A hybrid sequential sampling strategy for sparse polynomial chaos expansion based on compressive sampling and Bayesian experimental design

Abstract

Sparse representation of Polynomial Chaos Expansion (PCE) has been widely used in the field of Uncertainty Quantification (UQ) due to its simple model structure and low computational cost. The sample quality is a crucial issue that affects the precision of sparse PCE model. In this paper, a hybrid sequential sampling strategy is proposed to collect samples with high quality and in relatively small quantities for training PCE model. To achieve fast convergence rate and modelling stability, the proposed strategy takes into account both input information and target model feature by combining compressive sampling and Bayesian experimental design. First, a sequential sampling framework is established to collect samples that approximately match the coherence-optimal distribution, which is derived from the compressive sampling theory, during the iteration process. Then, by resorting to the Bayesian Compressive Sensing (BCS) method and information theory, favourable sampling points in each iteration are determined according to the modelling results, substituting for randomly selecting sampling points. The performance of the proposed sampling strategy is evaluated on several analytical functions through comparison with three input-dependent only sampling methods and two output-dependent only sampling methods. Results show that the proposed strategy outperforms the input-dependent only methods and has no worse performance than the output-dependent only methods in convergence rate and computational stability in most circumstances. The proposed strategy is further applied to two engineering cases for global sensitivity analysis of structural static and dynamic properties. It is illustrated that with automatically collected samples and observations, the PCE models can be obtained with desired accuracy, and the sensitivity analysis can be pursued with low computational cost and high precision.