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A local Gaussian process regression approach is presented, which allows to model nonlinearities of internal combustion engines more accurate than global Gaussian process regression. By building smaller models, the prediction of local system behavior improves significantly. In order to predict a value, the algorithm chooses the nearest training points. The number of chosen training points depends on the intensity of estimated nonlinearity. After determining the training points, a model is built, the prediction performed and the model discarded. The approach is demonstrated with a benchmark system and air charge test bed measurements. The measurements are taken from a turbocharged SI gasoline engine with both variable inlet valve lift and variable inlet and exhaust valve opening angle. The results show how local Gaussian process regression outmatches global Gaussian process regression concerning model quality and nonlinearities in particular.

Air charge calibration of turbocharged SI gasoline engines with both variable inlet valve lift and variable inlet and exhaust valve opening angle has to be very accurate and needs a high number of measurements. In particular, the modeling of the transition area from unthrottled, inlet valve controlled resp. throttled mode to turbocharged mode, suffers from small number of measurements (e.g. when applying Design of Experiments (DoE)). This is due to the strong impact of residual gas respectively scavenging dominating locally in this area. In this article, a virtual residual gas sensor in order to enable black-box-modeling of the air charge is presented. The sensor is a multilayer perceptron artificial neural network. Amongst others, the physically calculated air mass is used as training data for the artificial neural network.