Air flow measurements are very important in technological processes. A new air flow measurement method is proposed. The method is based on the interaction of air flow with the end of a fiber waveguide located in the flow. As the result of this interaction, random high frequency vibrations are generated in the fiber waveguide. The stochastic transducers are created for the realization of this method. The stochastic transducer consists of the fiber waveguide, the piezoceramic element and the preamplifie

M. Saunoris

V. Augutis

English

Augutis, V.

Saunoris, M.

JVE International

  VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  203360. A method for air flow measurement using high frequency vibrations   V. Augutis1,  M. Saunoris2  1, 2 Kaunas University of Technology Electronics and Measurements Systems Department Studentu 50-443, 51368 Kaunas, LITHUANIA  E-mail:   1 Vygantas.Augutis@ktu.lt,  2  Marius.Saunoris@ktu.lt  (Received 5 May 2008; accepted 13 June 2008)          Abstract. Air flow measurements are very important in technological processes. A new air flow measurement method is proposed. The method is based on the interaction of air flow with the end of a fiber waveguide located in the flow. As the result of this interaction, random high frequency vibrations are generated in the fiber waveguide. The stochastic transducers are created for the realization of this method. The stochastic transducer consists of the iber waveguide, the piezoceramic element and the preamplifier.  Keywords: Air flow measurement, gas flow measurement, stochastic processes, transducers.  Introduction  Air flow measurements are very important in the industry. Methods that are currently in use can be divided into two groups: aerodynamic and kinematic [1]. Aerodynamic methods are based on the interaction of the force with some artificial obstacle in the flow. The methods of differential pressure, vortex, turbine as well as variable area flow rate measurement are classified as aerodynamic methods [2-4]. The method of the differential pressure is based on the use of constrictive devices (such as diaphragms, nozzles, Venturi nozzles, etc.), which create the difference of pressures. Kinematic measur ment methods are based on the measurement of air flow velocity. If average air flow velocity or its profile in the space is known then the flow rate can be calculated. Thermo-anemometric, electromagnetic, ultrasound, laser flow rate measurement methods are kinematic ones [5-7]. The above-mentioned air flow methods are not able to operate in high-pressure, high-temperature environments. The air flow measurement method proposed in this paper is based on the interaction of the air flow with the end of the fiber waveguide located in the flow [8]. As a result of this interaction, random high frequency vibrations are generated in the fiber waveguide. The intensity of high frequency vibrations depends on the air flow velocity. The stochastic transducers are created for the realization of this method. The purpose of this work is to propose an air flow measurement method, to create a measurement transducer and to investigate its metrological characteristics. The structure and working principle of the stochastic transducer  The stochastic transducer consists of the fiber waveguide, the piezoceramic element and the preamplifier. The fiber waveguide can be made from various materials. In our case the waveguide is composed of a set of thin copper wires. Several fiber waveguides of different l gth were produced and analyzed.  The working principle of the stochastic transducer is based on the fact that air whirls are generated when air flow moves past the end of the fiber waveguide. They cause high frequency vibrations (fluctuations of the pressure) and their propagation in the waveguide. Random high frequency vibrations )(tξ  with power spectrumξG  are generated in the end of the waveguide. High frequency vibrations propagated along the waveguide are converted into voltage with the help of piezoceramic element. Then this voltage is amplified with a preamplifier. The block diagram of the stochastic transducer is shown in Fig. 1.  The power spectrum of the signal of the transducer output is:  ×⋅⋅=22)()(),,,()( ωωωω ξ WOpT KKTVPGG  22)()( ωω AP KK ⋅× ,                                                  (1)  where ),,,( TVPG pωξ  is the power spectrum of high frequency vibrations; pP  is the pressure fluctuation; V is  360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2    VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  204 air flow velocity; T is the temperature; )(ωOK  is the modulus of the acoustical transfer function of the space between the end of the fiber waveguide and the inner surface of the pipe. It depends on the diameter of the pipe, the pressure of the air, the sound speed in the air, and the diameter of the end of the fiber waveguide; )(ωWK  is the modulus of the transfer function of the fiber waveguide; )(ωPK  is the modulus of the transfer function of the piezoceramic element; )(ωAK  is the modulus of the transfer function of the preamplifier.      Fig. 1. Block diagram of the stochastic transducer: ST – stochastic transducer; A – preamplifier; P – piezoceramic element; FW – fiber waveguide; OK  – acoustical transfer function of the space between the end of the fiber waveguide and the inner surface of the pipe; WK  – transfer function of the fiber waveguide; PK  – transfer function of the piezoceramic element; AK  –  transfer function of the preamplifier; PU  – voltage of the output of the piezoceramic element; TU  – voltage of the output of the stochastic transducer  Experimental results and discussion  It can be assumed that the resulting signal at the transducer output is random and has a Gaussian distribution because the elements of fiber waveguide interact with the flow and create elementary random signals at the transducer output. Propagation channel a d air flow velocity will determine the power spectrum of this signal. A measurement system shown in Fig. 2 is formed in order to check this assumption.  