a gear-based vehicle emission model for co2 ... faculteit...transfer function model engine speed...
TRANSCRIPT
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A GEAR-BASED VEHICLE EMISSION MODEL FOR CO2, CO AND NOX ESTIMATION
Hajar Hajmohammadi
Centre for Transport Studies, UCL
Benjamin Heydecker Professor of Transport studies, UCL
MATTS 2018
Mathematics Applied in Transport and Traffic Systems
17-19 October 2018
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Introduction
2
Why we need vehicle emission model?
To evaluate the impacts of traffic policies on the air quality
To develop traffic control policies that can reduce air pollution in critical areas
Influential variables in the vehicle emission modelling:
Vehicle-related parameters: e.g. model, engine size, fuel and catalyst type and technology level
Operational factors: driving cycle
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Vehicle type
Measurements
emission: CO2, CO, THC, NOx, PMn
vehicle: Roll speed, Engine speed
3
Dataset: Laboratory vehicle emission tests
Fuel Petrol - Diesel
Transmission Automatic โ Manual
Engine Size from 1000 to 3200 cc
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4
Real Driving Cycle for London
Traffic Conditions:
Free Flow
AM peak
Inter peak
[SERIES NAME] Suburban [SERIES NAME]
0
20
40
60
80
100
120
0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250
Sp
ee
d (
km
/h)
Time (s)
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5
0
0,02
0,04
0,06
0,08
0,1
0,12
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120
NO
x (
mg
/se
c)
CO
2 (
mg
/se
c)
speed (km/h)
CO2 NOx
Statistical modelling
Vehicle B, Diesel, manual, 1400 cc
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6
Background
Single model
๐ฆ = ๐ + ๐ฝ๐๐ฅ๐
๐ฝ
๐=1
+ ๐ ๐ฆ= emission
๐ฅ= Roll Speed, ๐ฃ
Acceleration, ๐ Power demand
๐๐๐ = ๐ด ๐ ๐ฃ + ๐ต๐ ๐ฃ2 + ๐ถ ๐ ๐ฃ
3 + (๐ + ๐ ๐ ๐๐ ๐ )๐ฃ
Classified model: Acceleration, Cruising, Idling, Deceleration (CADI)
๐ฆ =
๐๐ฅ๐( ๐ฟ๐,๐ ร ๐ฃ๐ ร ๐๐ ) ๐๐๐ ๐ โฅ 0
3
๐=0
3
๐=0
๐๐ฅ๐( ๐พ๐,๐ ร ๐ฃ๐ ร ๐๐
3
๐=0
3
๐=0
๐๐๐ ๐ < 0
VT-micro emission model
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7
0
0,02
0,04
0,06
0,08
0,1
0,12
0
1
2
3
4
5
6
7
8
9
10
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5
NO
x (
mg
/se
c)
CO
2 (
mg
/se
c)
gear
CO2 NOx
New latent variable, Gear=roll speed/engine speed
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8
Urban Motorway Sub-Urban
0
0,5
1
1,5
2
2,5
3
0 500 1000 1500 2000 2500 3000
g
Time (sec)
New latent variable, Gear=roll speed/engine speed
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9
F(๐ |ฯ;ฮธ)= ๐๐ F๐พ๐=1 ๐ ฮธk
๐ค๐ก๐ = ๐ ๐๐ก ฮธk ฯk
๐๐พ๐=1 ๐๐ก ฮธj ฯj Bayesโ theorem
๐๐๐ ๐ ฯ, ฮธ = (๐๐๐ ๐๐๐ (๐๐|ฮธk))๐พ๐=1
๐๐=1 Log-likelihood
Mixed distribution model
Maximization Expectation-Maximization (EM) algorithm
๐(๐, ๐)
๐, ๐ and ๐ for each component ๐
Gear-memberships
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10
Time (sec)
0 2000 4000 6000 8000 10000 12000
0.0
0.4
0.2
0.8
0.6
1.0 G
ea
r m
em
bers
hip
s
Component 1
Component 2
Component 3
Component 4
Component 5
Component 6
Component 7
Gear memberships
Vehicle B
Diesel โ Supermini โ Manual
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๐ = ๐ฑ. ฮฒ
๐ฑ: Explanatory variables ๐ฃ, ๐, ๐๐ฃ, ๐ฃ3
๐: Gear membership (latent variable)
๐ฑ.๐ฐ: Interaction
๐: Residuals
Gear-based emission modelling
๐ = ๐ฑ. ฮฒ + ๐ฐ.ฯ ๐ = ๐ฑ. ฮฒ + ๐ฐ.ฯ + ๐ฑ.๐ฐ . ฮณ + ๐
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13
Challenge: engine speed as a latent variable
gea๐, ๐ = ๐ฃ/๐
roll speed, ๐ฃ
gea๐, ๐ = ๐ฃ/๐
Latent variable
(estimated) ๐๐๐๐๐๐ ๐ ๐๐๐๐, ๐
๐๐๐๐๐๐ ๐ ๐๐๐๐, ๐ Observation
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๐๐ก = ๐ก(๐ต)๐ฃ๐ก +Nt
๐๐: engine speed at time ๐ก
๐๐: roll speed at time ๐ก
๐ต๐: noise- can be serially correlated
โ (๐ต)
๐ (๐ต) ๐๐ก= ๐๐ก
๐(๐ฉ): rational polynomial in B: ๐ค(๐ต)๐ต๐
๐ฟ(๐ต)
Systematic part
Stochastic part
Transfer Function Model
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15
๐๐ก = c+ ๐ค0+๐ค1๐ต+๐ค2๐ต
2
1โ๐ฟ1๐ตโ๐ฟ2๐ต2 ๐ฃ๐ก +
1โ โ 1๐ตโโ 2 ๐ต2
1โ๐1๐ตโ๐2๐ต2 (1 โ ๐ต) ๐๐ก
observed
fitte
d
R2 = 0.896
ACF and PACF of ๐
Transfer Function Model
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16
Driving Cycle
Gear-based emission modelling
๐ = ๐ฑ. ฮฒ + ๐ฐ.ฯ + ๐ฑ.๐ฐ . ฮณ + ๐
Mixed distribution model
Explanatory variables ๐ฃ, ๐, ๐๐ฃ, ๐ฃ3
Transfer Function Model
Engine speed
Gear =roll speed/ engine speed Gear-memberships
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Results
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
A,Petrol,Manual B, Diesel,Manual C,Diesel,Automatic
D,Diesel,Automatic
E,Petrol,Automatic
BIC
Vehicle type
BIC
Gear-based Single VT-micro
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
A,Petrol,Manual B, Diesel,Manual C,Diesel, Automatic D,Diesel, Automatic E,Petrol,Automatic
Vehicle type
๐ -squared
๐ 2
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18
Conclusion
โข Gear for driving mode instead of acceleration
โข Introducing gear-membership
โข Transfer function model
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Thank You !