Evaluation of Virtual NOx Sensor Models for Off Road Heavy Duty Diesel Engines

NOx and PM are the critical emissions to meet the legislation limits for Diesel engines. Often a value for these emissions is needed online for on board diagnostics, engine control, exhaust after treatment control, model based controller design or model in the loop simulations. Besides the obvious method of measuring these emissions, a sensible alternative is to estimate them with virtual sensors. A lot of literature can be found presenting different modeling approaches for NOx emissions. Some are very close to the physics and the chemical reactions taking place inside the combustion chamber, others are only given by adapting general functions to measurement data. Hence, generally speaking, there is not a certain method which is seen as the solution for modeling emissions. Finding the best model approach is not straightforward and depends on the model application, the available measurement channels and the available data set for calibration. This paper evaluates three different already published virtual sensor approaches for NOx engine raw emissions of a heavy duty Diesel engine in off-road applications. The three proposals consist of a black box polynomial mean value model using available data from the electronic control unit (ECU), a black box mean value model using mainly the measured indicated pressure profile and a crank angle based gray box model also based on the indicated pressure profile. The final evaluation of the three models was done with measurements of a highly dynamical test cycle for HD engines, coming from a wheel-loader application and conducted on a dynamical engine test bench, whereas dynamical behavior, integral error as well as transient deviations were analyzed.