INSTITUTE OF PHYSICS PUBLISHING
MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 16 (2005) 548–555
doi:10.1088/0957-0233/16/2/030
An ultrasonic air temperature
measurement system with self-correction
function for humidity
Wen-Yuan Tsai1,2, Hsin-Chieh Chen1 and Teh-Lu Liao1
1
Department of Engineering Science, National Cheng Kung University, Tainan, 701 Taiwan,
Republic of China
2
Department of Electrical Engineering, Kao Yuan Institute of Technology, Kaohsiung,
821 Taiwan, Republic of China
E-mail: [email protected]
Received 15 June 2004, in final form 20 October 2004
Published 21 January 2005
Online at stacks.iop.org/MST/16/548
Abstract
This paper proposes an ultrasonic measurement system for air temperature
with high accuracy and instant response. It can measure the average
temperature of the environmental air by detecting the changes of the speed
of the ultrasound in the air. The changes of speed of sound are computed
from combining variations of time-of-flight (TOF) from a binary frequency
shift-keyed (BFSK) ultrasonic signal and phase shift from continuous waves
[11]. In addition, another proposed technique for the ultrasonic air
temperature measurement is the self-correction functionality within a highly
humid environment. It utilizes a relative humidity/water vapour sensor and
applies the theory of how sound speed changes in a humid environment. The
proposed new ultrasonic air temperature measurement has the capability of
self-correction for the environment variable of humidity. Especially under
the operational environment with high fluctuations of various humidity
levels, the proposed system can accurately self-correct the errors on the
conventional ultrasonic thermometer caused by the changing density of the
vapours in the air. Including the high humidity effect, a proof-of-concept
experiment demonstrates that in dry air (relative humidity, RH = 10%)
without humidity correction, it is accurate to ±0.4 ◦ C from 0 ◦ C to 80 ◦ C,
while in highly humid air (relative humidity, RH = 90%) with
self-correction functionality, it is accurate to ±0.3 ◦ C from 0 ◦ C to 80 ◦ C
with 0.05% resolution and temperature changes are instantly reflected
within 100 ms.
Keywords: ultrasonic sensors, humidity sensors, temperature measurement
1. Introduction
In many industrial processes, such as refining, roasting etc,
the online control of temperature is often very important for
saving energy, guaranteeing product quality and raising the
productivity etc. Up to now, thermocouples and radiation
thermometers have been the two main methods for measuring
temperature in industry. Accurate and sensitive as the
thermocouple is, it cannot work durably at high temperature
and it is hard to realize online control. With the development
0957-0233/05/020548+08$30.00
of photoelectronic techniques, great improvements have been
made in radiation thermometers. However, because of its
susceptibility to fume and mist, accurate measurement is
difficult to obtain in the above hostile environments.
Over the past several decades, ultrasonic thermometry has
been evolving as a new temperature measurement technology
for environments where thermocouples, radiation pyrometers
and other conventional instruments have failed to operate
satisfactorily. Its principle is that the velocity of sound in
any object is a function of temperature, so that, in an ideal gas,
© 2005 IOP Publishing Ltd Printed in the UK
548
An ultrasonic air temperature measurement system with self-correction function for humidity
the velocity is directly proportional to the square root of the
absolute temperature, in most liquids the dependence is linear,
and in solid objects the velocity generally decreases with the
increment of the temperature. Thus, if the velocity of sound
is measured, the temperature is measured [1].
Therefore, the high-speed ultrasonic thermometer is
designed for measuring the temperature of high-temperature
gas streams. The areas of application include the heat power
industry, plasmatrons or other energy equipment, the chemical
industry, development and research of jet engines, etc. The
major advantages of the ultrasonic thermometer are its high
operating speed, reaching 1500 measurements per second, and
complete automation of measuring process [2].
Others have explored an ultrasonic method of sensing
cabin air temperature that could lead to automatic climate
control (ACC) with improved thermal comfort. Perceived
thermal comfort is better correlated with breath-level
temperature than it is with the output of the conventional in-car
sensor. To sense bulk air temperature, a method was proposed
transparent to the occupant—to send a pulse of ultrasound
through the air [3, 4, 11].
