[F1Verification of trip dynamic conditions with method 1 (Moving Averaging Window) U.K.
1. INTRODUCTION U.K.
The Moving Averaging Window method provides an insight on the real-driving emissions (RDE) occurring during the test at a given scale. The test is divided in sub-sections (windows) and the subsequent statistical treatment aims at identifying which windows are suitable to assess the vehicle RDE performance.
The ‘normality’ of the windows is conducted by comparing their CO 2 distance-specific emissions (1) with a reference curve. The test is complete when the test includes a sufficient number of normal windows, covering different speed areas (urban, rural, motorway).
Segmentation of the data and exclusion of cold start emissions;
Calculation of emissions by sub-sets or ‘ windows ’ (point 3.1);
Identification of normal windows; (point 4)
Verification of test completeness and normality (point 5);
Calculation of emissions using the normal windows (point 6).
2. SYMBOLS, PARAMETERS AND UNITS U.K.
Index (i) refers to the time step
Index (j) refers to the window
Index (k) refers to the category (t=total, u=urban, r=rural, m=motorway) or to the CO 2 characteristic curve (cc)
Index ‘gas’ refers to the regulated exhaust gas components (e.g. NO x , CO, PN)
—
difference
—
larger or equal
—
number
—
per cent
—
smaller or equal
—
coefficients of the CO 2 characteristic curve
—
coefficients of the CO 2 characteristic curve
—
distance covered by window j [km]
—
weighing factors for urban, rural and motorway shares
—
distance of windows to the CO 2 characteristic curve [%]
—
distance of window j to the CO 2 characteristic curve [%]
—
coefficients of the weighing function
—
coefficients of the weighing function
—
reference CO 2 mass [g]
—
mass or particle number of the exhaust component ‘ gas ’ [g] or [#]
—
mass or particle number of the exhaust component ‘ gas ’ in window j [g] or [#]
—
distance-specific emission for the exhaust component ‘ gas ’ [g/km] or [#/km]
—
distance-specific emission for the exhaust component ‘ gas ’ in window j [g/km] or [#/km]
—
number of windows for urban, rural, and motorway shares
—
reference points
—
time [s]
—
first second of the j th averaging window [s]
—
last second of the j th averaging window [s]
—
total time in step i [s]
—
total time in step i considering window j [s]
—
primary tolerance for the vehicle CO 2 characteristic curve [%]
—
secondary tolerance for the vehicle CO 2 characteristic curve [%]
—
duration of a test [s]
—
vehicle speed [km/h]
—
actual vehicle speed in time step i [km/h]
—
weighing factor for windows
—
weighing factor of window j.
3. MOVING AVERAGING WINDOWS U.K.
3.1. Definition of averaging windows U.K.
The instantaneous emissions calculated according to Appendix 4 shall be integrated using a moving averaging window method, based on the reference CO 2 mass. The principle of the calculation is as follows: the mass emissions are not calculated for the complete data set, but for sub-sets of the complete data set, the length of these sub-sets being determined so as to match the CO 2 mass emitted by the vehicle over the reference laboratory cycle. The moving average calculations are conducted with a time increment corresponding to the data sampling frequency. These sub-sets used to average the emissions data are referred to as ‘averaging windows’. The calculation described in the present point may be run from the last point (backwards) or from the first point (forward).
The following data shall not be considered for the calculation of the CO 2 mass, the emissions and the distance of the averaging windows:
the periodic verification of the instruments and/or after the zero drift verifications,
the cold start emissions, defined according to Appendix 4, point 4.4,
vehicle ground speed < 1 km/h,
any section of the test during which the combustion engine is switched off.
The mass (or particle number) emissions M gas,j shall be determined by integrating the instantaneous emissions in g/s (or #/s for PN) calculated as specified in Appendix 4.
Figure 1
Vehicle speed versus time — Vehicle averaged emissions versus time, starting from the first averaging window
The duration (t 2, j – t 1, j ) of the j th averaging window is determined by:
Where:
t 2, j shall be selected such as:
Where Δ t is the data sampling period.
The CO 2 masses are calculated in the windows by integrating the instantaneous emissions calculated as specified in Appendix 4 to this Annex.
