Abstract
Model calibration is a process aimed at adjusting unknown parameters to minimize the error between the simulation model output and experimental observations. In computer-aided engineering, uncertainties in physical properties and modeling discrepancies can generate errors. Among various model calibration approaches, Kennedy and O’Hagan (KOH)’s Bayesian model calibration is noted for its ability to consider a variety of sources of uncertainty. However, one of the difficulties in KOH’s Bayesian model calibration is the complexity of determining the prior distributions of hyperparameters, which is often challenging in real-world problems due to insufficient information. Most previous studies have relied on users’ intuition to mitigate this issue. Thus, this study proposes a statistical prior modeling method for the correlation hyperparameter of a model discrepancy, which affects the calibration performance. In this work, a radius-uniform distribution is introduced as a prior distribution of the correlation hyperparameter based on the properties of the Gaussian process. Three case studies are provided, one numerical and two engineering cases, to confirm that the proposed method results in lower error than any other previously proposed distribution without additional computational cost. Further, the proposed method does not require user-dependent knowledge, which is a significant advantage over previous methods.
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Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (No. 2020R1A2C3003644).
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Ministry of Science and ICT, Republic of Korea, 2020R1A2C3003644, Byeng D Youn.
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Byeng D. Youn (bdyoun@snu.ac.kr) and Hyejeong Son (son41524152@gmail.com) are co-corresponding authors of this paper.
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To facilitate the replication of results, the paper provides all model formulations and input parameters for each of the case studies. All computations in this work rely on MATLAB; calculation for Bayesian calibration requires the Statistics and Machine Learning Toolbox; the observation from the engineering case study was conducted using the Partial Differential Equation Toolbox. For the second engineering case study, the observation data were generated using the COMSOL and LiveLink™ for MATLAB, and the kriging model was generated by the DACE Toolbox. Important details required to calculate the bounds of the radius-uniform distribution (file name: psi_bound.m) and the probability density function (file name: radius_uniform_pdf.m) are provided as supplementary materials.
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Jeong, S., Choi, H., Youn, B.D. et al. Statistical prior modeling with radius-uniform distribution for a correlation hyperparameter in bayesian calibration. Struct Multidisc Optim 66, 69 (2023). https://doi.org/10.1007/s00158-023-03520-0
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DOI: https://doi.org/10.1007/s00158-023-03520-0
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