The most common sensors for air temperature are usually
sensor-by-contact. They rely on the sensors to contact the air
and use its radiant energy to cause changes in their physical
characteristics. This type of sensor usually does not respond
instantly and their range of measurement is limited. Thus
they are not ideal for dynamic tracking measurements of fast
changing temperature.
The speed of sound in gas has been widely explored. It is
commonly understood that the speed of sound is affected by
temperature, pressure, relative humidity and the constituents
of the air [5]. The theoretical expression for the speed of sound
c in an ideal gas is
γP
c=
(1)
ρ
where P is the ambient pressure, ρ denotes the gas density and
γ is the ratio of the specific heat of gas at constant pressure to
that at constant volume.
In an ideal gas, equation (1) may be rewritten as
1.4RT
c=
(2)
M
where R is the universal gas constant, T is the absolute
temperature and M is the mean molecular weight of the air.
√
From equation (2), we know c is proportional to T .
That is why the techniques of measuring the temperature of
air on the propagation path by sound speed are widely adopted
[6, 7].
All previous discussion assumed dry air. However,
moisture affects the speed of sound by changing the density
of the air and the mean molecular weight, as shown in
equations (1) and (2). Moist air is less dense than dry air
(not particularly obvious), so ρ in equation (1) gets smaller.
This causes an increase in the speed of sound. Moisture
also causes the specific-heat ratio to decrease, which would
cause the speed of sound to decrease. However, the decrease
in density dominates, so the speed of sound increases with
increasing moisture. In this paper, we propose an ultrasonic
air temperature measurement system with self-correction for
humidity. Furthermore, it is a contactless sensor and has an
instant response.
2. Correction for humidity
Two terms in equation (2) must be modified to accurately
include the effects of moisture (water vapour) on the speed
of sound. These are the specific-heat ratio γ (1.4 for dry air)
and M, the average molecular weight of the different types
of molecules in the air. Development of each of these terms
follows [8–10]. The terms R (universal gas constant) and
T (absolute temperature) remain unchanged.
The specific-heat ratio can be expressed as an exact
fraction by letting d equal the number of degrees of freedom
for the air molecules. This gives
d +2
γ =
.
(3)
d
Since the composition of dry air is mostly two atom molecules,
it is said to be a diatomic gas. Diatomic gases have five degrees
of freedom, three translational and two rotational; thus d = 5
and γ = 1.4, for dry air.
If h is defined to be equal to the fraction of molecules
that are water, then the presence of water (with six degrees
of freedom) causes the average number of degrees of freedom
per molecule to increase to 5 + h. Equation (3) can now be
rewritten to include the effects of moisture for air as
7+h
γw =
.
(4)
5+h
It is noted that equation (4) is an alternative but
equivalent expression to Humphreys’ equation as used in
thermodynamics [8].
The average molecular weight of air decreases with added
moisture. To see this, M is calculated first for dry air. Dry air
composition is
• 78% nitrogen (molecular weight = 28)
• 21% oxygen (molecular weight = 32)
• 1% argon (molecular weight = 40)
for a total molecular weight equal to
M = (0.78)(28) + (0.21)(32) + (0.01)(40) = 29.
The presence of water (with a molecular weight of 18)
causes the total average molecular weight to decrease to
29 − (29 − 18)h, or
Mw = 29 − 11h.
(5)
Equations (4) and (5) modify the two terms from equation (2)
affected by the addition of water vapour to air. Both are a
function of the introduced water molecule fraction h. Relative
humidity RH (expressed as a percentage) is defined such that
0.01RH e(T )
h=
(6)
p
where p equals ambient pressure (1.013 × 105 Pa for 1 atm
reference pressure) and e(T ) is the vapour pressure of water
at temperature T . For temperature values in degrees Celsius,
representative values of e(T ) are
e(5) = 872 Pa
e(10) = 1228 Pa
e(15) = 1705 Pa
e(20) = 2338 Pa
e(30) = 4243 Pa
e(40) = 7376 Pa.
