C rossover phenomenon in vehicle emissions with DFA

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