Adaptive Sparse Polynomial Chaos Expansion With Application To Structural Uncertainty Quantification

In recent years,the polynomial chaos expansion(PCE)has become one of the mainstream methods for the structural uncertainty quantification due to its rigorous theory,wide applicability,stable accuracy and efficient computing capacity.However,the problems such as the “curse of dimensionality” have always restricted its application in large complex structures with high dimensionality.To deal with the difficulties of traditional PCE algorithms in structural uncertainty quantification,this thesis combines the Bregman-iterative greedy coordinate descent(BGCD)with the prediction variance-based optimality criterion.A new method for constructing sparse PCE(termed adaptive BGCD)is proposed for the structural uncertainty quantification analysis,which provides a new research idea for the uncertainty quantification analysis of large complex engineering equipment.The main contributions of this thesis are as follows:(1)BGCD is combined with estimation-oriented and prediction-oriented optimality criteria at the same time and these two kinds of optimality criteria are also combined with least angle regression(LAR)and subspace pursuit(SP)to comprehensively verify the improved BGCD algorithm.(2)A new Adaptive BGCD algorithm is proposed by combining BGCD algorithm with the prediction variance-based adaptive sampling algorithm,and the Adaptive BGCD algorithm is applied to two classical benchmark functions,cantilever beam and offshore jacket platform.The modeling capacity of Adaptive BGCD for different dimensional problems is compared with the current popular PCE algorithms based on adaptive sampling.The results show that the proposed Adaptive BGCD has superior accuracy and robustness while requiring fewer number of samples,and its superiority becomes more significant for higher-dimensional problems.(3)The Adaptive BGCD algorithm is applied to the structural uncertainty quantification analysis.In the global sensitivity analysis,the application of Adaptive BGCD in classical Ishigami and Sobol functions,plane and space truss structures is researched.In the reliability analysis,the application of Adaptive BGCD in three classical reliability analysis examples and space truss structures is researched.Compared with other algorithms,the proposed Adaptive BGCD shows the characteristics of superior accuracy,low cost and strong stability in the field of the structural uncertainty quantification.