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Probabilistic Analysis of Bimodal State Distributions in SCR Aftertreatment Systems
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 14, 2020 by SAE International in United States
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Sensor selection for the control of modern powertrains is a recognised technical challenge. The key question is which set of sensors is best suited for an effective control strategy? This paper addresses the question through probabilistic modelling and Bayesian analysis. By quantifying uncertainties in the model, the propagation of sensor information throughout the model can be observed.
The specific example is an abstract model of the slip behaviour of Selective Catalytic Reduction (SCR) DeNOx aftertreatment systems. Due to the ambiguity of the sensor reading, linearization-based approaches including the Extended Kalman Filter, or the Unscented Kalman Filter are not successful in resolving this problem.
The stochastic literature suggests approximating these nonlinear distributions using methods such as Markov Chain Monte Carlo (MCMC), which is able in principle to resolve bimodal or multimodal results. However, the most effective methods are Hamiltonian solvers, which again struggle with the strongly nonlinear system behaviour, often getting stuck in just one of the possible solutions.
This paper compares how the different samplers of the MCMC methods perform in resolving the multi-modal distribution. Metropolis Hastings demonstrated the best ability to resolve problems of this nature.
CitationComissiong, R., Steffen, T., and Shead, L., "Probabilistic Analysis of Bimodal State Distributions in SCR Aftertreatment Systems," SAE Technical Paper 2020-01-0355, 2020, https://doi.org/10.4271/2020-01-0355.
- Simon , D. Optimal State Estimation: Kalman, H and Nonlinear Approaches Hoboken, NJ Wiley-Interscience 2006
- Hsieh , M.F. and Wang , J. An Extended Kalman Filter for NOx Sensor Ammonia Cross-Sensitivity Elimination in Selective Catalytic Reduction Applications Proceedings of the 2010 American Control Conference 2010 https://doi.org/10.1109/acc.2010.5531217
- Jiang , K. , Zhang , H. , and Lin , J. NH3 Coverage Ratio Estimation of Diesel-Engine SCR Systems by a Dual Time-Scale Extended Kalman Filter IEEE Transactions on Vehicular Technology 67 4 3625 3629 2018 https://doi.org/10.1109/tvt.2017.2785328
- Sowman , J. , Laila , D. , Truscott , A. , Fussey , P. , and Cruden , A. Real-Time Rejection of Ammonia Cross Sensitivity in Sensors for Diesel Aftertreatment Systems by Parallel Particle Filtering 2016 European Control Conference (ECC) 2016 https://doi.org/10.1109/ecc.2016.7810459
- Skaf , Z. , Aliyev , T. , Shead , L. , and Steffen , T. The State of the Art in Selective Catalytic Reduction Control SAE Technical Paper 2014-01-1533 https://doi.org/10.4271/2014-01-1533
- Olsson , L. , Sjövall , H. , and Blint , R.J. A Kinetic Model for Ammonia Selective Catalytic Reduction Over Cu-ZSM-5 Applied Catalysis B: Environmental 81 203 217 2008 https://doi.org/10.1016/j.apcatb.2007.12.011
- Wang , G. , Ali , H. , Zhang , J. , Qi , J. et al. Development of Model Predictive Control Strategy of SCR System for Heavy-Duty Diesel Engines with a One-State Control-Oriented SCR Model SAE Technical Paper 2018-01-1763 2018 https://doi.org/10.4271/2018-01-1763
- Murphy , K.P. Machine Learning: a Probabilistic Perspective Cambridge, MA MIT Press 2013
- Davidson-Pilon , C. Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference Addison-Wesley 2016
- Betancourt , M. The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo Annalen Der Physik 531 3 1700214 2018 https://doi.org/10.1002/andp.201700214
- Hoffman , M.D. and Gelman , A. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo Journal of Machine Learning Research 15 Apr 1593 1623 2014
- Salvatier , J. , Wiecki , T.V. , and Fonnesbeck , C. Probabilistic programming in Python using PyMC3 PeerJ Computer Science 2016 https://doi.org/10.7717/peerj-cs.55
- Theano Development Team