Robust topology optimization under loading uncertainties via stochastic reduced order models

An efficient approach for topology optimization under uncertainty is presented. Stochastic reduced order models (SROMs) are leveraged for the modeling and propagation of uncertainties within a robust topology optimization (RTO) formulation. The SROM approach provides an alternative to existing uncertainty quantification methods and yields a substantial improvement in efficiency over a classical Monte Carlo based approach while retaining similar accuracy when representing the uncertainty in system parameters. In particular, random input parameters can be discrete or continuous and specified either analytically (standard distributions) or numerically (dataset samples). Furthermore, multiple random quantities need not be treated as uncorrelated; an SROM can seamlessly model random vectors with arbitrary correlation structure. The nonintrusive nature of the SROM method yields an implementation that can be seen as a drop-in replacement for a simple RTO approach that leverages Monte Carlo simulation and is therefore straightforward to implement in existing topology optimization software. The proposed approach is demonstrated in the context of structural topology optimization with uncertainty in applied loads. Several numerical results are presented, covering a range of uncertainty distributions that illustrate the flexibility afforded by the general SROM method, while highlighting the efficiency and accuracy achieved in uncertainty propagation.