Hybrid Physical and Machine Learning-Oriented Modeling Approach to Predict Emissions in a Diesel Compression Ignition Engine

<div class="section abstract"><div class="htmlview paragraph">The development and calibration of modern combustion engines is challenging in the area of continuously tightening emission limits and the necessity for meeting real driving emissions regulations. A focus is on the knowledge of the internal engine processes and the determination of pollutants formations in order to predict the engine emissions. A physical model-based development provides an insight into hardly measurable phenomena properties and is robust against changing input data. With increasing modeling depth the required computing capacities increase. As an alternative to physical modeling, data-driven machine learning methods can be used to enable high-performance modeling accuracy. However, these are dependent on the learned data. To combine the performance and robustness of both types of modeling a hybrid application of data-driven and physical models is developed in this paper as a grey box model for the exhaust emission prediction of a commercial vehicle diesel engine. Internal engine processes are physically investigated to determine combustion characteristic quantities influencing the formation of NO<sub>x</sub>, CO, HC and soot emissions. With the physically modeled inputs, models based on machine learning methods, including Support Vector Machine and Feedforward Neural Network, are developed for emission modeling. The models are trained using the data from a commercial vehicle engine, validated against different hyperparameters and network architectures and tested against each other at 772 different operating points. A comparison is made to black box models formed from the measured data. In general, feedforward neural networks and support vector machines were enhanced by selecting the physically modeled inputs. The feedforward neural networks for HC and soot modeling were improved by approximately 20% and 10% with respect to the RMSE of the test data. For the support vector machines, CO and soot modeling benefited the most by 30% and 20% respectively of the RMSE of the test data. For a trained NO<sub>x</sub> model based on low load data its coefficient of determination regarding test data by high load is increased from 0.807 to 0.908.</div></div>

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