A two-stage support vector regression assisted sequential sampling approach for global metamodeling

Support vector regression (SVR), as a promising surrogate model, has been widely used to approximate expensive simulations in engineering design problem. To build a SVR model accurately and efficiently, a two-stage support vector regression (TSSVR) assisted sequential sampling approach is proposed in this paper with the consideration of SVR’s two unique features. In each sampling iteration of TSSVR, two SVR models are constructed successively based on the same training data. As for the first feature that only support vectors (SVs) have impact on the construction of SVR, the first-stage SVR with lower ε precision is built to prescreen some important samples as current SVs. As for the second feature that SVR model does not completely go through the samples, the second-stage SVR with higher ε precision is built to calculate the prediction errors at the SVs without any other computational cost, and the prediction errors are used to approximately measure the accuracy of the local regions around the SVs. Moreover, to describe the local regions around the SVs, the design space is partitioned into a set of Voronoi cells according to the current samples before prescreening SVs from the sample points. Then a new sample can be exploited in the corresponding Voronoi cell with the largest prediction error. In the next sampling iteration, the Voronoi cells and SVs are redefined. As the change of the local cell with the largest prediction error, global exploration is achieved. Finally, the proposed approach is validated by seven numerical examples and an engineering example. An overall comparison between the proposed approach and some other methods demonstrates that the proposed approach is efficient and suitable for engineering design problems involving computational-expensive simulations.