Multilevel decomposition based nondeterministic design optimization for structural systems

The paper presents a methodology for nondeterministic design optimization of hierarchically coupled structural systems. Deterministic multilevel decomposition-based design formulations for such systems have been modified to incorporate the presence of uncertainty in both the problem parameters, and in design variables at various levels of a multilevel hierarchical system. These formulations not only allow for robust design solution strategies, but also provide a mechanism for tracking the propagation of uncertainty in such hierarchical systems. For uncertain design variables distributed across several subsystems, an iterative problem formulation is proposed. A widely used numerical example based on the design of a portal frame is used to illustrate the problem complexities in this class of design problems, and to demonstrate the effectiveness of the proposed solution techniques.