Limitations and challenges of Bayesian calibration in complex fuel performance modeling scenarios

Fuel performance modeling involves complex, nonlinear systems with uncertain parameters that require rigorous calibration against experimental data to improve their prediction potential. In the presence of model bias, standard Bayesian calibration, typically combining Gaussian Process surrogates with Markov Chain Monte Carlo algorithms, may underestimate parameter uncertainty. This study compares standard Bayesian calibration with a hierarchical approach that moderates posterior uncertainty reduction by inflating parameter uncertainty, thereby reducing overconfidence in inferred parameters when model bias is present. Using Gaussian Process surrogates of the OpenFOAM Fuel BEhavior Analysis Tool solver to accelerate computationally intensive evaluations and Morris' screening for dimensionality reduction, we apply both calibration methods to a synthetic fuel performance dataset. The synthetic data are constructed to be representative of realistic fuel performance measurements while retaining known true parameter values, enabling an objective assessment of calibration accuracy and uncertainty quantification. Results show that hierarchical calibration outperforms standard techniques in the presence of systematic error, accurately recovering the true parameter value and consistently encompassing the synthetic experimental observations. The proposed framework provides a robust approach for quantifying uncertainties in complex fuel performance models. The paper also discusses challenges related to calibration performance, convergence diagnostics, and algorithm tuning, and outlines future enhancements, including advanced Markov Chain Monte Carlo methods and treatment of time-dependent outputs.