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Development of an Engine Calibration Model Using Gaussian Process Regression

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Abstract

To enhance the calibration efficiency, reduce the fuel consumption and improve the emission performance of the engine, a calibration method using Gaussian Process Regression (GPR) is proposed in this work. First, the design of experiment (DoE) is constructed by using the Space-filling method, and the engine bench sampling test is implemented according to results of DoE. Then, the square exponential covariance function is selected through the comparison of four covariance functions, and the corresponding hyper-parameters are optimized by using Newton gradient algorithm. Finally, the GPR model of the engine is established and its calibration performance is validated by the experimental data. The comparison shows that the performance of the developed GPR model is superior to the Polynomial model and Neural Network model, whose coefficient of determination (R2) of Fuel Consumption (FC), NOx emission (NOx) and Soot emission (Soot) are up to 0.9980, 0.9326 and 0.9247. The case study demonstrates that the virtual calibration optimization based on GPR model improves the fuel consumption performance greatly, while taking NOx and Soot emission indicators into account.

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Abbreviations

DoE:

design of experiment

NN:

neural network

SVM:

support vector machine

GPR:

gaussian process regression

GP:

gaussian process

SGD:

stochastic gradient descent

RMSE:

root mean square error

MAE:

mean absolute error

ECU:

engine control unit

PR:

polynomial regression

FC:

fuel consumption

NOx:

NOx emission

Soot:

soot emission

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Acknowledgement

This work was supported in part by the National Natural Science Foundation of China under Grant 61873113, the Key R&D Program of Jiangsu Province, China under Grant BE2018370, and the Key R&D Program of Zhenjiang under Grant GY2018013.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing of Minister of Education, School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, China

    Tianhong Pan

  2. School of Electrical & Information Engineering, Jiangsu University, Zhenjiang, 212013, China

    Yang Cai & Shan Chen

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  1. Tianhong Pan
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  2. Yang Cai
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Correspondence to Tianhong Pan.

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Pan, T., Cai, Y. & Chen, S. Development of an Engine Calibration Model Using Gaussian Process Regression. Int.J Automot. Technol. 22, 327–334 (2021). https://doi.org/10.1007/s12239-021-0031-5

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  • DOI: https://doi.org/10.1007/s12239-021-0031-5

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