To express the percentage increase in the speed of sound due
to relative humidity all that remains is to take the ratio of the
549
W-Y Tsai et al
T[deg C]
CHANGE IN VELOCITY (%)
1.2
Thermocouple
e-Readout
T=40
1.1
To PC
1.0
0.9
0.8
Receiver
0.7
Transmitter
T=30
0.6
Temperature/Humidity
Control Chamber
0.5
0.4
T=20
0.3
T=15
T=10
T=5
0.2
0.1
0.0
0
10
20
30
40
50
60
70
80
90
Preamplifier and
Gain-Controlled
Amplifier
Transmitted
Signal
Source
Power
Amplifier
89c51
Single Chip
Microprocessor
LCD
100
RELATIVE HUMIDITY IN PERCENT (RH%)
Figure 1. Relative humidity versus percentage change in speed of
sound as a function of temperature.
wet and dry speeds, subtract 1, and multiply by 100. Since
both wet and dry speed terms involve the same constant terms
(R and T), their ratio will cause these to cancel, giving the
increase in sound speed c(%)
√
cw
γw RT /Mw
c(%) =
− 1 × 100 = √
− 1 × 100
cd
γd RT /Md
γw
= 455.13
− 100.
(7)
Mw
Equation (7) is plotted in figure 1 as a function of relative
humidity for six temperature values. Figure 1 shows the
percentage increase in the sound speed due to relative humidity
only; the temperature values are for accurately specifying the
relative humidity.
RS232
Frequency
Detector
To accurately measure the temperature of the environmental
air, we use the effect of humidity on the speed of sound
stated above and combine the technique of transmit/receipt
ultrasonic signals of binary frequency shift-keyed (BFSK) and
continuous waves and obtain the average air temperature from
the data of time-of-flight (TOF) and phase shift (PS) [11–
13]. The ultrasonic sensor system for temperature is shown in
figure 2. An ultrasonic transmitter is installed on the righthand side of the temperature/humidity-controlled chamber,
the receiver is on the left-hand side. The distance between the
transmitter and receiver is 100 cm so that the average of the
environmental air temperature can be measured.
3.1. TOF calculation
In figure 3, the elapsed time t, which is the travel time of the
signal from the transmitter to the receiver, can be calculated as
t = t2 − t1 where t1 is the time when the transmitted signal
changes frequency from f1 to f2 , and t2 is the time when
the corresponding received signal changes frequency from f1
to f2 . The speed of sound can be expressed by c = L/t,
where L is the distance between the transmitter transducer and
receiver transducer.
Digital
Phase Meter
40/42kHz
continuous wave
PC
Detection
&
Calibration
Figure 2. Block diagram of the ultrasonic temperature measurement
system.
Amplitude
∆t
t1
t2
t
0
f1
f2
Transmitted signals
f1
f2
Received signals
Figure 3. Transmitted signals and received signals.
3. Ultrasonic measurement of temperature
550
Relative Humidity/
Water Vapor Pressure
e-Readout
T1
f1
Transmitted signals
Received signals
θ1
f1
T2
θ2
f2
f2
Figure 4. Illustration of the phase shifts θ1 and θ2 .
3.2. Phase shift detection
The detection of the phase shift is based on the two-frequency
continuous wave method of ultrasonic distance measurement
[12]. The phase shifts of θ1 and θ2 can be detected by
the received signals corresponding to the transmitted signals.
Figure 4 shows a continuous wave with frequency f1 and a
received signal with frequencies f1 and f2 . Phase shift θ1
is the difference in phase between the continuous wave and
the received signal at f1 . Phase shift θ1 can be calculated
as θ1 = 2π(t2 − t1 )/T1 , where T1 is the period of the
received signal with frequency f1 . Similarly, phase shift θ2 is
the difference in phase between the continuous wave and the
received signal at frequencyf2 . The following will calculate
An ultrasonic air temperature measurement system with self-correction function for humidity
∆θ
λ
2π(6.28)
#n
π(3.14)
0 0.5 1
n-2 n-1
n n+1
Distance
L
Figure 5. Relation between L = c × t and L = (n − 1) × λ +
(θ/2π ) × λ.
the speed of sound by comparing the two phase shifts.
Note that the distance between the transmitter transducer and
receiver transducer remains unchanged.
