EFFECT OF WIND DIRECTION SENSOR OFFSET VALUE ON UNCERTAINTY
by Salih ÇAKIL, Yusuf Salih EROĞLU
Turkish State Meteorological Service
Observing Systems Directorate
Kütükçü Alibey Street. No:4 06120 Kalaba-Ankara-TÜRKİYE
Tel: +90 312 302 22 03, +90312302 27 64
Fax:+90-312-361 23 53
e-mail: [email protected], [email protected]
ABSTRACT
This paper aims to describe the factors that affect the uncertainty in calibration of mechanical and
ultrasonic wind direction sensors, to calculate measurement uncertainty to declare in calibration
certificates, and to derivate the detailed formula of offset uncertainty component arising from
adjusting the components used in measurement uncertainty to north of the wind direction sensor.
INTRODUCTION
Calibration is a comparison between measurements – one of known magnitude or correctness
made or set with one device and another measurement made in as similar a way as possible with a
second device. The device with the known or assigned correctness is called the standard. The
second device is the unitunder test, test instrument, or any of several other names for the device
being calibrated.
The calculations used in this paper is applicable to both mechanical and ultrasonic wind direction
sensors. We preferred to study with mechanical wind direction sensors in our tests and case studies.
Potentiometrical and optoelectronic components used inside mechanical wind direction sensors are
important factors that affectthe uncertainty. Main subject of this paper is to analyze the test offset
uncertainty component which is the one of most important factors. Here we will review theeffect of
offset uncertainty component on total uncertainty.
Wind measurement is one of the key parameters in meteorological observation stations. So, low
uncertainty levels in this measurement is very important for measuring quality. The uncertainty in
the calibration certificate of the sensor used at meteorological observation station must be reduced
as possible asfor this measuring quality. The uncertainty arising from mounting of wind direction
sensor usedat meteorological observation station must be taken into consideration. The uncertainty
component for mounting of the wind direction sensor at calibration stage and the formulation of
this uncertainty component will be described later in this study.
SECT
TIONS OFMECHAN
NICAL WIN
ND DİREC
CTION SEN
NSOR
t
are diffferences byy brand and model, mechanical wiind direction
n sensor is formed
f
of
Although there
two main ssections :
Mechanical part
p driving the sensor shaft
s
accordding to wind
d.
1. Winnd Vane:M
C
section that coonverts thee movemennt received
d from winnd vane too
2. Traansducer: Center
elecctrical signaal. There arre bearings,, parts usedd for fixing the wind diirection sennsor to polee
or ccentre physiically, electtronic cards and optionnal heaters in
i this centrre.
Im
mages of som
me wind direection sensoors:
Figure 1-a:Images
1
s from wind
d direction sensors.
Figure 1-b:
1 Imagess from wind
d direction
n sensors.
MOU
UNTING OF
O WIND DIRECTIO
D
ON SENSOR
R TO ANA
AWOS
An importaant point too note whilee mounting the wind diirection sennsors used in
n AWOS too mast or too
platform iss to adjustthhe sensors’’ cursor thaat indicates north to thhe northernm
most point. Otherwisee
even thouggh the senssor measurees the corrrect value, our result will
w be inccorrect becaause of thee
incorrect offset
o
adjustment.Northh adjustmennt of wind vane must be done caarefully andd in a veryy
accurate w
way at the monuting
m
stagge of Autom
matic Weathher Observaation Station
n (AWOS).
u
is desired for wind diirection sennsors (this is
i required especially),,
If low meaasurement uncertainty
detection oof north dirrection and installationn of sensor mıst be donne with higgh accuracyy. These aree
someof thee most imp
portant facttors affectinng accuracyy of Autom
matic Meteoorological Observation
O
n
Station (AW
WOS).
Figure 2:Im
mages of noorth cursorr of differen
nt wind dirrection sensor modelss.
d
seensor has bbeen introdu
uced abovee. The northh cursor iss
Mechanicaal parts of the wind direction
necessary tto be adjustted to the noorthern poin
nt while mounting the two
t main moving
m
sections to mastt
or to platfoorm at systeem installattion or calibbration phase. Errors occuring
o
du
ue to this addjustment iss
called offsset error. Offset error depends onn person whho made thhe adjustmeent, equipmeent used inn
direction fi
finding meth
hods, physiccal conditions, etc.