A stable air flow is generated supplying air by theair compressor. This air flow is measured simultaneously using the stochastic transducer and the flow meter. A calibrated Venturi nozzle is used for flow measurement. The signals are amplified and visualized in the oscilloscope. Then the signals are measured using the Agilent Technologies digital oscilloscope 54622A with the sampling frequency 200 MHz and the 8-bit analog/digital converter. Afterwards the signals are fed to a computer. The Matlab software was used for data analysis.     Fig. 2. The experimental measurement system: C – air compressor; ST – stochastic transducer; FM – flow meter; AM – amplifier; O – oscilloscope; PC – computer; F – air flap; CB – control block; TU  – voltage of the output of the stochastic transducer  To test whether a single distribution function obtained from an experiment is Gaussian, we run the Jarque-Bera test (Matlab, Statistics Toolbox) for goodness-of-fit at a significance level of 0.01 (99 % confidence level). The Jarque-Bera test evaluates the null hypothesis that t e given sample data has the Gaussian distribution, against the alternative hypothesis that the same sample data does not have a Gaussian distribution. The distribution of the output signal of the stochastic transducer is present d in Fig. 3.    -0.4 -0.2 0 0.2 0.4 0 2 4 6 8 x 10 4 Amplitude, V Number of value 2 1  Fig. 3. The distribution of the output signal of the stochastic transducer – 1; the Gaussian distribution – 2. Results are obtained for the stable air flow velocity   The signal characteristics at the transducer output in the frequency domain as well as in the time domain are important. This paper presents the characteristics of the four created stochastic transducers. The calculated power spectrum densities for different stochastic transducers are given in Fig. 4 and Fig. 6. The signals of the stochastic transducers have resonance character and different shapes of the power spectrum densities as illustrated in Fig. 4 and Fig. 6. They depend upon the parameters of the stochasti  transducers.   360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2    VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  205The relationship between the calculated power spectrum density and air flow velocity is presented in Fig. 4. It is demonstrated that the positions of the frequency band resonances do not depend upon the air flow velocity.   Fig. 4. The relationship between power spectrum density of the stochastic transducer signals and air flow velocity (the parameters of the stochastic transducer are presented in the Table 1 – 1)  Each stochastic transducer has analogous structure but different parameters. The structures of the stochastic transducers are presented in Fig. 6 (b,d,f) and Fig. 8. The values and the parameters of the stochastic transducers are presented in Table 1, Fig. 5 and Fig. 6.   Table 1. The parameters and values of the stochastic transducers  Notations d, mm Shape and a, mm m, mm s, mm l, mm Characteristics 1 4 □     6 6 0.4 40 Figs. 4, 8, 2 1 ○  2.5 2.5 0.1 130 Figs. 6(a), 6(b) 3 4 ○     4 2.5 0.1 90 Figs. 6(c), 6(d) 4 4 □     6 5 0.1 80 Figs. 6(e), 6(f)     Fig. 5.  Stochastic transducers  In order to evaluate the maximum speed of measurement it is necessary to establish the quadratic correlation interval. The measurement duration should be longer than the quadratic correlation interval [9]. For this eason the autocorrelation is calculated and it allows to estimate the necessary minimum measurement duration. The minimum measurement duration ensures statistically reliable and non-correlated measurement result.  The minimum measurement duration (the quadratic correlation interval) is evaluated according to the following equation:  ∫∞=02. )( ττρτ dqk ,                                                  (2)  where qk.τ  is the quadratic correlation interval; )0()()(RR ττρ =  is the standard autocorrelation function. In our case 3. 105.0−⋅≈qkτ s. It can be noted that signals, obtained by dividing the measured signal into time intervals of a length qk.τ , do not correlate with each other [9-10]. The standard autocorrelation function of the stochastic transducer signal is presented in Fig. 7. The measured output signal of the stochastic transducer is a noise type non-stationary signal. It can be described by the root mean square (RMS) value and the envelope [11]. RMS value of the stochastic transducer signal is calcul ted according to the following equation:  ∑=−=NnT nUNRMS12 )(11,                                              (3)  where )(nUT  is the digitized time signal of the stochastic transducer; N is a number of points.  The signal envelope is a slowly varying function, which can be estimated by using various algorithms [11]. The signal envelope is calculated by dividing the output signal of the stochastic transducer into overlapping M-length segments and calculating their RMS:  ,)(11)( 2∑+=−=MrrnT nUMrENV ),1(,...,2,1 −−= mNr      (4)  where M is the length of a segment; )(nUT  is the digitized time signal of the stochastic transducer. The calibration of the stochastic transducer showing the dependence of the output signal RMS of the stochastic transducer on the air flow velocity has been performed. The relationship between measured RMS values of the stochastic transducer signals and air flow velocity is presented in Fig. 8. The RMS values are measured 10 times at the each point of the calibration curve. The measurement duration for each RMS value is 5 ms. The averages of the RMS values ( AVERMS ) are used for the calibration curve (Fig. 8).   