G. Alcan, M. Unel, V. Aran, M. Yilmaz, C. Gurel, K. Koprubasi
Measurement, Volume 137, Pages 71-81
Publication date: April, 2019


Diesel engines are still widely used in heavy-duty engine industry because of their high energy conversion efficiency. In recent decades, governmental institutions limit the maximum acceptable hazardous emissions of diesel engines by stringent international regulations, which enforces engine manufacturers to find a solution for reducing the emissions while keeping the power requirements. A reliable model of the diesel engine combustion process can be quite useful to search for the best engine operating conditions. In this study, nonlinear modeling of a heavy-duty diesel engine NOx emission formation is presented. As a new experiment design, air-path and fuel-path input channels were excited by chirp signals where the frequency profile of each channel is different in terms of the number and the direction of the sweeps. This method is proposed as an alternative to the steady-state experiment design based modeling approach to substantially reduce testing time and improve modeling accuracy in transient operating conditions. Sigmoid based nonlinear autoregressive with exogenous input (NARX) model is employed to predict NOx emissions with given input set under both steady-state and transient cycles. Models for different values of parameters are generated to analyze the sensitivity to parameter changes and a parameter selection method using an easy-to-interpret map is proposed to find the best modeling parameters. Experimental results show that the steady-state and the transient validation accuracies for the majority of the obtained models are higher than 80% and 70%, respectively.


  • Data-driven modeling of diesel engine NOx emissions using sigmoid NARX model.
  • A new design of experiments which include both chirp and ramp-hold signals.
  • Reduction of testing time and improved modeling accuracy in transient cycle.
  • An easy-to-interpret map as a convenient means for suitable parameter selection.
  • Higher than 80% and 70% steady-state and transient validation accuracies.


  • Diesel engine
  • Combustion process
  • NOx emissions
  • Experiment design
  • Sigmoid NARX model


  title={Predicting NOx emissions in diesel engines via sigmoid NARX models using a new experiment design for combustion identification},
  author={Alcan, Gokhan and Unel, Mustafa and Aran, Volkan and Yilmaz, Metin and Gurel, Cetin and Koprubasi, Kerem},