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. Two newly developed uncertainty propagation techniques, the full numerical factorial integration method and the univariate dimension reduction method, are compared through their employment in probabilistic design of multilevel system. The Probabilistic Analytical Target Cascading (PATC) approach is used for solving the probabilistic multilevel hierarchical problems as well as demonstrating the two uncertainty propagation techniques. Covariance among the interrelated responses between neighboring levels is considered to improve the accuracy of the statistics estimation of upper-level outputs. Linear transformation of the correlated interrelated responses is adopted to facilitate the application of the uncertainty propagation techniques in PATC. The Monte Carlo method is used as the benchmark to verify the accuracy of these techniques.