An integrated surrogate modeling method for fusing noisy and noise-free data

Datasets in engineering applications often contain multiple types of data, i.e., noise-free data, noisy data with known noise variances, and noisy data with unknown noise variances. In this paper, a data fusion method, termed as multi-type data fusion (MTDF) model, is proposed to fully utilize the information provided by each of these types of data. The proposed model strives to capture the underlying trend implied in the multiple types of data better by approximately interpolating the noise-free data while regressing with the noisy data. To evaluate the prediction accuracy of the MTDF model, it is compared with multiple surrogate models including interpolation models, regression models, and multi-fidelity models on both numerical and practical engineering problems. The results show that the proposed MTDF model presents a more outstanding performance than the other benchmark models. The key issues, i.e., the effect of noise level, the effect of the sample size of noise-free data, and the robustness of the MTDF model are also investigated. The results illustrate that the MTDF model possesses satisfactory feasibility, practicality, and stability.