Advertisement

Topics in Catalysis

, Volume 62, Issue 1–4, pp 288–295 | Cite as

Modelling the Exhaust Gas Aftertreatment System of a SI Engine Using Artificial Neural Networks

  • Klemens SchürholzEmail author
  • Daniel Brückner
  • Dirk Abel
Original Article
  • 107 Downloads

Abstract

In this paper recurrent neural networks are used for modelling of the exhaust gas aftertreatment system of a spark-ignition engine including a three-way catalytic converter and oxygen sensors. Different network architectures are compared based on their achieved mean squared error. We find that physically inspired architectures surpass naive architectures built without knowledge of the physical system. The best resulting model is evaluated by giving the quantiles of the absolute error.

Keywords

Three-way catalytic converter Oxygen sensors Artificial neural networks 

References

  1. 1.
    Auckenthaler TS (2005) Modelling and control of three-way catalytic convertersGoogle Scholar
  2. 2.
    Bailer-Jones CAL, MacKay DJC, Withers PJ (1998) A recurrent neural network for modelling dynamical systems. Netw Comput Neural Syst 9(4):531–547CrossRefGoogle Scholar
  3. 3.
    Bengio Y, Frasconi P, Simard P (1993) The problem of learning long-term dependencies in recurrent networks. In: IEEE International Conference on Neural Networks, pp 1183–1188Google Scholar
  4. 4.
    Bishop CM (2006) Pattern recognition and machine learning, vol 4. Springer, New YorkGoogle Scholar
  5. 5.
    Chatterjee D, Deutschmann O, Warnatz J (2001) Detailed surface reaction mechanism in a three-way catalyst. Faraday Discuss 119:371–384CrossRefGoogle Scholar
  6. 6.
    Cho K, van Merrienboer B, Bahdanau D, Bengio Y (2014) On the properties of neural machine translation: encoder - decoder approaches. Syntax, semantics and structure in statistical translation, pp 103–111Google Scholar
  7. 7.
    Cho K, van Merrienboer B, Gulcehre C, Bahdanau D, Bougares F, Schwenk H, Bengio Y (2014) Learning phrase representations using RNN encoder-decoder for statistical machine translation. In: Proceedings of the 2014 conference on empirical methods in natural language processing (EMNLP), pp 1724–1734Google Scholar
  8. 8.
    Chung J, Gulcehre C, Cho K, Bengio Y (2014) Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv preprint. arXiv:14123555, pp 1–9
  9. 9.
    Feßler DK (2010) Modellbasierte On-Board-Diagnoseverfahren fr Drei-Wege-KatalysatorenGoogle Scholar
  10. 10.
    Gers FA, Schmidhuber J, Cummins F (2000) Learning to forget: continual prediction with LSTM. Neural Comput 12(10):2451–2471CrossRefGoogle Scholar
  11. 11.
    Graves A, Wayne G, Danihelka I (2014) Neural Turing Machines. arXiv preprint arXiv:14105401
  12. 12.
    Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780CrossRefGoogle Scholar
  13. 13.
    Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366CrossRefGoogle Scholar
  14. 14.
    Jozefowicz R, Zaremba W, Sutskever I (2015) An empirical exploration of recurrent network architectures. In: Proceedings of the 32nd international conference on machine learning (ICML-15), pp 2342–2350Google Scholar
  15. 15.
    Kingma DP, Ba JL (2014) Adam: a method for stochastic optimization. arXiv preprint arXiv:14126980
  16. 16.
    Kumar P, Makki I, Kerns J, Grigoriadis K, Franchek M, Balakotaiah V (2012) A low-dimensional model for describing the oxygen storage capacity and transient behavior of a three-way catalytic converter. Chem Eng Sci 73:373–387CrossRefGoogle Scholar
  17. 17.
    Pascanu R, Mikolov T, Bengio Y (2013) On the difficulty of training recurrent neural networks. In: International conference on machine learning, vol 28(3). pp 1310–1318Google Scholar
  18. 18.
    Pontikakis GN, Konstantas GS, Stamatelos AM (2004) Three-way catalytic converter modeling as a modern engineering design tool. J Eng Gas Turbines Power 126(10):906–923CrossRefGoogle Scholar
  19. 19.
    Schrholz K, Brckner D, Gresser M, Abel D (2018) Modeling of the three-way catalytic converter by recurrent neural networks. IFAC-PapersOnLine 51(15):742–747CrossRefGoogle Scholar
  20. 20.
    Welch BL (1947) The generalization of student’s problem when several different population variances are involved. Biometrika 34(1/2):28–35CrossRefGoogle Scholar
  21. 21.
    Yadaiah N, Sowmya G (2006) Neural network based state estimation of dynamical systems. In: The 2006 IEEE international joint conference on neural networks, pp 1042–1049Google Scholar
  22. 22.
    Yao Y, Rosasco L, Caponnetto A (2005) On early stopping in gradient descent learning. Constr Approx 26(2):289–315CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.BMW AGMunichGermany
  2. 2.Institute of Automatic ControlRWTH Aachen UniversityAachenGermany

Personalised recommendations