WIND
W
DIRE
ECTION SENSOR CA
ALIBRATION STAG
GE
Wind Dirrection Sen
nsor Test Offset Un
ncertainty:: This is the
t
uncertaainty originnated from
m
installationn of wind diirection sennsor for the system at thhe installatiion or calib
bration stagee. The mostt
important point to bee consideredd during the installatioon of sensoor is adjusting the nortth indicatorr
writing or mark
m
indicatting that is necessary
n
too set to the north)
n
to the north. Thee followingg
(the sign, w
assembly hhas been esttablished too measure uncertainties
u
s arising froom this adju
ustment andd to controll
the calcullations. Th
he temperaature of laboratory
l
ambient conditions
c
were keppt constantt
(Temperatuure: 23 ± 3 °C Hum
midity:%45
5 ±10). The followingg componeents were used
u
in thee
assembly.
Figure 3-aa: Theodoliite
Figurre 3-b:Linee Laser
F
Figure
3- c)) Interconn
nection Equ
uipment
Electronic theodolitee which prrovided intternational traceabilityy is used for refereence anglee
measuremeents. Line laaser is usedd for axis coontrol. Interconnection equipment is used for connectionn
between thheodolite annd sensors. During
D
calibbration, meaasurements were takenn for each seensor at 45⁰⁰
intervals inn clockwisee and counteerclockwisee directions after offsett adjustmen
nt has been made. Onee
of the mosst important requiremeents while setting
s
the device’s orrientation iss that the vane’s northh
indicator must
m
be witthin the bouundaries off the laser line.
l
This condition mu
ust be checcked beforee
taking meaasurement reesults.
Figure 4:Image of the devicees on the axxis line.
T
TEST
OFFSET UNCE
ERTAINTY
Y
Figure 5:A
Abbreviatiions used foor Vane Diimensions.
=
=
=
=
Distancce from winnd vane's no
orth indicatoor cursor to the center of
o sensor
Width of
o the windd vane's nortth indicator cursor
Distancce from winnd vane nortth indicator to the centeer of sensorr
Width of
o the vane direction inndicator
v
may vary depennd on brand and model,, but the deffinitions is same
s
for
The appearrances and values
all of them
m.
1)In the innitial phase of calibration, the laseer line is fixxed to the center
c
of thee reference device. Too
achieve thaat linewidthh (Lk) of lasser line on reference device
d
is 1m
mm,the distaance from line
l
laser too
reference device
d
is addjusted. It iss paid attenttion for linee laser to bee at the nortth of reference device..
It is left fixxed at this point.
p
2)- The noorth indicattor cursor of
o the windd direction sensor whiich is connected to ceenter of thee
reference ddevice is sett to indicatee the line lasser. This proocess is the process of adjusting thhe sensor too
the northerrn point (coonsidering when
w
you loook sensor--based, situaation that thhe laser is in
i the northh
of the senssor).
3)-After fixxing the sennsor to nortth, the endppoint of vane’s north cuursor has too be fixed. During thiss
process,it m
must be paidd attention ffor sensor's north cursoor not to driift from the northern pooint.
b accurate in the firstt stage, thee
Because of the setting of the reference devvice was acccepted to be
o
adjusttment of thee device willl be accepteed as zero(00).
uncertaintyy from the offset
s points and
a the radiii effect unccertainty. Thhese effectss
In the secoond and thirrd stage, wiidth of the set
will be calcculated sepaarately.
mula consissts of three main
m components.
Offset unceertainty form
c
by the
t linewiddth of laserr, width annd positionn of vane’ss
1-The unccertainty coomponent caused
endpoint. T
The laser lin
ne must poiint to the vaane’s endpooint in all measurement
m
ts.An error is occurredd
resulting fr
from the diffference bettween the laargest(J2) and
a the smaallest (J1) anngles whosee endpointss
point to thhe laser. Thhis error is a systematiic error andd can be caalculated. The
T uncertaiinty arisingg
from this eerror is calleed the unceertainty arisiing from thhe vane's phhysical struccture. The error
e
causedd
by this diffference can be calculated by the foollowing forrmula.
.
. .
b examineed in the system, the foormula wheen the laserr
Because onnly the effeect of the seensor will be
width takenn zero
:
.
. .
c
by liinewidth of laser, widthh and position of vane’s endpoint.