We have
θ1
c
L = n1 +
(8)
×
2π
f1
θ2
c
L = n2 +
× .
2π
f2
(9)
Here Lis the distance between the two transducers, n1 and n2
are integers.
Due to the difference in frequencies, the phase shift can
be deduced from (8) and (9) as follows:
f
θ = 2π × L ×
(f = f1 − f2 ).
(10)
c
The integers n have only two possible values: n1 = n2 and
n1 = n2 + 1. So the difference of the phase shifts can be
defined by the following algorithm:
Figure 6. Block diagram of the transmitted signal source.
From equation (2) we know the temperature in degrees Celsius
is
c 2
−1 .
(13)
T = 273.15 ×
331.45
This equation does not consider the variable of humidity. From
equation (7) we know the sound speed increase due to humidity
increase is c. So to include the effect of humidity on the
sound speed, the sound speed equation would become
cc = c ×
1
.
1 + c
The calculation for temperature would become
cc 2
Tc = 273.15 ×
−1
331.45
(14)
(15)
where cc is the speed of sound with humidity effect correction
and Tc is the temperature with humidity effect correction.
1. if θ1 > θ2 , θ = θ1 − θ2 ,
2. if θ1 < θ2 , θ = θ1 + 2π − θ2 .
Hence
4. System implementation
c=
θ
2π
L
×
1
f
(11)
.
The variation of the ultrasonic velocity can be uniquely
determined by the difference of the phase shifts (θ) if
the maximum variation does not exceed one period of the
frequency difference (f ). Otherwise phase ambiguity will
occur. The minimum resolution and the maximum range of
the temperature measurement are determined by the choice of
frequencies (f1 , f2 ).
3.3. Temperature calculation
The distance L can be expressed as L = c × t where t
is TOF. In figure 5, the distance L is divided into regions
[(n − 1)λ, nλ] (n = 1, 2, 3, . . .), λ is the
wavelength of fc .
× f
The distance L can be expressed as L = (n − 1) + θ
2π
where n is an integer. The region defined by [(n − 1)λ, nλ]
is called #n region. The n − 1 integer can be obtained by an
integer operation Int(t × f ). The speed of sound can then
be expressed as
c= L
Int(t × f ) +
θ
2π
×
1
f
.
(12)
Figure 2 is a block diagram of the complete system which
consists of a temperature/humidity-controlled chamber, a
thermocouple-based thermometer, a relative humidity/water
vapour pressure meter, two acoustic transducers with matching
exponential horns, a signal generation system, power amplifier,
preamplifier and gain-controlled system, frequency detector
and digital phase meter. The thermocouple is used to measure
the air temperature and compare the measurement with the
output of the ultrasonic system. A microprocessor controls
the operation of the entire system and a PC will examine the
measurement result and perform calibration.
4.1. Hardware
4.1.1. Transmitted signal source. The transmitted pulse is
made up of two sinusoids (40 and 42 kHz). Figure 6 shows a
crystal oscillator circuit used to generate a steady signal with
a base frequency of 80 MHz. The divisors of two dividers are
set at 2000 and 1904 which is applied to the base frequency.
Two frequencies 40 kHz and 42 kHz are then produced and
sent to the multiplexer (MUX). The MUX is controlled by an
89c51 microprocessor.
551
W-Y Tsai et al
Figure 7. Block diagram of the frequency detector.
The thermocouple voltage is converted into a temperature
reading with a Testo 946 thermometer. The accuracy in the
specification of this instrument is said to be ±0.2 ◦ C. We
use an ice–water bath to check the accuracy. The difference
from the actual temperature at 0 ◦ C was + 0.1 ◦ C within the
claimed accuracy. The output of the thermometer is sent to
a PC used as the standard temperature. The measurement of
the relative humidity/water vapour pressure meter is by Sable
System RH-200 meter (accuracy±1%). Therefore, the PC
has t, the elapsed time of the ultrasound, phase shift data
and the temperature measured by the thermocouple and the
relative humidity/water vapour pressure measured by the gas
sensor. From these data, the PC can calculate the errors of the
temperature measurement and build up a calibration system.
4.2. Software
Figure 8. Block diagram of the digital phase meter.
