Data-driven emission model structures for diesel engine management system development

This article discusses some specific data-driven model structures suitable for prediction of NOx and soot emissions from a diesel engine. The model structures can be described as local linear regression models where the regression parameters are defined by two-dimensional lookup tables. It is highlighted that this structure can be interpreted as a B-spline function. Using the model structure, models are derived from measured engine data. The smoothness of the derived models is controlled by using an additional regularization term, and the globally optimal model parameters can be found by solving a linear least squares problem. Experimental data from a five-cylinder Volvo passenger car diesel engine is used to derive NOx and soot models, using a leave-one-out cross-validation strategy to determine the optimal degree of regularization. The model for NOx emissions predicts the NOx mass flow with an average relative error of 5.1% and the model for soot emissions predicts the soot mass flow with an average relative error of 29% for the measurement data used in this study. The behavior of the models for different engine management system settings regarding boost pressure, amount of exhaust gas recirculation, and injection timing has been studied. The models react to the different engine management system settings in an expected way, making them suitable for optimization of engine management system settings. Finally, the model performance dependence on the selected model complexity and on the number of measurement data points used to derive the models has been studied.