An Integrated Surrogate Modeling Method for Fusing Noisy and Noise-Free Data

Abstract Many datasets in engineering applications are heterogeneous mixtures of noise-free data, noisy data with known noise variances, and noisy data with unknown noise variances. This article proposes a data fusion method called the multi-type data fusion (MTDF) model, which fully utilizes the information provided by each of these types of data. To capture the underlying trend implied in the multiple types of data, the method approximately interpolates the noise-free data, while regressing the noisy data. The prediction accuracy of the MTDF model is compared with those of various surrogate models (interpolation models, regression models, and multi-fidelity models) on both numerical and practical engineering problems. In the experiments, the proposed MTDF model demonstrates higher performance than the other benchmark models. The effects of noise level and sample size of the noise-free data on the model performance are investigated, along with the robustness of the MTDF model. The results demonstrate the satisfactory feasibility, practicality, and stability of the MTDF.