360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2    VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  206  (a)   (b)   (c)   (d)   (e)   (f)  Fig. 6. (a), (c), (e) The power spectrum densities for different stochastic transducers; (b), (d), (f) the relationship  between measured RMS values of the different stochastic transducers signals and air flow velocities; (a), (b) first stochastic transducer (Table 1 – 2); (c), (d) second stochastic transducer (Table 1 – 3); (e), (f) third stochastic transducer (Table 1 – 4)      Fig. 7. The standard autocorrelation function of the stochastic transducer signal (the parameters of the stochastic transducer are presented in Table 1 – 1)   360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2    VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  207  Fig. 8. The relationship between measured RMS values (with the uncertainties) of the output signals of the stochastic transducer and air flow velocity (the parameters of the stochastic transducer are presented in Table 1 – 1)    The uncertainties are estimated experimentally and calculated for each point of this curve. The RMS values at each point of the calibration curve are calculated according to:  ∑==NnAVE nRMSNRMS1)(1,                                           (5)  where AVERMS is the average of the RMS values at each point; N is the number of the RMS values.  The standard uncertainty of the measured signal RMS values is calculated in the following way:   ∑=−−=NnAVERMS RMSnRMSNNu12))(()1(1.            (6)  The expanded uncertainty of the measured signal RMS values can be obtained:  RMSEXP uku ⋅= ,                                                   (7)    where k is the coverage factor. The coverage factor will be k =2, providing a level of confidence of approximately 95%. The results of the calculated uncertainties of the RMS values are present d in Table 2 and in Fig. 8. One of the most important transducer properties is its dynamics. The measurement system shown in Fig. 2 is used in order to evaluate the transient response of the stochastic transducer. The air flap opens and closes th  pipe (it is used to change the air flow). Fig. 9 shows the transient response of the stochastic transducer. This transient response enables to define a settling time s . The settling time is used to evaluate the transient respon e characteristic of the stochastic transducer. It is defined as the time for RMS value to vary from 0 – 90 % of steady-state value. For the present stochastic transducer st  is approximately 20 ms as is indicated in Fig. 9. The transient change in the air flow velocity is shorter than thesettling time of the stochastic transducer.  A filter that distinguishes a certain frequency band can be used in order to increase signal-to-noise ratio. In the case of the analyzed transducer (Fig. 4), the best signal-to-noise ratio is equal to 39 if the filter of 30 kHz – 60 kHz frequency band is used.     Fig. 9. Dynamic characteristic of the stochastic transducer (white line indicates the envelope of the measured signal; the parameters of the stochastic transducer are presented in Table 1 – 1).  Table 2. The results of the calculated uncertainties of the RMS values at each point of the calibration curve (Fig. 8) Flow velocity, m/s 4.69 6.48 8.29 8.96 9.77 10.44 10.86 AVERMS , mV 6.10 8.61 23.25 32.52 46.81 67.14 81.26 RMSu ,mV 0.0467 0.1961 0.78 0.87 1.02 1.70 1.86 Coverage factor 2 2 2 2 2 2 2 EXPu , mV 0.0935 0.3922 1.56 1.74 2.05 3.40 3.73 EXPu , % 1.53 4.55 6.71 5.35 4.38 5.06 4.59    360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2    VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716  208 Concluding remarks  A new air flow measurement method was proposed as well as stochastic transducers for air flow measurement were developed. Transducers are based on high-frequency vibrations measurement. It is demonstrated that these stochastic transducers have a simple construction and their working principle is based on the generation of high- frequency vibrations in the fiber waveguide. The stochastic transducers can be used for high-pressure, high temperature environments since fiber waveguide is made from copper. It is estimated that the settling time of stochastic transducer is approximately 20 ms and the accuracy of the measurement of air flow velocity is approximately 7 %. Further work will be devoted to investigate the application of the stochastic transducer for the measurement of the different ranges of air flow velocity. Investigation of the application of the stochastic transducer under different environmental conditions is also in the scope of our future research.  References  [1] Flow Sensors, Available: http://www.sensorsportal.com/HTML/SENSORS/Flow.htm  [2] Upp E. L. and LaNasa P. J. Fluid flow measurement. 2nd ed, Gulf Professional Publishing, 2002.                               [3] Baker R. C. Flow measurement handbook: industrial designs, operating principles, performance, and applications. Cambridge University Press, New York, 2005.  [4] Spitzer D. W. Industrial Flow Measurement. 3rd Edition, ISA-Instrumentation, Systems, and Automation, 2004.  [5] Popa N. C., Potencz I. and Vekas L. Magnetic fluid flow meter for gases. Magnetics, IEEE Transactions on, vl. 30, issue 2, part 1-2, 1994, p. 936–938.   [6] Liptak B. G. Instrument Engineers Handbook, 4th Edition - Process Measurement and Analysis, Vol. 1, ISA/CRC Press, 2003.  [7] Fujita H., Ohhashi T., Asakura M., Yamada M. and Watanabe K. A thermistor anemometer for low-flow-rate measurements. Instrumentation and Measurement, IEEE Transactions on, vol. 44, issue 3, 1995, p. 779–782.  [8] Augutis V. and Saunoris M. The Application of a Stochastic Transducer for Air Flow Measurement. IMTC/06. Proceedings of the 23rd IEEE, 2006, p. 1999–2002.  [9] Mirskij G. J. Estimation of the characteristics of the stochastic processes. Energija, Moscow, 1972. [In Russian].  [10] Bendat J. S. and Piersol A. G. Random Data Analysis and Measurement Procedures. 2nd ed, John Wiley & Sons, New York, 1986.  [11] Augutis V. and Nakutis Z. Measurement of quasistacionary random signal envelope. Proceedings of XVI IMEKO World Congress, Viena, vol. VI, 2000, p. 129-134. 

