Improvements to the probability density evolution method integrated with the change of probability measure on quantifying hybrid uncertainties.

The probability density evolution method (PDEM) synthesizing the change of probability measure (COM) provides a compatible framework for quantifying simultaneous aleatory and epistemic uncertainties. Nonetheless, when the effective support for the change of measure becomes narrow, the quantification error of the PDEM-COM may increase, and the PDEM-COM may even be invalid if the effective support is an empty set. To address this issue, in the present paper, the error analysis of the PDEM-COM is firstly explored, and the generalized F-discrepancy via the COM is utilized to measure the similarity of two different distributions. Then, an augmenting approach is proposed to improve the performance of the PDEM-COM by adding a number of computational simulations. The results indicate that, the PDEM-COM can still be relatively accurate as long as the effective support is sufficiently large, even when there is a significant shift in the probability measure. However, if the effective support turns to be extremely narrow, the error of hybrid uncertainty quantification via the PDEM-COM may be unsatisfied, but it can be significantly reduced by the suggested augmenting approach. Numerical examples are investigated to demonstrate the accuracy and efficiency of the proposed method. Some issues to be further studied are also outlined. • Error analysis of the PDEM-COM is studied. • Numerical illustration of the PDEM-COM for different changes of probability measure. • An augmenting approach is proposed to improve the PDEM-COM. • The accuracy and efficiency of the proposed method is validated by three engineering applications. [ABSTRACT FROM AUTHOR]