4.1.2. Preamplifier and gain-controlled amplifier. The
bandwidth of the ultrasonic transducers used in our system
is narrow.
To reduce error from acoustic attenuation,
the gain of the amplifier must dynamically adjust as the
frequency of the ultrasound changes. Therefore, the error
incurred from acoustic attenuation is minimized in the gaincontrolled amplifier by keeping the received signal amplitude
dynamically constant.
4.1.3. Frequency detector. Figure 7 shows the block diagram
of the frequency detector. The frequency detector detects the
time when the frequency of the received signal changes from
f1 (40 kHz) to f2 (42 kHz). The detected time is then used by
the microprocessor to calculate TOF.
4.1.4. Digital phase meter. The phase shift is transformed
into pulse width by two D-type flip-flops, as shown in figure 8.
An 80 MHz signal is used to count the pulse width. The
resolution of the phase metre is 0.05% for a 40 kHz signal.
Finally, the counter is cleared by a reset signal generated by
the microprocessor for counting the next phase shift.
4.1.5. 89c51 single-chip microprocessor. The measurement
system is controlled by an 89c51 single-chip microprocessor
(Atmel, made in USA). The functions of the microprocessor
include controlling the BFSK signals of the ultrasound,
obtaining the digital phase shift and humidity/vapour pressure
data, calculating the TOF and the air temperature and
displaying it.
4.1.6. Calibration system. As shown in figure 2, a chamber
with constant temperature/humidity inside has an internal fan
to maintain the inside air temperature/humidity uniform. A
thermocouple measures the air temperature inside the chamber.
552
The algorithm of the software program in the microprocessor
can be explicated by the flowchart shown in figure 9. First,
the 89c51 microprocessor will fetch the actual temperature T1
measured by the thermocouple and the relative humidity/water
vapour pressure meter measured by the sensor from the PC.
Next, it will calculate the increase in sound speed due to
the increased humidity c, assign the transmitted signal,
adjust the gain-controlled amplifier, wait for the interrupt from
either the frequency detector or the digital phase metre to
calculate the TOF, obtain θ1 and θ2 and calculate the corrected
speed of sound cc and the temperature T2 . Then, it will
compare T1 with T2 . If |T2 − T1 | < 1 ◦ C, it will display T2 on
the LCD. Otherwise, the PC will recalculate according to the
temperature data and humidity variables from the calibration
system. If the waiting time is longer than 50 ms, 89c51 will
reassign the transmitted signal. TOF, θ1 , θ2 , c and cc are all
sent to the PC via the RS232 interface of the 89c51.
5. Experimental results and discussions
5.1. Ultrasonic experiment
To collect data, we first measure the air temperature
and humidity/vapour pressure in the chamber with the
thermocouple and gas sensor. Secondly, three times we
record the TOF of the BFSK ultrasonic pulse in the chamber,
the θ1 and θ2 from continuous waves. Then, we measure
the air temperature and humidity/vapour pressure with the
thermocouple and gas sensor for a second time. Finally, we
compare the average of the three TOF, θ1 and θ2 measurements
with the average of the two thermocouple measurements. Both
can represent the air temperature at the same point of time, i.e.
halfway through the measurement cycle. From 0 ◦ C to 80 ◦ C
with 1 ◦ C as the interval, we will repeat the measurement
and record the data at different temperatures. Using this
measurement system and calculating the speed of sound with
equation (12), we can obtain the average temperature of the
air on the propagation path.
5.2. Experimental results
Figure 10 shows, from 0 ◦ C to 80 ◦ C, the data diagram of the
temperature measured by the ultrasonic thermometer without
humidity correction and the actual temperature measured
An ultrasonic air temperature measurement system with self-correction function for humidity
Figure 9. The flowchart of the software.
0.4
Error Temperature [deg C]
Ultrasonic Temperature [deg C]
80
60
40
20
0.2
0.0
-0.2
-0.4
0
0
20
40
60
80
0
20
40
60
Thermocouple Temperature [deg C]
Thermocouple Temperature [deg C]
(a )
(b)
80
Figure 10. (a) At relative humidity = 10%, without humidity correction, a logged data graph of the actual thermocouple temperature versus
calculated ultrasonic temperature with humidity correction. (b) The plot of temperature error.
by thermocouple, when the relative humidity RH of the
environment is 10%. The maximum error is ±0.4 ◦ C.
