Dynamic modelling of diesel engine emissions using the parametric Volterra series

Abstract

The design of powertrain controllers relies on the availability of data-driven models of the emissions formation from internal-combustion engines. Typically these are in the form of tables or statistical regression models based on data obtained from stabilised experiments. However, as the complexity of engine systems increases, the number of experiments required to obtain the effects of each actuator becomes large. In addition, the models are only valid under stable operating conditions and do not give any information as to dynamic behaviour. In this paper, the use of the Volterra series (dynamic polynomial models) calculated from dynamic measurements is presented as an alternative to the steadystate models. Dynamic measurements of gaseous exhaust emissions were taken for a 2.0 l automotive diesel engine installed on a transient engine dynamometer. Sinusoidally based excitations were used to vary the engine speed, the load, the main injection timing, the exhaust gas recirculation valve position and the fuel injection pressure. Volterra models calculated for nitrogen oxide and carbon dioxide emissions presented high levels of fit with R 2 values of 0.85 and 0.91 respectively and normalised r.m.s. error values of 6.8% and 6.6% respectively for a cold-start New European Driving Cycle. Models for carbon monoxide and total hydrocarbon emissions presented poorer levels of fit (normalised r.m.s. errors of 26% and 17% respectively), with difficulties in obtaining the high non-linearities of the measured data, notably for very high emission levels.

Vehicle Engine Torque Estimation via Unknown Input Observer and Adaptive Parameter Estimation

“…The engine dynamics are measured as presented in Fig 8. Sine sweep excitation signals were used to vary the engine speed. The load with both slow and fast transient operating conditions is simulated [36] in the practical data collection experiments.…”

Fast NOx emission prediction methodology via one-dimensional engine performance tools in heavy-duty engines

“…Burke et al 22 worked on modelling of diesel engine NO x , CO 2 , CO and UHC emissions using the parametric Volterra Series of a 2.0-L diesel engine. Results showed that RMSE values of NO x emissions and CO 2 emissions are 6.8% and 6.6%, respectively.…”

Advantages and applications of transforming empirical model input space with dimensional models

“…That work and other investigators have relied on specially designed dynamic training data. 23,24,46,66 However, none of those works or any other in the published literature has investigated nonparametric algorithms such as kNN to model dynamic emissions based on steady-state training data (which has significant advantages over dynamic training data). Table 5 shows kNN results with EOP, BCT and SCT over an FTP sub-cycle that excludes idling and low smoke operating points, to save computational time required for dynamic GT-Power simulations.…”