Robust hierarchical multiscale design using PATC and PCE

Multiscale design for dealing with 2-scale material and product system is implemented by employing the probabilistic analytical target cascading (PATC) and polynomial chaos expansion (PCE) approaches in this paper. PATC allows design autonomy at each scale subsystem by formulating the multiscale design problem as a hierarchical structure. PCE ensures uncertainties to be propagated within and across each scale accurately and efficiently. In addition, correlation between the random inputs is also considered during uncertainty propagation. Comparative study on a multiscale bracket design problem shows that the results obtained by our strategy are very close to the reference values. It is demonstrated that PATC and PCE are effective and applicable on multiscale design.