Global Sensitivity And Structural Reliability Analysis

Polynomial chaos expansion has been a mainstream method for global sensitivity and reliability analysis of structures due to its theoretical rigor,wide capability,convenient applicability and fast convergence in recent years.However,curse of dimensionality and multicollinearity have always been bottlenecks that prevent its application to large complex structures with high dimensions.To deal with the difficulties of traditional polynomial chaos expansion in global sensitivity and reliability analysis,in this thesis,partial least squares regression procedures are integrated into polynomial chaos expansion.The proposed methods provide new ideas to the sensitivity and reliability analysis for large complex structures.The contents of this thesis are summarized as follows:(1)Based on the direct combination of partial least squares regression and polynomial chaos expansion,global sensitivity and reliability analysis methods are established and compared with the ones based on ordinary least squares regression;(2)Based on the direct combination approach,the idea of hierarchical modeling is introduced to build first and second order hierarchical partial least squares regression algorithms.The corresponding global sensitivity and reliability analysis methods are built with three partition schemes of polynomial matrices.Numerical experiments show that the proposed methods can drastically enhance computational efficiency with an acceptable accuracy,especially for the problems with low effective stochastic dimension;(3)Based on the direct combination approach,the idea of variable selection is introduced.Based on the regression coefficients and the variable importance projection,sparse partial least squares regression algorithms are proposed with the utilization of regularization and direct penalization procedures,respectively.The corresponding global sensitivity and reliability analysis methods are subsequently built.Numerical experiments show that the ratio principle-based direct penalization of regression coefficients algorithm outperforms the other algorithms;(4)Based on the hierarchical approaches,by performing variable selection with sparse partial least squares regression techniques in the level of latent explanatory variables and explanatory variables,respectively,the hierarchical sparse partial least squares regression algorithms of class A and B are proposed.And the corresponding global sensitivity and reliability analysis methods are built with the ratio principle-based direct penalization of regression coefficients algorithm as an example.Numerical experiments show that the efficiencies of the hierarchical sparse approaches are no less than the hierarchical counterparts.