3.2. Calculation of window emissions and averages U.K.
The following shall be calculated for each window determined in accordance with point 3.1:
the distance-specific emissions M gas,d,j for all the pollutants specified in this annex,
the distance-specific CO 2 emissions M CO2,d,j ,
4. EVALUATION OF WINDOWS U.K.
4.1. Introduction U.K.
The reference dynamic conditions of the test vehicle are set out from the vehicle CO 2 emissions versus average speed measured at type approval and referred to as ‘vehicle CO 2 characteristic curve’.
To obtain the distance-specific CO 2 emissions, the vehicle shall be tested using the road load settings prescribed in the UNECE Global Technical Regulation No 15 — worldwide harmonised light vehicles test procedure (ECE/TRANS/180/Add.15).
4.2. CO 2 characteristic curve reference points U.K.
The reference points P 1 , P 2 and P 3 required to define the curve shall be established as follows:
4.2.1. Point P 1 U.K.
4.2.2. Point P 2 U.K.
4.2.3. 
(average speed of the High Speed phase of the WLTP cycle) U.K.
4.2.4. Point P 3 U.K.
4.2.5. 
(average speed of the Extra High Speed phase of the WLTP cycle) U.K.
4.3. CO 2 characteristic curve definition U.K.
Using the reference points defined in point 4.2, the characteristic curve CO 2 emissions are calculated as a function of the average speed using two linear sections ( P 1 , P 2 ) and ( P 2 , P 3 ). The section ( P 2 , P 3 ) is limited to 145 km/h on the vehicle speed axis. The characteristic curve is defined by equations as follows:
4.4. Urban, rural and motorway windows U.K.
4.4.1. Urban windows are characterised by average vehicle ground speeds 
smaller than 45 km/h, U.K.
4.4.2. Rural windows are characterised by average vehicle ground speeds 
greater than or equal to 45 km/h and smaller than 80 km/h, U.K.
4.4.3. Motorway windows are characterised by average vehicle ground speeds 
greater than or equal to 80 km/h and smaller than 145 km/h U.K.
5. VERIFICATION OF TRIP COMPLETENESS AND NORMALITY U.K.
5.1. Tolerances around the vehicle CO 2 characteristic curve U.K.
The primary tolerance and the secondary tolerance of the vehicle CO 2 characteristic curve are respectively tol 1 = 25 % and tol 2 = 50 %.
5.2. Verification of test completeness U.K.
The test shall be complete when it comprises at least 15 % of urban, rural and motorway windows, out of the total number of windows.
5.3. Verification of test normality U.K.
The test shall be normal when at least 50 % of the urban, rural and motorway windows are within the primary tolerance defined for the characteristic curve.
If the specified minimum requirement of 50 % is not met, the upper positive tolerance tol 1 may be increased by steps of 1 % until the 50 % of normal windows target is reached. When using this mechanism, tol 1 shall never exceed 30 %.
6. CALCULATION OF EMISSIONS U.K.
6.1. Calculation of weighted distance-specific emissions U.K.
The emissions shall be calculated as a weighted average of the windows distance-specific emissions separately for the urban, rural and motorway categories and the complete trip.
The weighing factor w j for each window shall be determined as such:
Then w j = 1
If
Then w j = k 11 h j + k 12
with k 11 = 1/(tol 1 – tol 2 )
and k 12 : tol 2 /(tol 2 – tol 1 )
If
Then w j = k 21 h j + K 22
with k 21 = 1/(tol 2 – tol 1 )
and k 22 = k 21 = tol 2 /(tol 2 – tol 1 )
If
or
Then w j = 0
Where:
6.2. Calculation of severity indices U.K.
The severity indices shall be calculated separately for the urban, rural and motorway categories:
and the complete trip:
Where f u , f r f m are equal to 0,34, 0,33 and 0,33 respectively.
6.3. Calculation of emissions for the total trip U.K.
Using the weighted distance-specific emissions calculated under point 6.1, the distance-specific emissions in [mg/km] shall be calculated for the complete trip each gaseous pollutant in the following way:
And for particle number:
Where f u , f r f m are respectively equal to 0,34, 0,33 and 0,33.
