Friedrich, C., Auer, M., and Stiesch, G., "Model Based Calibration Techniques for Medium Speed Engine Optimization: Investigations on Common Modeling Approaches for Modeling of Selected Steady State Engine Outputs," SAE Int. J. Engines 9(4):1989-1998, 2016, doi:10.4271/2016-01-2156.
Due to the increasing number of engine setting parameters to be optimized, model based calibration techniques have been introduced to medium speed engine testing to keep the number of engine tests low. Polynomials in combination with d-optimal test plans have been proven to be a good choice for modeling the stationary behavior of selected engine outputs. Model approaches like artificial neural networks (ANNs) have been rarely used for medium speed purposes since they require quite high amounts of testing data for model training. To evaluate the potential of these model approaches radial basis function networks, a subclass of neural networks, as well as Gaussian processes have been investigated as alternatives to polynomials. A manageable amount of tests according to an adapted d-optimal test plan was carried out at a test bench. Based on the test results polynomials, radial basis function networks (RBFs) as well as Gaussian process models (GPMs) have been fitted for selected engine outputs. Furthermore, an extensive appraisal and comparison of these model approaches, using statistical criteria for regression evaluation, was executed.The results show that radial basis function networks or Gaussian processes are promising alternatives to polynomials even if the amount of testing data is limited. The quality of the approximation results of the model types is on a comparable level. However, an advantage of radial basis function networks and Gaussian processes is the higher flexibility allowing a better representation of local nonlinear behavior of modeled engine outputs in comparison to polynomials.