Extending the Range of Data-Based Empirical Models Used for Diesel Engine Calibration by Using Physics to Transform Feature Space

A new method that allows data-enabled (empirical) models, commonly used for automotive engine calibration, to extrapolate beyond the range of training data has been developed. This method used a physics-based system-level one-dimensional model to improve interpolation and allow extrapolation for three data-based algorithms, by modifying the model input (feature) space. Neural network, regression, and k-nearest neighbor predictions of engine emissions and volumetric efficiency were greatly improved by generating 736,281 artificial feature spaces and then performing feature selection to choose feature spaces (feature selection) so that extrapolations in the original feature space were interpolations in the new feature space. A novel feature selection method was developed that used a two-stage search process to uniquely select the best feature spaces for every prediction. The selected feature spaces also improved interpolation significantly, suggesting that they were advantageous in terms of local data density and gradients. Results were found to be relatively insensitive to the geometrical parameters and calibration of the one-dimensional physical model. Hence a “Toy Model” concept is proposed, where if physical knowledge is incomplete or computationally prohibitive, the insufficient physical model is used as a transfer function to reformulate the learning task, by transforming the feature space.