A new polynomial chaos expansion method for uncertainty analysis with aleatory and epistemic uncertainties

The probability and evidence theories are frequently used tool to deal with the mixture of aleatory and epistemic uncertainties. Due to the double-loop procedure for the mixed uncertainty quantification (UQ), the computational cost is daunting. Therefore, this study proposes a new polynomial chaos expansion (PCE) method for UQ problems with random variables and evidence variables. To enhance the computational accuracy and efficiency of the PCE model, a new low-discrepancy sequence sampling method is proposed, and the sample weights are redefined according to the Christoffel prior. Then, a weighted sparse Bayesian learning method is developed to construct the PCE model with a small sample size. Finally, the proposed method is verified through two numerical examples and one practical engineering problem and compared with three common surrogate methods. Results illustrate the proposed method has obvious advantages in computational accuracy and efficiency over the compared methods, and is powerful for the UQ problems with aleatory and epistemic uncertainties.