Kjh= The eerror value caused
Figure 6:Images of
o maximum
m and minimum anglles showingg North.
d from laserr linewidth,, width andd
2- The seccond sectionn of the forrmula is thee componennt originated
position off the north cursor enddpoint. It is the error value
v
causeed by the difference
d
b
between
thee
maximum((a2) and minimum(a1) angles of the
t northernn point show
wing laser in
n the setup phase. Thee
error originnated from this
t differennce can be calculated
c
b the follow
by
wing formula:
,
.
. .
Because onnly the effeect of the seensor will bbe examineed in the system, the foormula wheen the laserr
width takenn zero
:
. . .
= The error value caused by the
t width annd position of the northh cursor.
nimum valu
ues for senssor showingg North.
Figure 7:Maximum and min
b
of th
he measurement errorw
which remaiining constaant or
3- The connstant valueccaused by because
showing prredictable changes
c
oveer a set of measurement
m
ts of magnittudeis a perrpendicular
componentt.
√
m of the firstt and second error term
ms.
Salih equattion is obtaiined by sum
,
.
i the calcuulation of syystematic errror, it is muultiplied byy
Because thhere is perpendicular coomponent in
systematic error consttant. As a reesult, the offfset uncertaainty can be calculated.
,
.
/ √
Calculation of Measurement Uncertainty for Calibration of Mechanical Wind Direction
Meter
Acorrection= f(Atest , A ref , δAref cal , δAref res, δAref drift , δAref offset , δAtest res, δAtest rep, δAtest offset , δAcalres,
δAcalcal , δAcal drift , δAHys Unc,δAother)
Acorrection-Difference between the angle value given from the reference and the angle value read from
the test device.
Atest
- Angle value read from test device
Aref
- Angle value given from the reference device
δAref cal
- Uncertainty from calibration certificate of the reference device
δAref res
- Resolution of the reference device
δAref drift
- Annual drift of reference device
δAref offset
- The uncertainty value when the offset of reference device done.
δAtest res
-Resolution of the test device
δAtest rep
- Repeatability of the test device
- Offset uncertainty of the test device
δAtest offset
δAcal çöz,
- Resolution of the caliper reference (meter)
-Uncertainty from calibration certificate of the caliper reference (meter)
δAcal kal
δAcal drift
-Annual drift of caliper reference
δAHys Unc
- Hysteresis uncertainty
- Other uncertainty components
Aother
Uδtotal
- Total uncertainty
Umeas unc
- Measurement Uncertainty
Source of
uncertainty
Quantity
Standard
Uncertainty
i
u xi 
Distrib
ution
factor
Sens.
Coeff.
ci
partial
variance
Ui
N.
1
Uref cal2
Reference
Calibration
Reference
Resolution
Uref cal
UδAref cal = aref cal / k
Uref res
UδAref res= aref res/ 2 3
Rec.
1
Uref res2
Reference Drift
Uref drift
UδAref drift = aref drift/
Rec.
1
Uref drift2
Reference
offset
uncertainty
Uref offset UδAref offset = aref offset/ 2 3
Rec.
1
Uref offset2
Utest res
Utest rep
Utest
Rec.
N.
1
1
Utest res2
Utest rep2
Rec.
1
Utestoffset2
Rec.
1
Ucalres2
N.
1
Ucal cal2
Rec.
1
Ucal drift2
Rec.
1
Rec.
Uother2
Utotal2 = ∑ Ui2
Utotal
Umeas unc= Utotal* k
Test Resolution
Test repeat.
Test Offset
Uncertainty
Caliper
resolution
UδAtest res= atest res/ 2 3
UδAtest rep= atest rep
,
offset
UAcal res
3
.
/ √
UδAcalres= acal res/ 2 3
Caliper
Calibration
Ucal cal
Caliper drift
Ucal drift
Hysteresis
uncertainty
UHys Unc. Absolute Value(Xi1 Xi2 ) /
Other
Uother
Uδcal cal= rcal cal/ k
UδAcal drift = acal drift /
UδIother= aother/ 3
Total Partial Variance
Standard Uncertainty
Measurement Uncertainty (k=2)
3
3
1
Charts below show the uncertainty results and the contribution percentage of the components
making up the uncertainty for four different brand and model. Since the aim is not to compare
brands and models, the brand and model names are not given. Only studies were enumerated. When
calculating these uncertainty values, same measurements were made for all sensors.
