DOE-based Polynomial Regression&nbsp;&nbsp;Model of Emissions and Predictive
Validation

Vehicle Engine ›› 2026, Vol. 0 ›› Issue (1) : 64-70.

DOE-based Polynomial Regression Model of Emissions and Predictive Validation

LYU Xiaohui^1,2,ZHANG Jun^1,2,LI Wanli^1,2,TANG Zhigang^1,2

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Abstract

Taking a certain in-line six-cylinder diesel engine as the research object, the design of experiments (DOE) for bench testing was conducted. Based on the experimental data, second-order and third-order polynomial regression emission models for NO_x and soot from the original engine were constructed and compared. The results indicated that the second-order polynomial NO_x emission model achieved a coefficient of determination (R²) of 0.999 3 and a root mean square error (RMSE) of 13.27×10^－6 on the training set, while the soot model achieved R² of 0.949 1 and RMSE of 0.343 2 mg/m³ on the training set, which demonstrated a good model fitting. The third-order polynomial model exhibited a higher R² value on the training set, but it had poorer prediction accuracy for operating points outside the training set. Based on the results, the second-order polynomial models were applied to predict the emissions of world harmonized transient cycle (WHTC) and plateau conditions. The results showed that the prediction errors for NO_x and soot specific emissions of hot WHTC were －0.51% and －1.13% respectively. At an altitude of 2 200 m, the proportion of operating points for the relative error of NO_x specific emissions within ±10% is 86.3%. The accuracy of second-order polynomial regression model met the needs of engineering predictions and had generalization capability for emission predictions at high-altitude conditions.

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polynomial regression / emission model / prediction accuracy / generalization ability

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LYU Xiaohui, ZHANG Jun, LI Wanli, TANG Zhigang. DOE-based Polynomial Regression Model of Emissions and Predictive Validation[J]. Vehicle Engine. 2026, 0(1): 64-70