Uncertainty propagation techniques in probabilistic design of multilevel systems

In hierarchical multilevel systems, information (interrelated responses) is passed among levels following a bottom-up sequence. One of the primary challenges for multilevel system design optimization under uncertainty is associated with the quantification of uncertainty propagated across multiple levels. In this paper, two newly developed uncertainty propagation techniques, full numerical factorial integration and univariate dimension reduction, are investigated by employing them for uncertainty propagation (UP) in probabilistic multilevel design, which is solved by the probabilistic analytical target cascading (PATC) approach. Covariance among the interrelated responses is considered to improve the accuracy of optimal solution in PATC. Subsequently, linear transformation is employed to facilitate UP. The Monte Carlo method is used as the benchmark to verify the accuracy of these techniques.