A sequential sampling strategy to improve the global fidelity of metamodels in multi-level system design

In engineering design, complex systems that involve a multitude of decision variables and parameters are often decomposed into several submodels (also called subsystems and/or components) with a hierarchical (multi-level) manner to manage complexity. Metamodeling techniques are widely used to replace the original time-consuming computer simulation models to further reduce computational burden in multi-level system performance analysis and design optimization. However, due to the limited samples from simulation models, metamodels may contain metamodeling uncertainties at un-sampled sites. Such metamodeling uncertainties arising from metamodels across the entire hierarchy will propagate from the lower to upper levels and eventually impact the top-level response of interest. With the aim of improving the global fidelity of metamodels for multi-level system performance analysis and design optimization, a new sequential sampling strategy is proposed in this paper. The proposed method contains two basic elements: (1) quantifying metamodeling uncertainty propagated from the lower-level metamodels to the top-level response of interest and (2) seeking a new sample site at which the global fidelity of the multi-level system model can be maximally improved. As exemplified by the two numerical examples and a multi-scale bracket structure example, with the same amount of samples from computer simulation models, the new sequential sampling strategy is superior to existing sequential sampling strategies in terms of improving the global fidelity of the metamodels of multi-level systems.