Non-Constant Variance - Emission Modeling Methods for Offline Optimization and Calibration of Engine Management Systems 2003-32-0010
Calibrating the engine control unit to satisfy pollutant and performance objectives can be a challenging task. Due to the large number of variables and their interactive complexities, many firms apply design of experiment methods and modeling techniques to the acquired test data. This establishes a “black box” or “gray box” simulation model that predicts power and emissions as a function of the engine parameters. An offline optimization procedure on the fitted model(s) will identify the engine control strategy that best satisfies pollutant and performance objectives.
A review of the literature reveals that the General Linear Modeling method and Neural Network modeling architectures are widely used in the development of “black box” or “gray box” simulation models. While Neural Network methods are “assumption free”, the General Linear Model method is limited to those problems in which the errors, ε, are normally distributed and have constant variance, σ2.
Using the Harley-Davidson 1450 CC 2-cylinder SI engine and Horiba Series 200 emissions analyzer equipment, this study provides evidence that the distribution and constant variance assumptions are not satisfied with HC, NOx, and CO data; as a result, the estimated regression coefficients obtained by the General Linear Model method are no longer minimum variance unbiased estimators. Thus, it is necessary to apply other modeling approaches to the problem.
Citation: Dvorak, T., Rohrer, R., Lamb, P., Hoekstra, R. et al., "Non-Constant Variance - Emission Modeling Methods for Offline Optimization and Calibration of Engine Management Systems," SAE Technical Paper 2003-32-0010, 2003, https://doi.org/10.4271/2003-32-0010. Download Citation
Todd Dvorak, Robert Rohrer, Patrick Lamb, Robert Hoekstra, Roy Meyer
Statistical Consultant, Harley-Davidson Motor Company, University of Central Florida
Small Engine Technology Conference & Exposition