continuous moving measurement method for thermal ...continuous moving measurement method for thermal...

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Continuous Moving Measurement Method for Thermal Environmental Distributions in Streets Masaki NAKAO*, Minako NABESHIMA, Masashi MIZUNO, Masatoshi NISHIOKA, Oosaka City University, Osaka, Japan Tomoko HASAGAWA Kyoto University, Kyoto, Japan

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Continuous Moving MeasurementMethod for Thermal Environmental

Distributions in Streets

Masaki NAKAO*, Minako NABESHIMA,Masashi MIZUNO, Masatoshi NISHIOKA,

Oosaka City University, Osaka, Japan Tomoko HASAGAWA

Kyoto University, Kyoto, Japan

Pyrgeometer

GPS

Pyranometer

Air temperature

Infrared thermometer

1000mm

1500

mm

赤外放射計日射計

GPS

熱電対日射遮蔽シェルター

放射温度計

350㎜

Vehicle for continuous moving measurent

Pyrgeometer

Pyranometer

Infrared thermometerSensors and GPS attached

②Delay time in the GPS terminal

① Time lag of the sensors

Why error occurs

GPSTrue ValueMeasured Data

Val

ue

Position of the Sensor    X

Measurement errors

PyranometerStep Response

① Time lag of the sensors

0100200300400500600700

0 5 10 15 20Time s

Am

ount

of c

hang

e W

/m2

②Delay time in the GPS terminals

            location

GPS receiver

receiving signalsfrom satellites

X

Sensing data at time tat the location X

[logging data ]X+⊿X

Sensing and logging dataat time t+⊿t as thelocation X, but at thelocation X+⊿X

Processing time ⊿t

Estimation system

Estimation System

Sensing Data

Position  X

True Value

Position  X

Data measuring position x

dVtttVxx !!+= )( 00

t : Timex : Data measuring position at time tx0 : Initial position of the sensorV : Moving speed of the sensort0 : Initial timetd : GPS delay time from receiving from the satellites to outputting the positioning informationxp : The sensor position at time t

The sensor position xp at time t :)( 00 ttVxxp !+=

Data measuring position x at time t :(1)

(2)

Input/output relation of the sensor

MeasurementTrue value ofthe spatialdistributionf(x)=u(t)

Measurementvalue g(t) ofthe sensor inthe timedomain

u(t): True value of the measured property at time t

f(x) : True value of the measured property at the positon x

g(t) : Instantaneous value of the data measured by the sensor at time t

Assuming the sensor response as a first-order lag system,

)()()(

tutgdx

tdgT =+

( ) !! "##+##=t

t

dssuTTsttgTtttg

0

)(/}/)(exp{)(}/exp{)( 00

the solution is the following equation.

Assuming u(t) is constant over the time interval, thisequation is transformed to the following discrete system.

)()1()()( tuetgettg T

t

T

t !"

!"

"+=!+

(3)

(4)

(5)

An Inverse system of responsecharacteristics of the sensor

An inversesystem of thesensor

Input u(t)to thesensor

Measurementvalue g(t) ofthe sensor

The inverse system of the equation will bethe following equation.

)1/()()()( T

t

T

t

etgettgtu

!"

!"

"#$%

&'(

"!+=

Moving average

Movingaverage

Movingaverage u(t)of input tothe sensor

Input u(t)to thesensor

)12/()()( +!+= "#=

Ntitutu

N

Ni

Transformation of the input signal of thesensor to the spatial distribution

Transformationfrom time domainto spatial domain

Estimatedvalue F(x)of the spacedistribution

Movingaverage u(t)of input signalto the sensor

Also, a transformation from time to space is made bysubstituting ( ) VtVxxtt

d/

00+!+=

The spatial distribution F(x) will be obtained.( ) )/()( 00 VtVxxtuxF

d+!+=

Step responses of the pyranometer

Step response ofthe pyranometer

An approximationof first-order lagsystem

An approximation of first-order lagsystem

Sola

r rad

iatio

n [

W/m

2 ]

Time [s]0

100200300400500600700

0 5 10 15 20 25 30 35

Pyranometer

Step responses of the pyrgeometer(IRradiometer)

Infr

ared

radi

atio

n [

W/m

2 ] Step response of thepyrgeometer(IR radiometer)

An approximation offirst-order lag system

Time [s]

05

1015202530354045

0 10 20 30 40

Step responses of the infraredthermometer

Step response of theinfrared thermometer

An approximation offirst-order lag system

Tem

pera

ture

cha

nge

[K]

Time [s]

02468

10121416

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Step responses of the thermocoupleTe

mpe

ratu

re c

hang

e [K

]

Step response of thermocouple(0.1mmφ)

An approximation of first-order lag system(0.1mmφ)

Step response of thermocouple(0.3mmφ)An approximation of first-order lag system(0.3mmφ)

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14 16Time [s]

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14 16

Time constants of the sensors

The time constant[s]

2

6.70.25

φ0.1 1.1φ0.3 2.6

Pyranometer MS-802the pyrgeometer(IR radiometer) MS-202

Infrared thermometer IRTS-P

T type thermocouple

Instruments

Installation of the sensors

1000mm

1500

mm

Solar shading

Air temperature

GPS

Pyranometer

Pyrgeometer(IR radiometer)

Datalogger

Infraredthermometer

350m

m

Themocouple

PyranometerGPS

Pyrgeometer(IR radiometer)

Field testDate: 2005/10/12Place : Osaka city, JapanSpeed: 5km/h    10km/h    20km/h    40km/h

data sampling interval:0.2 sGPS delay time:1 s

500 m

E

A BWE

Moving measurement result of the pyranometer

0

200

400

600

800

135.5095135.5105135.5115135.5125135.5135135.5145Longitude

Sola

r rad

iatio

n [W

/m2

]

