Application of Probabilistic Distribution Matching PATC on Robust Multi-Scale Design

Multiscale design dealing with a 2-scale material and product system is implemented by employing the probabilistic distribution matching probabilistic analytical target cascading method (PATC-PCE) in this paper. PATC-PCE allows design autonomy at each scale subsystem by formulating the multiscale design system as a multilevel design structure. The probabilistic distribution matching strategy in PATC-PCE can quantify the stochastic interrelated responses accurately enough. Comparative study on a multiscale bracket design problem shows that the results obtained by our method are very close to the benchmark values. PATC-PCE is demonstrated to be highly effective and applicable on multi-scale design.

Robust Multiscale Design Using PATC and WSRSM

Multiscale design dealing with 2-scale material and product system is implemented by employing probabilistic analytical target cascading (PATC) and weighted stochastic response surface method (WSRSM) in this paper. PATC allows design autonomy at each scale subsystem by formulating the multiscale design system as a multilevel structure. WSRSM ensures uncertainties to be propagated within and across each scale accurately and efficiently. 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 WSRSM are highly effective and applicable on multiscale design.

Probabilistic Analytical Target Cascading: A Moment Matching Formulation for Multilevel Optimization Under Uncertainty

Analytical target cascading (ATC) is a methodology for hierarchical multilevel system design optimization. In previous work, the deterministic ATC formulation was extended to account for uncertainties using a probabilistic approach. Random quantities were represented by their expected values, which were required to match among subproblems to ensure design consistency. In this work, the probabilistic formulation is augmented to allow introduction and matching of additional probabilistic characteristics. Applying robust design principles, a particular probabilistic analytic target cascading (PATC) formulation is proposed by matching the first two moments of random quantities. Several implementation issues are addressed, including representation of probabilistic design targets, matching interrelated responses and linking variables under uncertainty, and coordination strategies for multilevel optimization. Analytical and simulation-based optimal design examples are used to illustrate the new PATC formulation. Design consistency is achieved by matching the first two moments of interrelated responses and linking variables. The effectiveness of the approach is demonstrated by comparing PATC results to those obtained using a probabilistic all-in-one (PAIO) formulation.