Bilevel Data-Driven Modeling Framework for High-Dimensional Structural Optimization under Uncertainty Problems

Optimization under uncertainty (OUU) is a robust framework to obtain optimal designs for real engineering problems considering uncertainties. The numerical solution for large-scale problems involving millions of degrees-of-freedom is typically computation-intensive in nature. Also, OUU problems constitutes an uncertainty analysis, involving a computation-intensive numerical solver for large-scale systems. Hence, the solution of OUU problems are computationally demanding in nature. In this study, a bilevel data-driven modeling framework is proposed using proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) metamodels. A heuristic particle swarm optimization (PSO) technique is used for optimization. The effectiveness of the POD-PCE metamodel combined with PSO is demonstrated for two practical large-scale structural optimizations under uncertainty problems. From the case studies, it has been observed that the proposed method gives solutions that are almost hundreds and thousands of times faster as compared to the crude Monte Carlo simulation.