Low speed 10km/h 20km/h 40km/h Position of trees along the street

EAST WEST

Moving measurement result of the pyrgeometer(IRradiometer)

360

380

400

420

440

135.5095135.5105135.5115135.5125135.5135135.5145

Longitude

Infr

ared

radi

atio

n[W

/m2 ]

10km/hLow speed 20km/h 40km/h Position of trees in the street

EAST WEST

40km/h

0

100

200

300

400

500

600

700

800

900

1000

135.509135.51135.511135.512135.513135.514

全天日射量

[ W / m 2 ]

経度[ƒ]

Comparative result of the moving measurement value, thetrue value and the estimated value of the pyranometer

Sola

r rad

iatio

n [W

/m2 ]

Longitude

Moving directionof the sensor

The estimatedvalue F(x)

True value f(x) (measurementvalue at the low speed of 5 km/h)

Measured data at 40 km/h

EAST WEST

360

370

380

390

400

410

420

430

440

135.509135.51135.511135.512135.513135.514

赤外放射量

[ W / m 2 ]

経度[ƒ]

Comparative result of the moving measurement value, thetrue value and the estimated value of pyrgeometer(IRradiometer)

Infr

ared

radi

atio

n [

W/m

2 ] Measured data at the speed of 40 km/h

True value f(x)(measurement value at 5 km/h)

The estimated valueF(x)

Longitude

Moving directionof the sensor

EAST WEST

Conclusion

1. A method to estimate the spatial distribution from datawhich was obtained by continuously measuring instreets, using sensors which have a response lag andGPS which has a time delay.

2. The measurement error of the pyranometer with a 2.0-second time constant was extremely small.

3. The error was much larger for the pyrgeometer (IRradiometer) with a comparably large 6.7-second timeconstant.

4. By applying this method, it became obvious thatmeasurement error can be effectively decreased.

500mW A B E500m500mW A B E

0

200

400

600

800

0 5 10 15 20

time[sec]

resp

on

se[W

/ !]

measurmentapproximation

( ) !"#

$%& ''=

T

ttt

)(exp 0(

T: time constant[sec]

ContinuousMoving

MeasurementTrue

distribution

Sensing Data andLocation output ofGPS

EstimationSystem

Estimateddistribution

360

370

380

390

400

410

420

430

440

135.509135.51135.511135.512135.513135.514

!"#$%

[W/m2]

&' [ƒ]

Infr

ared

rad

iati

on

[

W/m

2]

Measured data at the speed of 40 km/h

True value f(x)

(measurement value at 5 km/h)

The estimated value

F(x), a dash line

Longitude

Moving direction

of the sensor

EAST WEST

360

370

380

390

400

410

420

430

440

135.509135.51135.511135.512135.513135.514

!"#$%

[W/m2]

&' [ƒ]

Infr

ared

rad

iati

on

[

W/m

2]

Measured data at the speed of 40 km/hMeasured data at the speed of 40 km/h

True value f(x)

(measurement value at 5 km/h)

True value f(x)

(measurement value at 5 km/h)

The estimated value

F(x), a dash line

The estimated value

F(x), a dash line

Longitude

Moving direction

of the sensor

EAST WEST

Exampleofcontinuousmovingmeasurement

2008年8月2日19時半の気温分布図(移動観測データ+定点観測データ)

START

GOAL

300m

d.土佐公園

e.日吉公園

a.堀江公園

b.南堀江公園c.高台橋公園

j.島津公園 i.阿波座南公園

h.新町北公園

g.新町南公園

f.松島公園

※赤☆は定点観測地点、赤・緑・青線は移動観測経路堀江周辺地図

Measurement plan

Spatial frequency to measure<Cut-off spatial frequency

Moving velocity

Sampling interval

21[1/m]π

μ<μ TVc=

21][

21[km/h] 0

μs

μπ

Vtt

TVV

s=≤

=≤

[m/s]Velocity Time constant

:V[s]:T

0

20

40

60

80

100

0 0.02 0.04 0.06 0.08 0.1Cut-off Spatial frequency [1/m]

Spee

d [k

m/h

]

Infrared thermometerPyranometerPyrgeometer

Measurement PlanChoice of Speed

Spatial frequency⇒Instrument⇒Speed

0.04[1/m]

60km

25m

0

1

2

3

4

5

0 0.02 0.04 0.06 0.08 0.1Spatial frequency[1/m]

Sam

plin

g in

terv

al [s

]

20km40km60km80km

0.8

Interval<0.8sec

Measurement PlanSampling interval

• 残った誤差の原因は– However,theaveragelevelofestimatedvalueisdifferentfromthatof

thetruevalue,whichseemstobecausedbythefactthatbothmeasurementswerenotcarriedoutsimultaneously.

• 移動速度が変化した場合に適用できるか.– Yes,itcanbeappliedtothevariablespeed.Buttheinversesystemcan

notbeappliedwhenthevehiclestops.

• 温度計測についてやらなかったのか– 温度計測にもこの手法は適用できるが,温度分布は速度を変えて何度か走行すると,大きく変化するので,本手法の検証には温度計測を使用しなかった.

• 温度センサーや放射温度計はこの推定法を適用する必要は無いか.– 40km/h程度の速度の場合,センサーの応答が速いので,適用する必要は無いと思う.

– 観測したいカットオッフ空間周波数による.• 大気汚染関連のセンサーは時定数が30秒程度とさらに長くなるので,本推定法の効果はさらに大きくなる.