10. Data-Based Modeling for the Crank Angle Resolved CI Combustion Process

For new combustion control concepts such as Combustion Rate Shaping, a crank angle resolved model of the compression ignition (CI) combustion process is necessary. The complex CI combustion process involving fuel injection, turbulent flow, and chemical reactions has to be reproduced. However, to be suitable for control, it has to be computationally efficient at the same time. To allow for learning-based control, the model should be able to adapt to the current measurement data. This paper proposes two algorithms that model the CI combustion dynamics by learning a crank angle resolved model from past heat release rate (HRR) measurement data. They are characterized by short learning and evaluation times, low calibration effort, and high adaptability. Both approaches approximate the total HRR as the linear superposition of the HRRs of individual fuel packages. The first algorithm approximates the HRR of a single fuel package as a Vibe function and identifies the parameters by solving a nonlinear program having the squared difference between the measured HRR and the superposition as cost. The second algorithm approximates the individual packages’ HRRs as Gaussian distributions and estimates the parameters by solving a nonlinear program with the Kullback–Leibler divergence between the measurement and the superposition as cost function using the expectation–maximization algorithm. Both algorithms are validated using test bench measurement data.