVIM function is defined and its estimator is derived with the same set of sample used for computing the PVIM.The PVIM function is well interpreted by considering its relation with the Sobol's total effect index,and can provide the analysts with more plenty of sensitivity information.The proposed PVIM function as well as the estimator for computing it are demonstrated with Ishigami function,a unilateral asymmetric movement failure model of aircraft flap and a multi-indicator system model.4.Regional sensitivity analysis for model with multivariate output is investigated in this paper.Generalized variance in multivariate statistical theory is firstly introduced to describe the uncertainties in multivariate output.By discussing its geometric interpretation,it is clear that the generalized variance represents both the uncertainties in each dimension of model output and the correlations between different model output.The generalized variance ratio function is defined to investigate the effect of the subranges of input variables on the uncertainties of multivariate output.Two efficient computational process as called single-loop Monte Carlo simulation and sparse grid,are developed to plot the proposed regional index.