Comparison of Bayesian Model Calibration Techniques for Future Application to Fuel Performance Behavior Models

This paper explores data assimilation methods in the context of Bayesian Calibration for fuel performance models. It compares deterministic and stochastic approaches, concentrating on the Generalized Linear Least Squares (GLLS) method and stochastic techniques, including the Monte Carlo sampling Bayesian updating procedure (MOCABA), Bayesian Monte Carlo (BMC), and one Markov Chain Monte Carlo (MCMC) sampler, the Adaptive Metropolis (AM). GLLS relies on a first-order approximation of the model and encounters challenges when dealing with non-linear relationships between input and output parameters, particularly for input parameters with substantial uncertainties. While MOCABA and BMC address these limitations, they exhibit discrepancies in certain scenarios. In contrast, MCMC methods, which generate samples directly from arbitrary posterior distributions, offer advantages for models with non-normal parameter distributions, large uncertainties, and strong non-linearities. This study evaluates the applicability limits of GLLS, MOCABA, and BMC, emphasizing the characteristics of the AM sampler as a good candidate for application to fuel performance calculations. To save computational time, we examine three academic application cases designed to represent key features of fuel performance models. The results reveal discrepancies between the data assimilation techniques, highlighting the superior performance of AM for these models. Finally, we assess the computational cost of each technique, demonstrating the larger number of function evaluations needed for the stochastic methods.