An active learning radial basis function modeling method based on self-organization maps for simulation-based design problems

Abstract

The radial basis function has been widely used in constructing metamodels as response surfaces. Yet, it often faces the challenge of accuracy if a sequential sampling strategy is used to insert samples sequentially and refine the models, especially under the constraint of computational resources. In this paper, a sensitive region pursuing based active learning radial basis function (SRP-ALRBF) metamodeling approach is proposed to sequentially exploit the already-acquired knowledge in the modeling process for obtaining a desirable estimation of the relationship between the input design variables and the output response. In this method, the leave-one-out (LOO) errors of each sample point are taken to identify the boundaries of sensitive regions. According to the obtained LOO information, the original design space is divided into some subspaces by adopting the self-organization maps (SOMs). The boundary of the most sensitive region, where the output response is multi-modal or non-smooth with abrupt changes, is determined by the topological graph generated by cluster analysis in SOMs. In the most sensitive region, infill sample point searching is performed based on an optimization formulation. Ten numerical examples are used to compare the proposed SRP-ALRBF with four existing active learning RBF metamodeling approaches. Results show the advantage of the proposed SRP-ALRBF approach in both prediction accuracy and robustness. It is also applied to three engineering cases to illustrate its ability to support complex engineering design.