Sensitivity-based adaptive sequential sampling for metamodel uncertainty reduction in multilevel systems

Decomposition-based technique is often used in the analysis and design of complex engineering systems for reducing the computational complexity by studying the subsystems decomposed from multilevel systems. Metamodels, as a replacement of original simulation models, can further alleviate the computational burden. However, discrepancy between the simulation models and metamodels, which is defined as metamodel uncertainty, may be introduced in the analysis process of multilevel systems owing to the lack of data. The metamodel uncertainties of sub-models will be further amplified because of the hierarchical uncertainty propagation and interaction between uncertainties, which will have a great impact on the system results. An adaptive sequential sampling strategy based on sensitivity is proposed in this paper so as to improve the prediction accuracy of system response. In this strategy, polynomial-chaos expansion is used to realize the forward propagation of metamodel uncertainty quantified by the Kriging model. The forward propagation is combined with optimization based on maximum variance criterion for searching the input locations that results in the largest variance of system response. Then, the indices of subsystems are obtained to make decisions about which subsystem needs extra samples by combining Karhunen-Loeve expansion and sensitivity analysis. The effectiveness of the proposed sequential sampling strategy method is verified by two mathematical examples and a multiscale composite material.