Refinement of Gaussian Process Regression Modeling of Pilot-Ignited Direct-Injected Natural Gas Engines

This paper presents a sensitivity-based input selection algorithm and a layered modeling approach for improving Gaussian Process Regression (GPR) modeling with hyperparameter optimization for engine model development with data sets of 120 training points or less. The models presented here are developed for a Pilot-Ignited Direct-Injected Natural Gas (PIDING) engine. A previously developed GPR modeling method with hyperparameter optimization produced some models with normalized root mean square error (nRMSE) over 0.2. The input selection method reduced the overall error by 0.6% to 18.85% while the layered modeling method improved the error for carbon monoxide (CO) by 52.6%, particulate matter (PM) by 32.5%, and nitrogen oxides (NO_X) by 29.8%. These results demonstrate the importance of selecting only the most relevant inputs for machine learning models. This also shows that a layered approach to modeling could be implemented to further refine the inputs and provide a reduction in machine learning modeling error.