Appendix 7a F1F2

This Appendix describes the calculation procedures to verify the overall trip dynamics, to determine the overall excess or absence of dynamics during urban, rural and motorway driving.

RPA

relative positive acceleration

‘ acceleration resolution a _res ’

minimum acceleration > 0 measured in m/s ²

T4253H

compound data smoother

‘ positive acceleration a _pos ’

acceleration [m/s ² ] greater than 0,1 m/s ²

Index (i) refers to the time step

Index (j) refers to the time step of positive acceleration datasets

Index (k) refers to the category (t = total, u = urban, r = rural, m = motorway)

Δ

difference

>

larger

≥

larger or equal

%

per cent

<

smaller

≤

smaller or equal

a

acceleration [m/s ² ]

a _i

acceleration in time step i [m/s ² ]

a _pos

positive acceleration greater than 0,1 m/s ² [m/s ² ]

a _pos,i,k

positive acceleration greater than 0,1 m/s ² in time step i considering the urban, rural and motorway shares [m/s ² ]

a _res

acceleration resolution [m/s ² ]

d _i

distance covered in time step i [m]

d _i,k

distance covered in time step i considering the urban, rural and motorway shares [m]

M _k

number of samples for urban, rural and motorway shares with positive acceleration greater than 0,1 m/s ²

N _k

total number of samples for the urban, rural and motorway shares and the complete trip

RPA _k

relative positive acceleration for urban, rural and motorway shares [m/s ² or kWs/(kg × km)]

t _k

duration of the urban, rural and motorway shares and the complete trip [s]

v

vehicle speed [km/h]

v _i

actual vehicle speed in time step i [km/h]

v _i,k

actual vehicle speed in time step i considering the urban, rural and motorway shares [km/h]

(v · a) _i

actual vehicle speed per acceleration in time step i [m ² /s ³ or W/kg]

(v · a _pos ) _j,k

actual vehicle speed per positive acceleration greater than 0,1 m/s ² in time step j considering the urban, rural and motorway shares [m ² /s ³ or W/kg].

(v · a _pos ) _k _[95]

95th percentile of the product of vehicle speed per positive acceleration greater than 0,1 m/s ² for urban, rural and motorway shares [m ² /s ³ or W/kg]

${\bar{v}}_k$

average vehicle speed for urban, rural and motorway shares [km/h]

Dynamic parameters like acceleration, v · a _pos or RPA shall be determined with a speed signal of an accuracy of 0,1 % above 3 km/h and a sampling frequency of 1 Hz. This accuracy requirement is generally fulfilled by wheel (rotational) speed signals.

The speed trace shall be checked for faulty or implausible sections. The vehicle speed trace of such sections is characterised by steps, jumps, terraced speed traces or missing values. Short faulty sections shall be corrected, for example by data interpolation or benchmarking against a secondary speed signal. Alternatively, short trips containing faulty sections could be excluded from the subsequent data analysis. In a second step the acceleration values shall be ranked in ascending order, in order to determine the acceleration resolution a _res = (minimum acceleration value > 0).

If a _res ≤ 0,01 m/s ² , the vehicle speed measurement is accurate enough.

If 0,01 < a _res ≤ r _max m/s ² , smoothing by using a T4253 Hanning filter.

If a _res > r _max m/s ² , the trip is invalid.

The T4253 Hanning filter performs the following calculations: The smoother starts with a running median of 4, which is centred by a running median of 2. It then re-smoothes these values by applying a running median of 5, a running median of 3, and Hanning (running weighted averages). Residuals are computed by subtracting the smoothed series from the original series. This whole process is then repeated on the computed residuals. Finally, the smoothed residuals are computed by subtracting the smoothed values obtained the first time through the process.

The correct speed trace builds the basis for further calculations and binning as described in paragraph 3.1.2.

The following calculations shall be performed over the whole time-based speed trace (1 Hz resolution) from second 1 to second t _t (last second).

