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

Abstract

This paper 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 look-up 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 5-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.

On the integration of physics-based and data-driven models for the prediction of gas exchange processes on a modern diesel engine

“…In the past, data-driven models have been used to capture emissions from diesel engines [16][17][18] and aftertreatment systems. 19 They have also been applied to whole engine systems to predict emissions as well as variables including power, torque, efficiency, and fuel consumption based on characteristics like engine speed, injection timing, and fuel and air properties.…”

Semi-physical NOx and soot model for CI engines: Study of its calibration procedure and portability

“…Similar to ANN models; map-based models rely on many data points but use more traditional techniques to interpolate between these points. Grahn et al 19 presented a data driven emission model for diesel engine where they use basis spline function to interpolate. More interestingly, the authors have analysed how the performance of their model depended on the number of measured data points used for calibration.…”

“…The number of points can be unclear, the calibration procedure and calibration parameter’s values remain undisclosed. The two aspects of ‘portability’ of the model and sensitivity to training point number 19 are important, yet seldom published. It is therefore believed that this paper provides an original and interesting contribution to this field of work:…”

A review of soot sensors considered for on-board diagnostics application

“…The soot emission values at points within a free of data space in the torque–speed map are interpolated by various mathematical models including the local linear regression and the neuro-fuzzy models. 27,28 Under a transient engine operating condition, the soot emission predicted from the map for a steady-state condition has to be modified, so that the spiky higher soot emission due to a short-term oxygen deficit could be taken into account.…”