On the ensemble of metamodels with multiple regional optimized weight factors

Metamodels are often used as surrogates for expensive high fidelity computational simulations (e.g., finite element analysis). Ensemble of metamodels (EM), which combines various types of individual metamodels in the form of a weighted average ensemble, is found to have improved accuracy over the individual metamodels used alone. Currently, there are mainly two kinds of EMs called as pointwise EM and average EM. The pointwise EM generally has better prediction accuracy than the average EM, but it is much more time-consuming than the average EM. In most cases, as a metamodel, EM is often used in the engineering design optimization which needs to invoke EM tens of thousands of times. Therefore, the average EM is still the most extensively used EM. To the authors’ best knowledge, the most accurate average EM is the EM with optimized weight factors proposed by Acar et al. However, the EM proposed by Acar et al. is often too “rigid” and may not have sufficient accuracy over some regions of the design space. In order to deal with this problem and further improve the prediction accuracy, a new EM with multiple regional optimized weight factors (EM-MROWF) is proposed in this study. In this new EM, the design space is divided into multiple subdomains each of which is assigned a set of optimized weight factors. This new EM was constructed by combining three typical individual metamodels, i.e., polynomial regression (PR), radial basis function (RBF), and Kriging (KRG). The proposed technique was evaluated by ten benchmark problems and two engineering application problems. The ten benchmark problems are typical mathematical functions for evaluating the approximation performance in previous studies. And, the two engineering application problems refer to the vehicular passive safety in the field of crashworthiness design. The study results showed that the EM-MROWF performed much better than the other existing average EMs as well as the three individual metamodels.