Figure 11(a) shows, from 0 ◦ C to 80 ◦ C, the data diagram
of the temperature measured by the ultrasonic thermometer
without humidity correction and the actual temperature
measured by thermocouple, when the relative humidity RH
of the environment is 90%. From the diagram, we can
observe that the temperature measured by the ultrasonic
553
80
130
120
110
100
90
80
70
60
50
40
30
20
10
0
Ultrasonic Temperature [deg C]
Ultrasonic Temperature [deg C]
W-Y Tsai et al
0
10
20
30
40
50
60
70
Thermocouple Temperature [deg C]
70
60
50
40
30
20
10
0
0
80
80
(a)
(a )
45
0.3
Error Temperature [deg C]
Error Temperature [deg C]
10
20
30
40
50
60
70
Thermocouple Temperature [deg C]
40
35
30
25
20
15
10
5
0.2
0.1
0.0
-0.1
-0.2
-0.3
0
0
10 20 30 40 50 60 70
Thermocouple Temperature [deg C]
80
0
10
20
30
40
50
60
70
Thermocouple Temperature [deg C]
80
(b )
(b )
Figure 11. (a) At relative humidity = 90%, without humidity
correction, a logged data graph of the actual thermocouple
temperature versus calculated ultrasonic temperature without
humidity correction. (b) The plot of temperature error.
Figure 12. (a) At relative humidity = 90%, with humidity
correction, a logged data graph of the actual thermocouple
temperature versus calculated ultrasonic temperature with humidity
correction. (b) The plot of temperature error.
thermometer is far higher than the actual temperature because
of the humidity effect. The errors are shown in figure 11(b).
As the temperature rises, the error increases. When the
actual temperature is 80 ◦ C, the temperature measured by
the ultrasonic thermometer without humidity correction is an
astounding 124.8 ◦ C. The reason for this large error is that the
relative humidity in the environment caused an increase in the
speed of sound.
Figure 12(a) shows the data diagram of the temperature
measured by ultrasonic thermometer with humidity correction
and the actual temperature measured by thermocouple, when
the relative humidity RH of the environment remains 90%.
Figure 12(b) shows the errors between these two measured
temperatures. The standard error of measurement is calculated
as follows:
n
[RP (i) − P P ]2
SE = (16)
n
i
5.3. Discussions
where RP is the temperature of the ultrasonic measurement,
P P is the temperature measured by thermocouple, n is the
number of measurements. The average error is 0.19 ◦ C and
the standard error is 0.24 ◦ C. Through repeated experiments,
if the temperature is under 80 ◦ C, the difference between
the ultrasonic measurement and the actual temperature
consistently remains within ±0.3 ◦ C.
554
We have established a new ultrasonic air thermometer with
the function of humidity correction. Our system successfully
combines the techniques of TOF, PS and humidity sensor.
With the transmission of BFSK signals, upon receiving the
ultrasonic pulse, the TOF is readily calculated by the time the
change between each discrete frequency occurs. To achieve
higher accuracy, continuous wave transmission is used to
calculate the phase shift between the transmitting and receiving
signals.
Phase shift operation offers a special advantage by
eliminating a class of attenuation problems that often
accompany short-burst transmissions which go through
nonlinear signal distortion during start up as a result
of transmitting transducer mechanical spring coefficients
producing audio signals with slow-onset envelopes. The slow
onset makes the exact signal start time unclear to the receiver.
Continuous wave transmission has similar start/stop envelope
problems. But during continuous operation these problems
are gone. With the help of a humidity sensor, the error
caused by environmental humidity is effectively corrected in
our ultrasonic thermometer system.
From the experiments, the error between the actual
temperature measured by thermocouple and the temperature
measured by our system is only ±0.3 ◦ C. This is the result
An ultrasonic air temperature measurement system with self-correction function for humidity
when the system repeats the measurement every 0.1 s. This
level of accuracy with the speed of ultrasonic system detection
is more than adequate for average temperature control systems.
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