Iterative experimental design for model uncertainty quantification with a novel likelihood function incorporating error dependence on condition parameters

Automatic optimization and uncertainty quantification (UQ) methods are often applied in the development of chemical mechanisms to calibrate models against a number of experiments. For the reduction of experimental effort, design of experiments (DOE) methods can be used to find most valuable data. In each iteration of model-based DOE, the most informative experiment is supposed to be selected for the improvement of the current model performance. The iteration repeats until the desired prediction accuracy is achieved. The likelihood function, which can be regarded as the objective function of UQ, determines the posterior distributions of model parameters, is expected to affect the results of iterative DOE. Often, the likelihood function is derived based on the assumption that error of each measurement is independent. However, the experimental observations and their errors are dependent on various physical condition parameters, such as temperature. Recently, surface-matching (SM) method is proposed in our previous work to quantify the dissimilarity between surface shapes and values of simulation and experiment. By minimizing the SM-based objective function, the joint dependence of model predictions on various physical conditions is optimized. Thus, in this work, an iterative experimental design framework with Bayesian UQ method and SM-based likelihood function is proposed. The SM-based function is expected to incorporate error dependence on physical conditions into UQ. Based on this framework, the most informative experiments can be selected iteratively to improve the model performance in terms of joint dependence on physical conditions. The application of this framework is demonstrated by designing ignition delay experiments for the optimization of a dimethyl ether mechanism. For comparison, iterative DOEs are implemented with the point-wise and curve matching (CM)-based likelihood functions. Different results on the selection of experiments and development of model improvement provided by the iterative DOEs with various likelihood functions demonstrate the significant impact of likelihood function definition. • Dependence of experimental errors on conditions incorporated in DOE. • Successful application of the new DOE framework to design ignition delay experiments. • Calibration of joint dependence of model predictions on condition parameters in DOE. • Significant impacts of likelihood function definition on DOE results are revealed.