This content is not included in your SAE MOBILUS subscription, or you are not logged in.
Prediction of Fuel Maps in Variable Valve Timing Spark Ignited Gasoline Engines Using Kriging Metamodels
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 14, 2020 by SAE International in United States
This content contains downloadable datasetsAnnotation ability available
Creating a fuel map for simulation of an engine with Variable Valve Actuation (VVA) can be computationally demanding. Design of Experiments (DOE) and metamodeling is one way to address this issue. In this paper, we introduce a sequential process to generate an engine fuel map using Kriging metamodels which account for different engine characteristics such as load and fuel consumption at different operating conditions. The generated map predicts engine output parameters such as fuel rate and load. We first create metamodels to accurately predict the Brake Mean Effective Pressure (BMEP), fuel rate, Residual Gas Fraction (RGF) and CA50 (Crank Angle for 50% Heat Release after top dead center). The last two quantities are used to ensure acceptable combustion. The metamodels are created sequentially to ensure acceptable accuracy is achieved with a small number of simulations. Two optimization problems are then solved using the developed metamodels, for full load and part load conditions, respectively. We demonstrate that the estimated fuel map is of high accuracy compared to the actual map. The map is obtained with about one tenth of the number of engine simulations for a full factorial design, leading to much faster predictions.
CitationTafreshi, A. and Mourelatos, Z., "Prediction of Fuel Maps in Variable Valve Timing Spark Ignited Gasoline Engines Using Kriging Metamodels," SAE Technical Paper 2020-01-0744, 2020, https://doi.org/10.4271/2020-01-0744.
Data Sets - Support Documents
|[Unnamed Dataset 1]|
|[Unnamed Dataset 2]|
|[Unnamed Dataset 3]|
|[Unnamed Dataset 4]|
|[Unnamed Dataset 5]|
|[Unnamed Dataset 6]|
- Jacobs, T., Assanis, D., and Filipi, Z. , “The Impact of Exhaust Gas Recirculation on Performance and Emissions of a Heavy-Duty Diesel Engine,” SAE Technical Paper 2003-01-1068, 2003, https://doi.org/10.4271/2003-01-1068.
- Schubiger, R., Bertola, A., and Boulouchos, K. , “Influence of EGR on Combustion and Exhaust Emissions of Heavy Duty DI-Diesel Engines Equipped with Common-Rail Injection Systems,” SAE Technical Paper 2001-01-3497, 2001, https://doi.org/10.4271/2001-01-3497.
- Gray, C. , “A Review of Variable Engine Valve Timing,” SAE Technical Paper 880386, 1988, https://doi.org/10.4271/880386.
- Bohac, S. and Assanis, D. , “Effect of Exhaust Valve Timing on Gasoline Engine Performance and Hydrocarbon Emissions,” SAE Technical Paper 2004-01-3058, 2004, https://doi.org/10.4271/2004-01-3058.
- Lenz, U. and Schroeder, D. , “Transient Air-Fuel Ratio Control Using Artificial Intelligence,” SAE Technical Paper 970618, 1997, https://doi.org/10.4271/970618.
- Fu, H., Chen, X., Mustafa, E., Trigui, N. et al. , “Analytical Investigation of Cam Strategies for SI Engine Part Load Operation,” SAE Technical Paper 2004-01-0997, 2004, https://doi.org/10.4271/2004-01-0997.
- Wu, B., Filipi, Z., Assanis, D., Kramer, D. et al. , “Using Artificial Neural Networks for Representing the Air Flow Rate through a 2.4 Liter VVT Engine,” SAE Technical Paper 2004-01-3054, 2004, https://doi.org/10.4271/2004-01-3054.
- Fang, K.-T. and Ma, C. , “Centered L2-Discrepancy of Random Sampling and Latin Hypercube Design, and Construction of Uniform Designs,” Mathematics of Computation 71(237), 1999.
- McKay, M.D., Beckman, R.J., and Conover, W.J. , “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code,” Technometrics 21(2):239-245, 1979.
- Owen, A.B. , “Orthogonal Arrays for Computer Experiments, Integration and Visualization,” Statistica Sinica 2(2):439-452, 1992.
- Johnson, M.E., Moore, L.M., and Ylvisaker, D. , “Minimax and Maximin Distance Designs,” Journal of Statistical Planning and Inference 26(2):131-148, 1990.
- Kennard, R.W. and Stone, L.A. , “Computer Aided Design of Experiments,” Technometrics 11(1):137-148, 1969.
- Gutmann, H.-M. , “A Radial Basis Function Method for Global Optimization,” Journal of Global Optimization 19(3):201-227, 2001.
- Booker, A. , “Using Metamodels for Engineering Design,” in INFORMS Seattle Fall 1998 Meeting, Seattle, WA, Oct. 25-28, 1998.
- Panagiotopoulos, D., Iqbal, O., Mourelatos, Z.P., and Papadimitriou, D. , “Optimal Water Jacket Flow Distribution Using a New Group-Based Space-Filling Design of Experiments Algorithm,” SAE Technical Paper 2018-01-1017, 2018, https://doi.org/10.4271/2018-01-1017.
- Li, Q., Yang, D., Hu, L., and Sheng, X. , “Optimization of Turbocharger Compressor Stages using DOE for Vehicle Engine Application,” SAE Technical Paper 2014-01-0406, 2014, https://doi.org/10.4271/2014-01-0406.
- Pischinger, S. , “Internal Combustion Engines,” Volume I, II, Lecture Notes, Institute for Combustion Engines, RWTH Aachen University, Aachen, 2016.
- Heywood, J. , Internal Combustion Engine Fundamentals (McGraw-Hill, 1988).
- GT Suite, Gamma Technologies, Westmont IL.
- Krige, D.G. , “A Statistical Approach to Some Mine Valuation and Allied Problems on the Witwatersrand,” M.Sc. thesis in Engineering, University of Witwatersrand, 1951.
- Sacks, J., Welch, W.J., Mitchell, T.J., and Wynn, H.P. , “Design and Analysis of Computer Experiments,” Statistical Science 4(4):409-435, 1989.
- Simpson, T.W., Mauery, T.M., Korte, J.J., and Mistree, F. , “Kriging Metamodels for Global Approximation in Simulation-Based Multidisciplinary Design Optimization,” AIAA Journal 39(12):2233-2241, 2001.
- Fang, K.-T., Li, R., and Sudjianto, A. , Design and Modeling for Computer Experiments (Chapman & Hall/CRC, 2005).
- Acar, E. , “Effects of the Correlation Model, the Trend Model, and the Number of Training Points on the Accuracy of Kriging Metamodels,” Expert Systems 30(5):418-428, 2013.
- Lophaven, S.N., Nielsen, H.B., and Søndergaard, J. , “DACE-A Matlab Kriging toolbox,” Version 2.0, 2002.