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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 (NOX) by 29.8%. These results demonstrate the importance of selecting only the most relevant inputs for machine learning models.

The emissions and efficiency of modern internal combustion engines need to be improved to reduce their environmental impact. Many strategies to address this (e.g., alternative fuels, exhaust gas aftertreatment, novel injection systems, etc.) require engine calibrations to be modified, involving extensive experimental data collection. A new approach to modeling and data collection is proposed to expedite the development of these new technologies and to reduce their upfront cost. This work evaluates a Gaussian Process Regression, Artificial Neural Network and Bayesian Optimization based strategy for the efficient development of machine learning models, intended for engine optimization and calibration. The objective of this method is to minimize the size of the required experimental data set and reduce the associated data collection cost for engine modeling.