1. Analyses related to dynamic effects in vehicle speed and NOx emission measurements
by H. Steven 1

2. Accuracy of vehicle speed measurements
Norbert Ligterink provided a vehicle speed trace of about 1800 s duration measured with the VBOX at a sample rate of 100 Hz.
The 100 Hz data was aggregated to 10 Hz and 1 Hz data with 2 methods:
Averaging over the aggregated time period (v_ave),
Taking the instantaneous value at the aggregated time value from the 100 Hz signal (v_actual).
The results are shown in trip100Hz_with_wo_faulty_samples.xlsx.
The following figures (1 to 3) show examples of the speed and acceleration traces. 2

3. Example of the 100 Hz speed trace
Figure 1 3

4. Example of the 100 Hz speed trace
Figure 2 4

5. Example of the 100 Hz speed trace
Figure 3 5

6. Accuracy of vehicle speed measurements
The first conclusion, that can be drawn: An accurate measurement device does not prevent the appearance of faulty speed trace sections.
So, a plausibility check and error control of the measured speed trace is absolutely necessary.
The second conclusion: The 10 Hz signal reproduces the speed trace almost as good as the 100 Hz signal, but has significantly lower acceleration fluctuation, which is advantageous.
The 1 Hz signal is not able to reproduce all quick changes in the vehicle speed trace, but the following analysis results are intended to assess, whether the higher accuracy of the 10 Hz signal will be necessary. 6

7. Accuracy of vehicle speed measurements
Figure 4 shows the acceleration distributions of the different traces. The faulty sections are still included.
The 100 Hz and 10 Hz distributions are almost identical, the 1 Hz distributions show slightly lower values, as expected, but the differences for the 98% percentiles are reasonably low (see table 1).
The 98% percentile was chosen, because the distribution contains also negative values, so that the 98% percentile would correspond to a 95% percentile for positive accelerations.
99.4% of the distribution is within a range of -2.7 m/s² to 3.15 m/s². The rest is related to the faulty sections. 7

8. Acceleration distributions
Figure 4 8

9. Acceleration percentiles
Table 1 9

10. Accuracy of vehicle speed measurements
This confirms the filter of -4.5 m/s² to 4.0 m/s², which was applied to the WLTP database in order to exclude faulty speed sections.
Figures 5 and 6 show the v*a_pos distributions for two thresholds:
a > 0 and
a > 0.1 m/s²
Figure 5 shows the distributions for 100 Hz and 10 Hz sample rates. They are almost identical.
The difference for the two thresholds is obvious. The percentages at 0 are significant: The sample size for the threshold a > 0 is about 45% higher that for the threshold a > 0.1 m/s² for all sample rates. 10

11. Distribution of v*a_pos
Figure 5 11

12. v*a_pos distributions
This 45% is added in the v*a_pos range from 0 to 3 m²/s³, with 80% of the 45% being in the range from 0 to 1 m²/s³.
These values do not contribute significantly to the NOx emissions and thus the acceleration threshold 0.1 m/s should be kept.
Figure 6 shows the distributions for 10 Hz actual and 1 Hz actual. The latter are calculated once on the basis of binned v*a values (0.5 m²/s³ bandwidth) and on the basis of individual values.
The 95% percentiles (v*a_pos_95 values) are shown in table 2. 12

13. Distribution of v*a_pos
Figure 6 13

14. v*a_pos percentiles
Table 2 14

15. v*a_pos distributions
The 1 Hz individual values are about 17% lower than the 10 Hz actual values, which are used as reference, because the 10 Hz trace shows lower acceleration fluctuations that the 100 Hz trace.
If it can be shown, that a 1 Hz NOx signal is accurate enough for the determination of an emission factor, the higher v*a_pos resulting from the 10 Hz speed signal would not be necessary.
It is only important to precisely describe the data preprocessing, the quality of the speed signal and the calculation method of the percentiles. 15

16. Comparison of 10 Hz and 1 Hz NOx signals
In an additional calculation step the 10 Hz and 1 Hz NOx emission data from some vehicles of the WLTP validation 2 database were compared with respect to the sum of the Nox emission in mg, the distance driven and the resulting emission factors.
An example is provided by veh_0_3_1.xlsx and veh_0_3_1_1Hz_actual.xlsx. The example is a Euro 5 Diesel car.
The results are shown in table 3.
If this result can also be confirmed for Euro 6 vehicles and PEMS measurements – and there are no obvious reasons to doubt that - there is no reason to require a higher sample rate. 16

17. 1 Hz vs 10 Hz NOx emission data
Table 3 17

18. Results of PEMS measurements in Stuttgart, Munich and Garmisch
A last step is dedicated to the results of PEMS measurements for three Euro 6 certified cars, measured in Stuttgart, Munich and Garmisch.
The vehicles were equipped with a SCR (veh 1), NSC (veh 2) and without any aftertreatment system and had mileages of about km, when the measurements were performed.
The results can be found in RDE_dynamic_boundary_limit_curves_with_PEMS_Stuttgart_Munich.xlsx. 18

19. Results of PEMS measurements in Stuttgart, Munich and Garmisch
Table 4 gives an overview of the results in terms of absolute values and time shares.
The upper part differentiates between stops (v < 1 km/h), sections with a > 0.1 m/s² and the rest.
60% to 67% of the NOx emission is dedicated to sections with positive accelerations (time share about 28%), but a significant part of the NOx emissions is still dedicated to the rest.
The lower part differentiates between time sections with NOx emissions > 8 mg/s (NOx peaks) and the rest.
Here the results are even more pronounced: 60% to 80% of the total NOx emission is dedicated to these peaks, whose time shares vary between 8% and 15%only. 19

20. Euro 6 PEMS results
Table 4 20

21. Results of PEMS measurements in Stuttgart, Munich and Garmisch
An analysis of the NOx emission time series shows, that NOx peaks are caused by acceleration events, but these peaks could include also constant speed or even deceleration events.
The v*a distributions of the time sections for those peaks are shown in figure 7 and confirm the statement before.
Nevertheless the average NOx emission increases with increasing v*a values for all three vehicles, as shown in figure 8.
Figure 9 shows the results of a RDE-like data analysis in comparison of the proposed dynamic parameter thresholds for v*a_pos_95 and RPA. 21

22. v*a distributions for NOx peaks
Figure 7 22

23. NOx emission vs v*a_pos
Figure 8 23

24. Dynamic parameter thresholds
Figure 9 24

25. End of presentation, thank you for your attention!25