Enhanced probabilistic analytical target cascading with application to multi-scale design

Probabilistic analytical target cascading (PATC) is an approach for multi-level multi-disciplinary design optimization under uncertainty. In the original PATC approach, only the mean and variance of each interrelated response and linking variable are matched in a multi-level hierarchy. The ignorance of response correlation introduces difficulties in finding optimal solutions especially when the covariance of interrelated responses has a significant impact. In this article, an enhanced PATC (EPATC) approach is proposed. In addition to matching the first two statistical moments, the covariance between the interrelated responses is also considered by applying a modified updating strategy for estimating the statistical performance of an upper-level subsystem. A mathematical example and a multi-scale design problem are used to demonstrate the effectiveness and efficiency of the proposed EPATC approach. This study shows that the EPATC approach outperforms the original PATC by providing more accurate optimal solutions.