Study 1
SOURCE OF UNCERTAINTY
ESTIMATED VALUE
DISTRIBUTION BENEFIT
STANDARD UNCERTAINTY COEFFICIENT
PARTIAL VARIANCE
Uncerta i nty of Reference
0,010000
Norma l
2,00
0,005000
1
0,00002500
Res ol uti on of Reference
0,000300
Recta ngul a r
3,46
0,000087
1
0,00000001
Annua l Dri ft of Reference
0,010000
Recta ngul a r
1,73
0,005774
1
0,00003333
Offs et Adjus tment of Reference
0,000300
Recta ngul a r
3,46
0,000087
1
0,00000001
Tes t Res ol uti on
10,000000
Recta ngul a r
3,46
2,886751
1
8,33333333
Tes t Repea ti bi l i ty
0,000000
Norma l 1,00
0,000000
1
0,00000000
Tes t Offs et Uncerta i nty
4,583662
Recta ngul a r
3,46
1,323189
1
1,75083005
Ca l i per Res ol uti on
0,100000
Recta ngul a r
3,46
0,028868
1
0,00083333
Ca l i per Certi fi ca te Uncerta i nty
0,010000
Norma l
2,00
0,005000
1
0,00002500
Ca l i per Annua l Dri ft
0,010000
Recta ngul a r
1,73
0,005774
1
0,00003333
Hys terezi s Uncerta i nty
0,000000
Recta ngul a r
1,73
0,000000
1
0,00000000
Other Uncerta i ni ti es
0,819964
Norma l
1,00
0,819964
1
0,67234089
0,00
0,000000
1
0,00000000
Total Variance
10,7575
0,000000
Standard Uncertainty
3,280
Expanded Uncertainty
6,5597
Percentage Rate
0,00
0,00
0,00
0,00
77,47
0,00
16,28
0,01
0,00
0,00
0,00
6,25
0,00
0,00
100,00
In this study, the most active variable affecting uncertainty is test resolution. The reason of this is
originated from the bigger resolution value of the sensor reader. Other factors affecting the
uncertainty are test offset uncertainty and other uncertainties respectively.
Study 2
SOURCE OF UNCERTAINTY
ESTIMATED VALUE
DISTRIBUTION BENEFIT
STANDARD UNCERTAINTY COEFFICIENT
PARTIAL VARIANCE
Uncerta i nty of Reference
0,010000
Norma l
2,00
0,005000
1
0,00002500
Res ol uti on of Reference
0,000300
Recta ngul a r
3,46
0,000087
1
0,00000001
Annua l Dri ft of Reference
0,010000
Recta ngul a r
1,73
0,005774
1
0,00003333
Offs et Adjus tment of Reference
0,000300
Recta ngul a r
3,46
0,000087
1
0,00000001
Tes t Res ol uti on
0,500000
Recta ngul a r
3,46
0,144338
1
0,02083333
Tes t Repea ti bi l i ty
0,000000
Norma l 1,00
0,000000
1
0,00000000
Tes t Offs et Uncerta i nty
3,308020
Recta ngul a r
3,46
0,954943
1
0,91191662
Ca l i per Res ol uti on
0,100000
Recta ngul a r
3,46
0,028868
1
0,00083333
Ca l i per Certi fi ca te Uncerta i nty
0,010000
Norma l
2,00
0,005000
1
0,00002500
Ca l i per Annua l Dri ft
0,010000
Recta ngul a r
1,73
0,005774
1
0,00003333
Hys terezi s Uncerta i nty
0,000000
Recta ngul a r
1,73
0,000000
1
0,00000000
Other Uncerta i ni ti es
0,249493
Norma l
1,00
0,249493
1
0,06224666
0,00
0,000000
1
0,00000000
Total Variance
0,9959
0,000000
Standard Uncertainty
0,998
Expanded Uncertainty
1,9959
Percentage Rate
0,00
0,00
0,00
0,00
2,09
0,00
91,56
0,08
0,00
0,00
0,00
6,25
0,00
0,00
100,00
The biggest factor affecting the uncertainty for this study is the test offset uncertainty.
