PriMera Scientific Engineering (ISSN: 2834-2550)

Research Article

Volume 4 Issue 2

A Method for real-time Combustion Metrics Estimation using Wiebe Model in Diesel Engine

Yao Liu*

January 27, 2024


Combustion closed-loop control is an important technology for intelligent energy saving and emission reduction of internal combustion engines. The real-time feedback of combustion indicators plays an important role in the accuracy and rapidity of closed-loop control. However, the calculation of the combustion midpoint based on the complete heat release rate curve often consumes more computing resources. In order to speed up the calculation speed, this paper proposed a method that the Wiebe model combined with neural network prediction combustion metric. Firstly, we match the Wiebe basis function for different working conditions by analyzing the heat release rate curve. then the RLS-DE algorithm is developed to identify the heat release rate curve with high precision, and the BP neural network combined with the Wiebe model parameters is used to calculate CA50. Finally, in the HIL real-time simulation environment, the calculation accuracy and calculation speed of the algorithm are verified. The results show that the use of different Wiebe basis functions combined with the RLS-DE algorithm can fit the heat release rate curves under different working conditions with high precision, and the fitting error is within 5%. The CA50 prediction algorithm based on the parameters of the Wiebe model has a different calculation accuracy under different loads. The algorithm error is 6%-8% at low load, and the error is 2%-4% under high load conditions. It is developed in the cRIO-9047 real-time computing platform. The algorithm time-consuming is 8-12 us, which has high real-time performance and engineering application value.


  1. Olsson J-O, Tunestål P and Johansson B. “Closed-Loop Control of an HCCI Engine”. SAE Technical Paper Series (2001).
  2. Beasley M Cornwell R., et al. “Reducing Diesel Emissions Dispersion by Coordinated Combustion Feedback Control”. SAE Technical Paper (2006).
  3. Beaumont A., et al. “Design of a rapid prototyping engine management system for development of combustion feedback control technology”. SAE Technical paper. Detroit, MI, USA: SAE (2006).
  4. Hülser H., et al. “EmIQ: Intelligent Combustion and Control for Tier2 Bin5 Diesel Engines”. SAE Technical Paper Series (2006).
  5. Kakoee A., et al. “Modeling combustion timing in an RCCI engine by means of a control-oriented model”. Control Engineering Practice 97 (2019): 104321.
  6. Kondipati NNT., et al. “Modeling, design and implementation of a closed-loop combustion controller for an RCCI engine”. 2017 American Control Conference (ACC) (2017).
  7. Sui W, González JP and Hall CM. “Modeling and control of combustion phasing in dual-fuel compression ignition engines”. Journal of Engineering for Gas Turbines and Power 141.5 (2018).
  8. Bahri B, Shahbakhti M and Aziz AA. “Real-time modeling of ringing in HCCI engines using artificial neural networks”. Energy 125 (2017): 509-518.
  9. Basina LNA., et al. “Data-driven modeling and predictive control of maximum pressure rise rate in RCCI engines”. 2020 IEEE conference on control technology and applications (CCTA). IEEE (2020): 94-99.
  10. Irdmousa BK., et al. “Data-driven modeling and predictive control of combustion phasing for RCCI engines”. 2019 American Control Conference (ACC). IEEE (2019): 1617-1622.
  11. Mohammad A, Rezaei R and Hayduk C. “Hybrid physical and machine learning-oriented modeling approach to predict emissions in a diesel compression ignition engine”. SAE Technical Paper (2021).
  12. Mishra C abd Subbarao PMV. “A comparative study of physics based grey box and neural network trained black box dynamic models in an rcci engine control parameter prediction”. SAE Technical Paper (2021): 1-17.
  13. Mishra C and Subbarao PMV. “Stochastic Cycle to Cycle Prediction in a Reactivity Controlled Compression Ignition Engine Using Double Wiebe Function”. SAE International Journal of Advances and Current Practices in Mobility (2021): 2672-2689.
  14. Mishra C and Subbarao PMV. “Design, Development, and Testing of RCCI Engine Hybrid Control Models Using Dual Wiebe Functions and Random Forest Machine Learning”. Control Engineering Practice 113 (2021): 104857.
  15. S Loganathan., et al. “Heat release rate and performance simulation of DME fuelled diesel engine using oxygenate correction factor and load correction factor in double Wiebe function”. Energy (2018): 77-91.
  16. Payri F., et al. “A complete 0D thermodynamic predictive model for direct injection diesel engines”. Applied Energy 88.12 (2011): 4632-4641.
  17. Sawant P, Warstler M and Bari S. “Exhaust Tuning of an Internal Combustion Engine by the Combined Effects of Variable Exhaust Pipe Diameter and an Exhaust Valve Timing System”. Energies 11.6 (2018): 1545.
  18. Firoozabadi MD., et al. “Thermodynamic control-oriented modeling of cycle-to-cycle exhaust gas temperature in an HCCI engine”. Applied Energy 110 (2013): 236-243.
  19. Jaeheun Kim, Chongsik Bae and Gangchul Kim. “Simulation on the effects of combustion parameters on the piston dynamics and engine performance using the Wiebe function in a free-piston engine”. Applied Energy (2013): 107.
  20. Galindo J., et al. “Correlations for Wiebe function parameters for combustion simulation in two-stroke small engines”. Applied thermal engineering 31.6-7 (2011): 1190-1199.
  21. Hu S., et al. “Automatic calibration algorithm of 0-D combustion model applied to DICI diesel engine”. Applied Thermal Engineering 130 (2018): 331-342.
  22. Jonathan M Borg. “On the application of Wiebe functions to simulate normal and knocking spark-ignition combustion”. International Journal of Vehicle Design 49.1/2/3 (2009): 52-69(18).
  23. Zhu Zhenxia., et al. “Zero-dimensional predictive combustion model and modeling method based on neural network”. Journal of Internal Combustion Engines 33.02 (2015): 163-170.
  24. Maroteaux F and Saad C. “Diesel engine combustion modeling for hardware in the loop applications: Effects of ignition delay time model”. Energy 57 (2013): 641-652.
  25. Yongrui Sun., et al. “Development and Validation of a Marine Sequential Turbocharging Diesel Engine Combustion Model Based on Double Wiebe Function and Partial Least Squares Method”. Energy Conversion and Management (2017): 69.
  26. Naber JD and Siebers DL. “Effects of gas density and vaporization on penetration and dispersion of diesel sprays”. SAE transactions (1996): 82-111.
  27. Jung D and Assanis DN. “Multi-zone DI diesel spray combustion model for cycle simulation studies of engine performance and emissions”. SAE transactions (2001): 1510-1532.
  28. Liu J and Dumitrescu CE. “Single and double Wiebe function combustion model for a heavy-duty diesel engine retrofitted to natural-gas spark-ignition”. Applied energy 248 (2019): 95-103.