Parameter Estimation Using a Gaussian Process Regression-Based Reduced-Order Model and Sparse Sensing: Application to a Methane/Air Lifted Jet Flame

The goal of this work is to perform parameter estimation by comparing a Reduced Order Model (ROM), built using Proper Orthogonal Decomposition (POD) and Gaussian Process Regression (GPR), with a Sparse Sensing (SpS) model. This framework is demonstrated by selecting the optimal set of the Partially Stirred Reactor (PaSR) coefficients used in the modelling of the Cabra flame. The Cabra flame is a methane flame in a vitiated coflow, consisting of the combustion products of hydrogen and air. The PaSR model necessitates the knowledge of 4 scalar coefficients, which are unknown a priori. To select the optimal set of coefficients, 57 simulations were performed with a different combination of PaSR coefficients. These simulations were used to build the ROM via POD and GPR. To compare the numerical solution with the experimental data, the SpS technique has been employed. SpS is a framework that leverages dimensionality reduction to predict the state of the system given few measurements. The optimal coefficients have been estimated by applying an optimization algorithm to the ROM, using the solution provided by SpS as target. Finally, the data assimilation framework has been used to provide a solution with lower uncertainty bounds. The results show that this framework is able to estimate the optimal set of coefficients, and it can be used to identify residual sources of uncertainty in the numerical model by highlighting the difference between the optimized model and the experimental values.