A grey-box machine learning based model of an electrochemical gas sensor

Abstract A grey-box machine learning based model of an electrochemical O 2 – NO x sensor is developed using the physical understanding of the sensor working principles and a state-of-the-art machine learning technique: support vector machine (SVM). The model is used to predict the sensor response at a wide range of sensor operating conditions in the presence of different concentrations of NO x and ammonia. To prepare a comprehensive training and test data set, the production sensor is first mounted on the exhaust system of a spark ignition, a diesel engine, and then on a fully controlled sensor test rig. The sensor is not modified, rather the sensor working temperature, all of the sensor cell potentials, and the pumping current of the O 2 sensing cell are the model inputs that can be varied while the pumping current of the NO x sensing cell is considered as the model output. A 9-feature low order model (LOM) and a 45-feature high order model (HOM) are developed with linear and Gaussian kernels. The model performance and generalizability are then verified by conducting input-output trend analysis. The LOM with Gaussian kernel and the HOM with linear kernel have shown the highest accuracy and the best response trend prediction.

[1]  Rui Guo,et al.  A Twin Multi-Class Classification Support Vector Machine , 2012, Cognitive Computation.

[2]  Changhee Lee,et al.  Modeling urea-selective catalyst reduction with vanadium catalyst based on NH3 temperature programming desorption experiment , 2016 .

[3]  Charles Robert Koch,et al.  Estimating tailpipe NOx concentration using a dynamic NOx/ammonia cross sensitivity model coupled to a three state control oriented SCR model , 2016 .

[4]  Y. Woo,et al.  Availability of NH3 adsorption in vanadium-based SCR for reducing NOx emission and NH3 slip , 2019, Journal of Industrial and Engineering Chemistry.

[5]  Panagiotis Tsiakaras,et al.  Characterization of proton-conducting electrolyte based on La0.9Sr0.1YO3 – δ and its application in a hydrogen amperometric sensor , 2016 .

[6]  Masoud Aliramezani,et al.  Production engine emission sensor modeling for in-use measurement and on-board diagnostics , 2019 .

[7]  Lei Dai,et al.  Effective improvement of sensing performance of amperometric NO2 sensor by Ag-modified nano-structured CuO sensing electrode , 2015 .

[8]  J. Thangaraja,et al.  Effect of exhaust gas recirculation on advanced diesel combustion and alternate fuels - A review , 2016 .

[9]  Jong-Min Lee,et al.  Conventional and New Materials for Selective Catalytic Reduction (SCR) of NOx , 2018 .

[10]  Gunter Hagen,et al.  Solid state mixed-potential sensors as direct conversion sensors for automotive catalysts , 2018 .

[11]  Charles Robert Koch,et al.  Amperometric solid electrolyte NO x sensors – The effect of temperature and diffusion mechanisms , 2017 .

[12]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[13]  Gunter Hagen,et al.  On the influence of the NO equilibrium reaction on mixed potential sensor signals: A comparison between FE modelling and experimental data , 2019, Sensors and Actuators B: Chemical.

[14]  A. K. Tyagi,et al.  Lanthanum gallate based amperometric electrochemical sensor for detecting ammonia in ppm level: Optimization of electrode compositions , 2018 .

[15]  Peng Sun,et al.  High-temperature NO2 gas sensor based on stabilized zirconia and CoTa2O6 sensing electrode , 2017 .

[16]  Charles Robert Koch,et al.  An electrochemical model of an amperometric NOx sensor , 2019, Sensors and Actuators B: Chemical.

[17]  W. Karush Minima of Functions of Several Variables with Inequalities as Side Conditions , 2014 .

[18]  Junmin Wang,et al.  Removal of NOx sensor ammonia cross sensitivity from contaminated measurements in Diesel-engine selective catalytic reduction systems , 2015 .

[19]  Alexander J. Smola,et al.  Support Vector Regression Machines , 1996, NIPS.

[20]  Alexander J. Smola,et al.  Learning with Kernels: support vector machines, regularization, optimization, and beyond , 2001, Adaptive computation and machine learning series.

[21]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[22]  Israel E. Wachs,et al.  A Perspective on the Selective Catalytic Reduction (SCR) of NO with NH3 by Supported V2O5–WO3/TiO2 Catalysts , 2018, ACS Catalysis.

[23]  Nicolas Petit,et al.  Closed-loop control of a SCR system using a NOx sensor cross-sensitive to NH3 , 2014 .

[24]  Robert Klikach,et al.  Investigation and Analysis of RCCI using NVO on a Converted Spark Ignition Engine , 2018 .

