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C rossover phenomenon in vehicle emissions with DFA. Wei Pan. College of Physical Science and Technology, Guangxi University, China. August 13, 2013. Plan. Introduction Data collection of vehicle emission Detrended Fluctuation Analysis (DFA) Crossover Phenomenon in vehicle emission - PowerPoint PPT Presentation
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CCrossover phenomenon rossover phenomenon in vehicle emissions in vehicle emissions
with DFAwith DFA
Wei Pan
College of Physical Science and Technology, Guangxi University, China.
August 13, 2013
IntroductionData collection of vehicle emissionDetrended Fluctuation Analysis (DFA)Crossover Phenomenon in vehicle emissionNotes
IntroductionIntroduction
http://auto.people.com.cn/GB/25959/98358/8362/11367000.html
Why so stuck!
The problem in the traffic flow:
The problem behind the traffic flow:
gasoline
oxygen
http://sichuan.sina.com/news/sc-all/2011-06-04/259-43291.html
Vehicle emissions
Data collectionData collectionPlace : Nathan Road, Mong Kok, Hong Kong
Time : Rush hours ( 6:59:25~9:01:56 in the morning 16:52:31~18:16:12 in the afternoon )
Instrument : TSI model 982
Target : CO and CO2
Cooperate with the City University of Hong Kong
0 1000 2000 3000 4000 5000
200
400
600
800
1000
1200
CO
2 in
ppm
CO2 Observations
(d) Afternoon
0 1000 2000 3000 4000 5000
200
400
600
800
1000
1200
CO2 Observations
CO
2 in
ppm
(c) Morning
0 1000 2000 3000 4000 50000
2
4
6
8
10
12
14
CO
in p
pm
CO Observations
(b) Afternoon
0 1000 2000 3000 4000 50000
2
4
6
8
10
12
14
CO
in p
pm
CO Observations
(a) Morning
Sequence of concentration for carbon emission
200 250 300 350 400 450 500 5500.00
0.05
0.10
0.15
0.20
0.25
Dis
trib
utio
n
Concentration(ppm)
Morning CO2
Afternoon CO2
(b)
0 1 2 3 4 50.00
0.05
0.10
0.15
0.20
0.25
Dis
trib
utio
n
Concentration(ppm)
Morning CO Afternoon CO(a)
Normalized distributions of concentrations
DFADFA
Detrended fluctuation analysis (DFA), first proposed by Peng et al. in 1994 [Phys. Rev. E 49, 1685–1689]
And now it becomes a scaling analysis method for detection of long-range correlations embedded in data sequence.
j
i
N
j
iuN
iujy1 1max
max1
max
1
2
max
1 N
ifit iyiy
NnF
maxNwhere is the length of the signal. Then divide the integrated signal )(ty
into boxes of equal length n and fit them by using a polynomial function . iy fit
For a given box size , n
Integrate the time series ( )u t
For different scales (box sizes ), we get n
nnF ~
5.0
5.0
5.0
is long-rang anticorrelation
is long-rang correlation
( )u t
( )u t
( )u t is no correlation
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0-2
-1
0
1
2
3
4
5
nx
S=1.50
L=0.64
nx=1.88
(d) Afternoon CO2
log 1
0F(n
)
log10n
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0-2
-1
0
1
2
3
4
5
nx
S=1.49
L=0.51
nx=1.91
(c) Morning CO2
log 1
0F(n
)
log10n
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0-2
-1
0
1
2
3
4
5
nx
S=1.59
L=0.51
nx=1.92
(b) Afternoon CO
log 1
0F(n
)
log10n
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0-2
-1
0
1
2
3
4
5
S=1.56
L=0.67
nx=1.77
log 1
0F(n
)
log10n (s)
(a) Morning CO
nx
DFA fluctuation function nF nversus the scale in log-log plots
Crossover phenomenonCrossover phenomenon
Statistical analysis suggests that the major concentration distributions of carbon emission have little change.
A crossover phenomenon has been found, which verifies the long-term dependence of carbon emission from vehicles.
NotesNotes
Ritz, B., Yu F. 1999. “The Effect of Ambient Carbon Monoxide on Low Birth Weight among Children Born in Southern California between 1989 and 1993,” Environmental Health Perspectives, 107(1):17-25.Peng , C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E. and Goldberger, A.L. 1994. “Mosaic Organization of DNA Nucleotides,” Phys. Rev. E, 49(2):1685-1689.K. Hu, P. Ch. Ivanov, Z. Chen, P. Carpena and H. E. Stanley. 2001. “Effect of Trends on Detrended Fluctuation Analysis.” Phys. Rev. E, 64(1):011114(19).Sprott, J. C. 2004. “Chaos and Time-Series Analysis,” Oxford University Press, pp. 218-219.N. K. Das, R. K. Bhandari, P. Sen and B. Sinha. 2009. “Scaling and Crossover Phenomena in Anomalous Helium Sequence,”arXiv:0906.0832.
ReferencesReferences