Professor of Mechanical Engineering and Smart Structures, School of Computing Engineering and Mathematics, Western Sydney University, Australia. His research interests cover Industry 4.0, Additive Manufacturing, Advanced Engineering Materials and Structures (Metals and Composites), Multi-scale Modelling of Materials and Structures, Metal Forming and Metal Surface Treatment.
Abstract—The multi-fidelity surrogate model, which can effectively balance the prediction accuracy and the modeling cost shows enormous potential in the design and optimization of mechanical products. Among them, the Co-Kriging multi-fidelity surrogate model based on Bayesian theory can provide the prediction error at the non-test points, which makes it especially attractive in the field of design optimization under uncertainty. However, in the Co-Kriging modeling process, high-fidelity (HF) and low-fidelity (LF) sampling points must be nested to satisfy the Markov property. If the Co-Kriging coefficients are obtained based on the full correlation, the modeling process will be complicated and result in low modeling efficiency. Therefore, this paper proposes an improved Co-Kriging multi-fidelity surrogate modeling method for non-nested sampling data. The proposed approach makes use of the characteristics of the stochastic kriging model to take the error of the LF surrogate model into consideration. Two independent processes are used to get the hyper-parameters of the LF surrogate model and the discrepancy model, respectively. The prediction accuracy and robustness of the proposed method are compared to the existing typical multi-fidelity surrogate modeling method on a standard numerical test example and an engineering example. The comparison results indicate that the proposed approach possesses not only excellent prediction accuracy but also outstanding robustness.
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