Refined dimension-reduction integration method for uncertainty propagation in stochastic systems: Estimation of statistical moments

In terms of precision, effectiveness and generality, the quantification and propagation of uncertainty for stochastic systems remains a challenge, especially for the estimation of statistical moments for stochastic responses. In this work, a mixed variables-based and vectors-based refined dimension-reduction model is developed to replace a complex response function by component functions that contain both variables and vectors. On the basis of the developed refined dimension reduction model, a new dimension-reduction integration method that takes into account accuracy and efficiency, termed the refined dimension-reduction integration method (RDIM), is put forth as a means of estimating moments of response functions. Two categories of examples, comprising several numerical examples and two engineering examples, are examined to demonstrate the functionality of the proposed RDIM. The findings indicate that the RDIM is adaptable and can maintain a balance between precision and effectiveness for each example.