3.4.1
Results from stationary data
The results for the model training and validation data, as described in Sect. 3.3, are shown in the measured versus predicted plots in Fig. 3.7. It can be seen that the NOx emissions are well mod-
elled over all magnitudes. The variation around the bisecting line is low for training and validation data. For the soot emissions the deviation from the bisecting line increases with an increase of the magnitude. This is expected, since the low values are modelled more accurate for the logarithmic transformation than the high values. The torque model shows a clustering of the measurement points. This is due to the strong coupling of the engine torque to the injected fuel mass. Since the measurements are rastered in the injected fuel mass, the clustering appears in the output.
The qualities of the applied models are summarised in Tab. 3.3. Qualities are given in coefficient of
determinationR2and as root mean square error RMSE. For the presented models, the crank angle of 50% mass fraction burnt 'Q50is applied. If no in-cylinder pressure sensor is available, 'Q50can be
modelled or the the crank angle of main injection 'mican be applied. The qualities of these models
differ only slightly from the models applying 'Q50, see App. B.2. For each of the 21 local models,
26 potential regressors are available, which makes 546 regressors for a global model. The numbers of selected regressors are stated in Tab. 3.3. Values are given for the modelled emission mass flow rates Pmnox and Pmsoot, the modelled emission concentrations cnox and csootand the modelled engine
torque Meng.
An extraction of the continuous regarded training data is shown in Fig. 3.8 for the engine operation point neng D 2000rpm and uinj D 25mm3=cyc. It can be seen that each value is hold for 15 s
Figure 3.7:Measured versus predicted plots for the 4584 stationary training data points (black
circles) and the 2262 stationary validation data points (grey crosses) for the emission mass flow rates of a) NOxand b) soot and c) the engine torque.
Table 3.3:Model qualities for training and validation data for NOx, soot and the engine torque.
The emissions are either modelled as mass flow rates Pmnoxand Pmsootor as concentrations cnox
and csoot. The number of parameters is the sum of the number of selected regressors for the 21
local models.
Model Training Validation # parameters
R2 RMSE R2 RMSE P mnox 0.996 1.45 mg/s 0.988 2.09 mg/s 424 P msoot 0.959 0.05 mg/s 0.903 0.06 mg/s 440 Meng 0.997 1.52 Nm 0.981 2.83 Nm 233 cnox 0.992 23.0 ppm 0.979 34.7 ppm 456 csoot 0.939 0.87 mg/m3 0.907 0.97 mg/m3 439
until the main dynamic effects are decayed. From this continuous data, only one stationary point is extracted every 15 s, which is then applied for the model training and validation as shown in Fig. 3.7. Besides the measured inputs and outputs, the model outputs are plotted into the lower three plots. It can be seen, that a relative good model accuracy is obtained for the stationary behaviour. The dynamic variations are due to sensor dynamics and will be discussed in more detail in the following section.
The stationary behaviour of the identified models is shown in Fig. 3.9 over the inputs mairand 'mi at the engine operation point neng D 2500rpm and uinj D 25mm3=cyc. The model inputs T2i and
p2iare kept constant. The black squares in the plot indicate the extrapolation regions of the models.
Note that the axis are swapped for the plot of the soot model for a better visualisation. It can be seen that soot performs in opposite direction to the NOx emissions and both emissions are more
affected by the air mass per cycle than by the crank angle of main injetion. On the other hand, a strong dependency on 'miis observable for the models for Meng and 'Q50.
Figure 3.8: Continuous measurements from which stationary points are extracted for model
training and validation. Each point is hold for 15 s and the stationary point is averaged over the last 1.5 s. The presented measurements are from the engine operation point neng D 2000rpm
and uinjD 25mm3=cyc.
3.4.2
Dynamic model results
For a validation of the model dynamics, measurements of the extra-urban part of the New European
Driving Cycle (NEDC)are presented in Fig. 3.10. The upper three plots show the measured model
inputs and the lower three plots the measured and modelled outputs. The applied trajectories for engine speed and injection quantity (topmost plot) correspond to a test run on a roller test bench. The air path states are adjusted by closed loop controls (second plot) with the actuators of the turbocharger and the high-pressure egr valve. The desired values for the controllers are taken from a series calibration, as is also the value for the injection angle 'mi. The low-pressure egr is disabled
Figure 3.9:Models for a) NOxb) soot, c) torque and d) the crank angle of 50 % mass fraction
burnt at the operation point neng D 2500rpm and uinj D 25mm3=cyc. The other model inputs
are kept constant at T2iD 60ıC and p2iD 1:5bar. Note that the axis for soot are swapped for a
better presentation of the look-up table. The black squares in the plot indicate the extrapolation region of the models.
for this measurement, why the intake temperature is not manipulated here. To compare the modelled emissions with the measured emissions, models for the emission concentrations cnox and csoot are
applied.
The modelled emissions and the engine torque are presented with and without a model for the measurement dynamics in the lower three plots in Fig. 3.10. The stationary behaviour is well de- scribed for all outputs. The dynamical performance is investigated in detail in the zoomed plots. The torque model fits well to the measured dynamics. Since no sensor model is assumed for the torque model, this proofs that the assumption of a batch process is well suited for a mean value model of the combustion process. It further proofs that the stationary model structure is capable to model the system dynamics, which are introduced to the model by the dynamically fast measured inputs. For the torque model, the visible dynamics mainly result from dynamics in the injection quantity and are therefore included in this input.
Figure 3.10:Dynamical validation of the combustion models for the extra-urban part of the
NEDC. Top three plots show the measured model inputs. Lower three plots show the measured emissions NOxand soot and the engine torque, together with their modelled values. Modelled
emissions are also filtered with the models for emission measurement dynamics from eq. (3.1) with parameters from Tab. 3.1. For the torque model, no measurement dynamics are assumed. Measured outputs are black, modelled outputs are dark grey and modelled outputs with mod- elled measurement dynamics are light grey.
In contrast to the torque model, there are dynamic deviations between the modelled (dark grey line) and measured (black line) emissions, see the zoomed plots. The modelled emissions are well before the measured emissions and react considerably faster to changes in the inputs. These differences are mainly due to measurement dynamics. The influences of the travelling time can be seen for both, the NOx and soot emissions. The shaping by the time constants is more pronounced for the
NOx measurement.
To compare the modelled emissions with the dynamic measured emissions, the models for the measurement dynamics, as in eq. (3.1), are applied to the modelled emissions (light grey). The parameters are taken from Tab. 3.1 with the volume flow rate of the exhaust Pvexhbeing calculated at
each time step. The modelled emissions in connection with the modelled measurement dynamics fit well to the dynamic measured emissions. This proofs that the observed dynamics in emission formation are mainly due to measurement dynamics and validates the emission models for dynamic applications. The application of the model for the measurement dynamics is non-trivial as the para- meters depend on the current volume flow rate of the exhaust, which again depends on the current states in the exhaust pipe. Influences of the measurement dynamics are discussed in more detail in Sect. 3.6.2.
The validation of the NOx, soot and torque model on the NEDC shows that the stationary model structure can be used to model the dynamic engine behaviour. Also transients, such as the gear shift at t D 980 s, are well covered by the stationary models. Furthermore, the emission models react considerably faster to changes in emission formation than the measurements, as they do not suffer from measurement dynamics.