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

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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.

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References

  1. Auckenthaler TS (2005) Modelling and control of three-way catalytic converters

  2. Bailer-Jones CAL, MacKay DJC, Withers PJ (1998) A recurrent neural network for modelling dynamical systems. Netw Comput Neural Syst 9(4):531–547

    Article  CAS  Google Scholar 

  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 1183–1188

  4. Bishop CM (2006) Pattern recognition and machine learning, vol 4. Springer, New York

    Google Scholar 

  5. Chatterjee D, Deutschmann O, Warnatz J (2001) Detailed surface reaction mechanism in a three-way catalyst. Faraday Discuss 119:371–384

    Article  CAS  Google Scholar 

  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 103–111

  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 1724–1734

  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. Feßler DK (2010) Modellbasierte On-Board-Diagnoseverfahren fr Drei-Wege-Katalysatoren

  10. Gers FA, Schmidhuber J, Cummins F (2000) Learning to forget: continual prediction with LSTM. Neural Comput 12(10):2451–2471

    Article  CAS  PubMed  Google Scholar 

  11. Graves A, Wayne G, Danihelka I (2014) Neural Turing Machines. arXiv preprint arXiv:14105401

  12. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780

    Article  CAS  Google Scholar 

  13. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366

    Article  Google Scholar 

  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 2342–2350

  15. Kingma DP, Ba JL (2014) Adam: a method for stochastic optimization. arXiv preprint arXiv:14126980

  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 73:373–387

    Article  CAS  Google Scholar 

  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 1310–1318

  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):906–923

    Article  CAS  Google Scholar 

  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):742–747

    Article  Google Scholar 

  20. Welch BL (1947) The generalization of student’s problem when several different population variances are involved. Biometrika 34(1/2):28–35

    Article  CAS  PubMed  Google Scholar 

  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 1042–1049

  22. Yao Y, Rosasco L, Caponnetto A (2005) On early stopping in gradient descent learning. Constr Approx 26(2):289–315

    Article  Google Scholar 

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Correspondence to Klemens Schürholz.

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Schürholz, K., Brückner, D. & Abel, D. Modelling the Exhaust Gas Aftertreatment System of a SI Engine Using Artificial Neural Networks. Top Catal 62, 288–295 (2019). https://doi.org/10.1007/s11244-018-1089-9

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