[25]  Feng Gao,et al.  NH3-SCR on Cu, Fe and Cu + Fe exchanged beta and SSZ-13 catalysts: Hydrothermal aging and propylene poisoning effects , 2017, Catalysis Today.

[26]  M. F. Ghazali,et al.  A review on the application of response surface method and artificial neural network in engine performance and exhaust emissions characteristics in alternative fuel , 2018 .

[27]  M. N. Murty,et al.  Support Vector Machines and Perceptrons: Learning, Optimization, Classification, and Application to Social Networks , 2016 .

[28]  Hui Zhang,et al.  NOx Sensor Ammonia-Cross-Sensitivity Factor Estimation in Diesel Engine Selective Catalytic Reduction Systems , 2015 .

[29]  M. Seibel,et al.  Simulation of a NOx Sensor for Model-Based Control of Exhaust Aftertreatment Systems , 2019, Topics in Catalysis.

[30]  Santosh Putta,et al.  Machine-learning models for combinatorial catalyst discovery , 2003 .

[31]  Tadashi Nakamura,et al.  NOx decomposition mechanism on the electrodes of a zirconia-based amperometric NOx sensor , 2003 .

[32]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[33]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[34]  R. Bellman The theory of dynamic programming , 1954 .

[35]  Charles Robert Koch,et al.  Phenomenological model of a solid electrolyte NOx and O2 sensor using temperature perturbation for on-board diagnostics , 2018, Solid State Ionics.

[36]  Lijiang Wei,et al.  NOx sensor ammonia cross-sensitivity estimation with adaptive unscented Kalman filter for Diesel-engine selective catalytic reduction systems , 2016 .

[37]  David James Scholl,et al.  Development of an Al2O3/ZrO2-Composite High-Accuracy NOx Sensor , 2010 .

[38]  Ian H. Witten,et al.  Data mining: practical machine learning tools and techniques, 3rd Edition , 1999 .

[39]  Ron Kohavi,et al.  Feature Subset Selection Using the Wrapper Method: Overfitting and Dynamic Search Space Topology , 1995, KDD.

[40]  Charles Robert Koch,et al.  A Variable-Potential Amperometric Hydrocarbon Sensor , 2019, IEEE Sensors Journal.

[41]  Tris Samberg,et al.  Student Study Guide to accompany Chemistry: The Molecular Nature of Matter and Change , 2002 .

[42]  Pingen Chen,et al.  An NOx Sensor-Based Direct Algebraic Approach-Newton Observer for Urea Selective Catalytic Reduction System State Estimations , 2018, Journal of Dynamic Systems, Measurement, and Control.

[43]  Peng Sun,et al.  Highly sensitive amperometric Nafion-based CO sensor using Pt/C electrodes with different kinds of carbon materials , 2017 .

[44]  Muhammad Tanveer Robust and Sparse Linear Programming Twin Support Vector Machines , 2014, Cognitive Computation.

[45]  Pak Kin Wong,et al.  Modeling and optimization of biodiesel engine performance using kernel-based extreme learning machine and cuckoo search , 2015 .

[46]  J. C. Amphlett,et al.  Performance modeling of the Ballard Mark IV solid polymer electrolyte fuel cell. II: Empirical model development , 1995 .

[47]  Franz Schubert,et al.  Self-heated HTCC-based ceramic disc for mixed potential sensors and for direct conversion sensors for automotive catalysts , 2017 .

[48]  Hwai Chyuan Ong,et al.  Evaluation of the engine performance and exhaust emissions of biodiesel-bioethanol-diesel blends using kernel-based extreme learning machine , 2018, Energy.

[49]  V. Vapnik Pattern recognition using generalized portrait method , 1963 .

[50]  G. Mauviot,et al.  Modeling of a DOC SCR-F SCR Exhaust Line for Design Optimization Taking Into Account Performance Degradation Due to Hydrothermal Aging , 2016 .

[51]  Gunter Hagen,et al.  A finite element model for mixed potential sensors , 2019, Sensors and Actuators B: Chemical.

[52]  Chi-Man Vong,et al.  Online extreme learning machine based modeling and optimization for point-by-point engine calibration , 2018, Neurocomputing.

[53]  Junmin Wang,et al.  An extended Kalman filter for NOx sensor ammonia cross-sensitivity elimination in selective catalytic reduction applications , 2010, Proceedings of the 2010 American Control Conference.

[54]  Gordon G. Parker,et al.  Model-based control system design in a urea-SCR aftertreatment system based on NH3 sensor feedback , 2009 .