Online Hyperparameter Tuning in Bayesian Optimization for Material Parameter Identification: An Application in Strain-Hardening Plasticity for Automotive Structural Steel

Effective identification of strain-hardening parameters is essential for predictive plasticity models used in automotive applications. However, the performance of Bayesian optimization depends strongly on kernel hyperparameters in the Gaussian-process surrogate, which are often kept fixed. In this work, we propose a likelihood-based online hyperparameter strategy within Bayesian optimization to identify strain-hardening parameters in plasticity. Specifically, we used the rational polynomial strain-hardening scheme for the plasticity model to fit the force vs. displacement response of automotive structural steel in tension. An in-house Bayesian optimization framework was first developed, and an online hyperparameter tuning algorithm was further incorporated to advance the optimization scheme. The optimization histories obtained from the fixed and online-tuning hyperparameters were compared. For the same number of iterations, the online hyperparameter adaptation reduced the final residual by approximately 20.4%, 24.0%, and 3.8% for Specimens 1–3, respectively. These results demonstrate that the proposed strategy can significantly improve the efficiency and quality of strain-hardening parameter identification. The results show that the online tuning scheme improved the optimization efficiency. This proposed strategy may be readily extensible to other materials and identification problems where enhancing optimization efficiency is needed.