Modified Multifidelity Surrogate Model Based on Radial Basis Function with Adaptive Scale Factor

Multifidelity surrogates (MFSs) replace computationally intensive models by synergistically combining information from different fidelity data with a significant improvement in modeling efficiency. In this paper, a modified MFS (MMFS) model based on a radial basis function (RBF) is proposed, in which two fidelities of information can be analyzed by adaptively obtaining the scale factor. In the MMFS, an RBF was employed to establish the low-fidelity model. The correlation matrix of the high-fidelity samples and corresponding low-fidelity responses were integrated into an expansion matrix to determine the scaling function parameters. The shape parameters of the basis function were optimized by minimizing the leave-one-out cross-validation error of the high-fidelity sample points. The performance of the MMFS was compared with those of other MFS models (MFS-RBF and cooperative RBF) and single-fidelity RBF using four benchmark test functions, by which the impacts of different high-fidelity sample sizes on the prediction accuracy were also analyzed. The sensitivity of the MMFS model to the randomness of the design of experiments (DoE) was investigated by repeating sampling plans with 20 different DoEs. Stress analysis of the steel plate is presented to highlight the prediction ability of the proposed MMFS model. This research proposes a new multifidelity modeling method that can fully use two fidelity sample sets, rapidly calculate model parameters, and exhibit good prediction accuracy and robustness.

Automated summary

This paper proposes a modified MFS model based on RBF, which can analyze two fidelity information by adaptively obtaining the scale factor. The performance of the model is compared with other MFS models and single-fidelity RBF, and the impact of different high-fidelity sample sizes on prediction accuracy is analyzed. The results show that the proposed model can fully utilize two fidelity sample sets and has good prediction accuracy and robustness.