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PMP 47th, May 16-17, 2018
TF1 — Interlab Statistical ReportWLTP brake dyno test + ISO 5725 standards
Carlos AGUDELO + Theodoros GRIGORATOS + Jarek GROCHOWICZGRPE-PMP web conference —15 July 2021
workflow to create the dataset for statistical assessments
WLTP Focus FA single setup 8 labs 2 tests each 6 x WLTP / test~260k values
8 labs x 2 tests x 6 repeats x 303 events x 11 parameters: braking speed, avg. dist. (torque, pressure, and COF), max. disc temps., cooling air temp. & cooling air RH
chapters and structure of the report
I. Rationale and justification
Introduction OverviewBackground of ILS-TF1Main lab elementsTest cycle
II. General statistical evaluation
Aggregate stats on speed & decelerationTemperature studySpecial temperature assessment
III. Statistics on time-resolved – EED
General conceptsVDA 305/EKB 3008Speed control: violations & RMSSE
IV. Statistics on event-based – EEC
VDA 305/EKB 3008ISO 5725-5 elementsRepeatability, lab, sample, and total reproducibility std. dev.Data scrutinyUncertainty on estimates sr and sR
IAnnexes (dataviz)
1. Heatmaps2. Flowcharts3. Std. dev. v avg.4. Std. dev. v. event5. Uncertainties (r & R)6. Mandel’s h* (avg.)7. Mandel’s k* (range)8. Mandel’s k* (test)
10 % 45 %20 %~10 %~15 %
interlaboratory accuracy study aims at determining the standard deviations for the main results
the assessment of brake emission measurements demands a deep understanding of test variability
main components include sample effect, lab effect, test repeatability, and total reproducibility
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
IAnnexes (dataviz)I. Rationale and justification
“Happy families are all alike; every unhappy family is unhappy in its own way.”— Leo Tolstoy, Anna Karenina, 1877
scatter of bias/accuracy of deceleration v. braking speed
bias/accuracy of speed control by type of drive
scatter of dyno v. nominal deceleration level
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
-40-35-30-25-20-15-10-505
10152025303540
Lab 1 Lab 2 Lab 3 Lab 4 Lab 5 Lab 6 Lab 7 Lab 8
Acc
urac
y of
bra
king
spee
d / k
m/h
All Urban Rural Motorway
y1 = 1.4274x - 0.0132R² = 0.994
y2 = 1.0156x + 0.0279R² = 0.9983
y3 = 0.9862x + 0.0617R² = 0.9964
y4 = 1.3192x + 0.0037R² = 0.9984
y5 = 1.0117x + 0.0323R² = 0.9988
y6 = 1.0479x - 0.1924R² = 0.9462
y7 = 0.8143x + 0.0795R² = 0.9928
y8 = 0.9577x + 0.0923R² = 0.9969
m = 1.1298xR² = 0.9985
-
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Dyn
amom
eter
dec
eler
atio
n / m
/s²
Vehicle deceleration / m/s²
y1
y2
y3
y4
y5
y6
y7
y8
Veh.
mj
IAnnexes (dataviz)
extensive use of graphical and tabular presentation of data
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120
Initi
al d
isc
tem
pera
ture
/ °C
Average braking speed (T1) for urban, rural, and motorway / km/hLab 1 Lab 2 Lab 3 Lab 4 Lab 5 Lab 6 Lab 7 Lab 8 AVR
IAnnexes (dataviz)
integration of flowcharts and tabular data with step-by-step numerical examples
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
IAnnexes (dataviz)
application of VDA 305/EKB 3008 with numerical examples for brake output data
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
IAnnexes (dataviz)
combination of tabular computations with step-by-step calculations per ISO 5725 math
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
IAnnexes (dataviz)
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
use of the ISO 5725 robust algorithms (A & S) to avoid bias and reduce sensitivity to extreme values
IAnnexes (dataviz)
tabular summaries of all standard deviations for 11 metrics on each trip
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
IAnnexes (dataviz)
flowcharts for all mathematical relationships: input data four components of test variability
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
IAnnex 1
T1
1
2
3
4
5
6
T1
1
2
3
4
5
6
T1
1
2
3
4
5
6
T2
1
2
3
4
5
6
T2
1
2
3
4
5
6
T2
1
2
3
4
5
6
m = general average
zijtk = test effect
Lab 1 Lab 8Lab 2 …
…
…
Hijt = sample effect
Bij = lab effect
pj’ = 8 labs
gj = 16 samples
nj = 96 results
nijt = 6
υLj
υHj
υrj
nij
Kij
Kj
K”j
K’j
SSHj SSLj SSrj
zijtk = test effect
Hijt = sample effect
s2Hj
s2rj
s2Lj
s2Rj
Bij = lab effect
yijtk
mj = general average
T1
1
2
3
4
5
6
T1
1
2
3
4
5
6
T1
1
2
3
4
5
6
T2
1
2
3
4
5
6
T2
1
2
3
4
5
6
T2
1
2
3
4
5
6
Lab 1 Lab 8Lab 2 …
…
…
pj’ = 8 labs
yij tk
s*
SSLj, Kj, K’j, K”j, nj, υLj
SS*rj
S* 2HjS* 2
rj
S* 2Lj S* 2
Rj
wit wi xi
w* w*
SS*Hj
syj
non-
robu
st
robu
st
IAnnex 2
heatmaps (using inferno colormaps) with comments for all 11 metricsa) perceptually uniform, b) colorblind-friendly, and c) non-biased conversion to grayscale
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
IAnnex 3-5
graphical representation of standard deviations and uncertainty for all 11 metrics
scatter of std. deviations v. average for each event
all std. deviations v. event number
uncertainty for std. deviations v. event number
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
IAnnex 6-8
graphical representation of stragglers (95 %) and outliers (99 %) per ISO 5725-2 for all 11 metrics
Mandel’s h* (between lab averages) Mandel’s k* (between sample ranges) Mandel’s k* (between test results)
I. Rationale and justification
II. General statistical evaluation
III. Statistics on time-resolved – EED
IV. Statistics on event-based – EEC
…what is possible for TF3 – ILS establish critical differences for key dyno metrics(speed, deceleration, cooling air)
PMP 47th, May 16-17, 2018
Special thanks to:Marcel MATHISSENRaviTeja VEDULA + Alejandro HORTET
"Statistical Assessment and Temperature Study from the Interlaboratory Application of the WLTP – Brake Cycle" https://www.mdpi.com/2073-4433/11/12/1309