Study 3
SOURCE OF UNCERTAINTY
ESTIMATED VALUE
DISTRIBUTION BENEFIT
STANDARD UNCERTAINTY COEFFICIENT
PARTIAL VARIANCE
Percentage Rate
Uncerta i nty of Reference
0,010000
Norma l
2,00
0,005000
1
0,00002500
Res ol uti on of Reference
0,000300
Recta ngul a r
3,46
0,000087
1
0,00000001
Annua l Dri ft of Reference
0,010000
Recta ngul a r
1,73
0,005774
1
0,00003333
Offs et Adjus tment of Reference
0,000300
Recta ngul a r
3,46
0,000087
1
0,00000001
Tes t Res ol uti on
1,000000
Recta ngul a r
3,46
0,288675
1
0,08333333
Tes t Repea ti bi l i ty
0,000000
Norma l 1,00
0,000000
1
0,00000000
Tes t Offs et Uncerta i nty
4,774648
Recta ngul a r
3,46
1,378322
1
1,89977219
Ca l i per Res ol uti on
0,100000
Recta ngul a r
3,46
0,028868
1
0,00083333
Ca l i per Certi fi ca te Uncerta i nty
0,010000
Norma l
2,00
0,005000
1
0,00002500
Ca l i per Annua l Dri ft
0,010000
Recta ngul a r
1,73
0,005774
1
0,00003333
Hys terezi s Uncerta i nty
0,000000
Recta ngul a r
1,73
0,000000
1
0,00000000
Other Uncerta i ni ti es
0,363690
Norma l
1,00
0,363690
1
0,13227037
0,00
0,000000
1
0,00000000
Total Variance
2,1163
0,000000
Standard Uncertainty
1,455
Expanded Uncertainty
2,9095
0,00
0,00
0,00
0,00
3,94
0,00
89,77
0,04
0,00
0,00
0,00
6,25
0,00
0,00
100,00
The biggest factor affecting the uncertainty for this subject is the test offset uncertainty.
Study 4
SOURCE OF UNCERTAINTY
ESTIMATED VALUE
DISTRIBUTION BENEFIT
STANDARD UNCERTAINTY COEFFICIENT
PARTIAL VARIANCE
Uncerta i nty of Reference
0,010000
Norma l
2,00
0,005000
1
0,00002500
Res ol uti on of Reference
0,000300
Recta ngul a r
3,46
0,000087
1
0,00000001
Annua l Dri ft of Reference
0,010000
Recta ngul a r
1,73
0,005774
1
0,00003333
Offs et Adjus tment of Reference
0,000300
Recta ngul a r
3,46
0,000087
1
0,00000001
Tes t Res ol uti on
1,000000
Recta ngul a r
3,46
0,288675
1
0,08333333
Tes t Repea ti bi l i ty
0,000000
Norma l 1,00
0,000000
1
0,00000000
Tes t Offs et Uncerta i nty
2,610141
Recta ngul a r
3,46
0,753483
1
0,56773637
Ca l i per Res ol uti on
0,100000
Recta ngul a r
3,46
0,028868
1
0,00083333
Ca l i per Certi fi ca te Uncerta i nty
0,010000
Norma l
2,00
0,005000
1
0,00002500
Ca l i per Annua l Dri ft
0,010000
Recta ngul a r
1,73
0,005774
1
0,00003333
Hys terezi s Unce rta i nty
0,000000
Recta ngul a r
1,73
0,000000
1
0,00000000
Other Uncerta i ni ti es
0,208490
Norma l
1,00
0,208490
1
0,04346798
0,00
0,000000
1
0,00000000
Total Variance
0,6955
0,000000
Standard Uncertainty
0,834
Expanded Uncertainty
1,6679
The biggest factor forming the uncertainty for this subject is the test offset uncertainty.
Percentage Rate
0,00
0,00
0,00
0,00
11,98
0,00
81,63
0,12
0,00
0,00
0,00
6,25
0,00
0,00
100,00
RESULT
When the percentage values are examined, it can be seen that uncertainty is resulting from test
offset uncertainty at 80%-90% ratio. In order to reduce uncertainty, it is considered to be paid
attention to certain parameters in measurements and in the design of sensors. It has been seen that
usage of partitioned line laser to reduce the uncertainty, can reduce effects resulting from the laser
line as much as the partition ratio. In addition to this, in the sensor designs of sensor manufacturers,
to make design according to these values which affects uncertainty would reduce the uncertainty
much more.
In sensor design, the thickness of north indicator cursor should be too thin and the radius of its
location should be as large as possible. Likewise, the width of vane's north cursor endpoint should
be very small but its radius should be as large as possible.