The distance increment per data sample shall be calculated as follows:

d _i = v _i /3,6, i = 1 to N _t

Where:

• d _i is the distance covered in time step i [m]

• v _i is the actual vehicle speed in time step i [km/h]

• N _t is the total number of samples

The acceleration shall be calculated as follows:

a _i = ( v _{i + 1} – v _{i – 1} )/(2 · 3,6), i = 1 to N _t

Where:

a _i is the acceleration in time step i [m/s ² ]. For i = 1: v _{i – 1} = 0, for i = N _t : v _{i + 1} = 0.

The product of vehicle speed per acceleration shall be calculated as follows:

(v · a) _i = v _i · a _i /3,6, i = 1 to N _t

Where:

(v · a) _i is the product of the actual vehicle speed per acceleration in time step i [m ² /s ³ or W/kg].

After the calculation of a _i and (v · a) _i , the values v _i , d _i , a _i and (v · a) _i shall be ranked in ascending order of the vehicle speed.

All datasets with v _i ≤ 60 km/h belong to the ‘ urban ’ speed bin, all datasets with 60 km/h < v _i ≤ 90 km/h belong to the ‘ rural ’ speed bin and all datasets with v _i > 90 km/h belong to the ‘ motorway ’ speed bin.

The number of datasets with acceleration values a _i > 0,1 m/s ² shall be bigger or equal to 150 in each speed bin.

For each speed bin the average vehicle speed ${\bar{v}}_k$ shall be calculated as follows:

${\bar{v}}_k=\left({\sum }_i{v}_{\mathrm{i,k}}\right)∕N_k$ , i = 1 to N _k ,k = u,r,m

Where:

N _k is the total number of samples of the urban, rural, and motorway shares.

The 95th percentile of the v · a _pos values shall be calculated as follows:

The (v · a) _i,k values in each speed bin shall be ranked in ascending order for all datasets with a _i,k ≥ 0,1 m/s ² and the total number of these samples M _k shall be determined.

Percentile values are then assigned to the (v · a _pos ) _j,k values with a _i,k ≥ 0,1 m/s ² as follows:

The lowest v · a _pos value gets the percentile 1/ M _k , the second lowest 2/ M _k , the third lowest 3/ M _k and the highest value M _k /M _k =100 %.

(v · a _pos ) _k _[95] is the (v · a _pos ) _j,k value, with j/M _k = 95 %. If j/M _k = 95 % cannot be met, (v · a _pos ) _k _[95] shall be calculated by linear interpolation between consecutive samples j and j + 1 with j/M _k < 95 % and ( j + 1)/ M _k > 95 %.

The relative positive acceleration per speed bin shall be calculated as follows:

RPA _k = Σ _j (Δ t · ( v · a _pos ) _j,k )/Σ _i d _i,k , j = 1 to M _k ,i = 1 to N _k ,k = u,r,m

Where:

RPA _k is the relative positive acceleration for urban, rural and motorway shares in [m/s ² or kWs/(kg*km)]

Δt

time difference equal to 1 second

M _k

the sample number for urban, rural and motorway shares with positive acceleration

N _k

the total sample number for urban, rural and motorway shares.

If ${\bar{v}}_k\le \mathrm{74,6}\mathrm{km}∕h$

and

is fulfilled, the trip is invalid.

If ${\bar{v}}_k>\mathrm{74,6}\mathrm{km}∕h$ and ${\left(v\times a_{\mathrm{pos}}\right)}_k\_\left[95\right]>\left(\mathrm{0,0742}\times {\bar{v}}_k+\mathrm{18,966}\right)$ is fulfilled, the trip is invalid.

If ${\bar{v}}_k\le \mathrm{94,05}\mathrm{km}∕h$ and ${\mathrm{RPA}}_k<\left(-\mathrm{0,0016}\times {\bar{v}}_k+\mathrm{0,1755}\right)$ is fulfilled, the trip is invalid.

If ${\bar{v}}_k>\mathrm{94,05}\mathrm{km}∕h$ and RPA _k < 0,025 is fulfilled, the trip is invalid.