Robust ensemble of metamodels based on the hybrid error measure

Metamodels have been widely used as an alternative for expensive physical experiments or complex, time-consuming computational simulations to provide a fast but accurate analysis. However, challenge remains in the prior determination of the most suitable metamodel for a particular case because of the lack of information about the actual behavior of a system. In addition, existing studies on metamodels have largely restricted on solving deterministic problems (e.g., data from finite element models), whereas some real-life engineering problems (e.g., data from physical experiment) are stochastic problems with noisy data. In this work, a robust ensemble of metamodels (EMs) is proposed by combining three regression stand-alone metamodels in a weighted sum form. The weight factor is adaptively determined according to the hybrid error metric, which combines global and local error measures to improve the accuracy of the EMs. Furthermore, three typical individual metamodels that can filter noise are selected to construct the EMs to extend their application in practical engineering problems. Three well-known benchmark problems with different levels of noise and three engineering problems are used to verify the effectiveness of the proposed EMs. Results show that the proposed EMs have higher accuracy and robustness than the individual metamodels and other typical EMs in major cases.