7. NUMERICAL EXAMPLES U.K.
7.1. Averaging window calculations U.K.
Table 1
Main calculation settings
Figure 6 shows how averaging windows are defined on the basis of data recorded during an on-road test performed with PEMS. For sake of clarity, only the first 1 200 seconds of the trip are shown hereafter.
Seconds 0 up to 43 as well as seconds 81 to 86 are excluded due to operation under zero vehicle speed.
The first averaging window starts at t 1,1 = 0s and ends at second t 2,1 = 524 s (Table 3). The window average vehicle speed, integrated CO and NO x masses [g] emitted and corresponding to the valid data over the first averaging window are listed in Table 4.
Figure 6
Instantaneous CO 2 emissions recorded during on-road test with PEMS as a function of time. Rectangular frames indicate the duration of the j th window. Data series named ‘Valid=100 / Invalid=0’ shows second by second data to be excluded from analysis
7.2. Evaluation of windows U.K.
Table 2
Calculation settings for the CO 2 characteristic curve
| CO 2 Low Speed WLTC (P 1 ) [g/km] | 154 |
| CO 2 High Speed WLTC (P 2 ) [g/km] | 96 |
| CO 2 Extra-High Speed WLTC (P 3 ) [g/km] | 120 |
The definition of the CO 2 characteristic curve is as follows:
For the section ( P 1 , P 2 ):
with
and: b 1 = 154 – (– 1,543) × 19.0 = 154 + 29,317 = 183,317
For the section ( P 2 , P 3 ):
with
and: b 2 = 96 – 0,672 × 56,6 = 96 – 38,035 = 57,965
Examples of calculation for the weighing factors and the window categorisation as urban, rural or motorway are:
For window #45:
For the characteristic curve:
Verification of:
124,498 × (1 – 25/100) ≤ 122,62 ≤ 124,498 × (1 + 25/100)
93,373 ≤ 122,62 ≤ 155,622
Leads to: w 45 = 1
For window #556:
For the characteristic curve:
Verification of:
105,982 × (1 – 50/100) ≤ 72,15 ≤ 105,982 × (1 + 25/100)
52,991 ≤ 72,15 ≤ 79,487
Leads to:
w 556 = k 21 h 556 + k 22 = 0,04 · (– 31,922) + 2 = 0,723
with k 21 = 1/( tol 2 – tol 1 ) = 1/(50 – 25) = 0,04
and k 22 = k 21 = tol 2 /( tol 2 – tol 1 ) = 50/(50 – 25) = 2
Table 3
Emissions numerical data
Table 4
Window numerical data
7.3. Urban, rural and motorway windows — Trip completeness U.K.
In this numerical example, the trip consists of 7 036 averaging windows. Table 5 lists the number of windows classified in urban, rural and motorway according to their average vehicle speed and divided in regions with respect to their distance to the CO 2 characteristic curve. The trip is complete since it comprises at least 15 % of urban, rural and motorway windows out of the total number of windows. In addition the trip is characterised as normal since at least 50 % of the urban, rural and motorway windows are within the primary tolerances defined for the characteristic curve.
Table 5
Verification of trip completeness and normality
| Driving Conditions | Numbers | Percentage of windows |
|---|---|---|
| All Windows | ||
| Urban | 1 909 | 1 909 / 7 036 × 100 = 27,1 > 15 |
| Rural | 2 011 | 2 011 / 7 036 × 100 = 28,6 > 15 |
| Motorway | 3 116 | 3 116 / 7 036 × 100 = 44,3 > 15 |
| Total | 1 909 + 2 011 + 3 116 = 7 036 | |
| Normal Windows | ||
| Urban | 1 514 | 1 514 / 1 909 × 100 = 79,3 > 50 |
| Rural | 1 395 | 1 395 / 2 011 × 100 = 69,4 > 50 |
| Motorway | 2 708 | 2 708 / 3 116 × 100 = 86,9 > 50 |
| Total | 1 514 + 1 395 + 2 708 = 5 617 | ] |
Textual Amendments
[F1For hybrids, the total energy consumption shall be converted to CO 2 . The rules for this conversion will be introduced in a second step.]