A method for air flow measurement using high frequency vibrations

Journal of Mechatronics and Artificial Intelligence in Engineering

Journal of Vibroengineering

  VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
203
360. A method for air flow measurement using high frequency vibrations 
 
 
V. Augutis1,  M. Saunoris2  
1, 2 Kaunas University of Technology 
Electronics and Measurements Systems Department 
Studentu 50-443, 51368 Kaunas, LITHUANIA 
 
E-mail:   1 Vygantas.Augutis@ktu.lt,  2  Marius.Saunoris@ktu.lt 
 
(Received 5 May 2008; accepted 13 June 2008) 
 
 
 
 
 
 
 
 
 
Abstract. Air flow measurements are very important in technological processes. A new air flow measurement method is 
proposed. The method is based on the interaction of air flow with the end of a fiber waveguide located in the flow. As the 
result of this interaction, random high frequency vibrations are generated in the fiber waveguide. The stochastic 
transducers are created for the realization of this method. The stochastic transducer consists of the fiber waveguide, the 
piezoceramic element and the preamplifier. 
 
Keywords: Air flow measurement, gas flow measurement, stochastic processes, transducers. 
 
Introduction 
 
Air flow measurements are very important in the 
industry. Methods that are currently in use can be divided 
into two groups: aerodynamic and kinematic [1]. 
Aerodynamic methods are based on the interaction of the 
force with some artificial obstacle in the flow. The 
methods of differential pressure, vortex, turbine as well as 
variable area flow rate measurement are classified as 
aerodynamic methods [2-4]. The method of the differential 
pressure is based on the use of constrictive devices (such 
as diaphragms, nozzles, Venturi nozzles, etc.), which 
create the difference of pressures. Kinematic measurement 
methods are based on the measurement of air flow 
velocity. If average air flow velocity or its profile in the 
space is known then the flow rate can be calculated. 
Thermo-anemometric, electromagnetic, ultrasound, laser 
flow rate measurement methods are kinematic ones [5-7]. 
The above-mentioned air flow methods are not able to 
operate in high-pressure, high-temperature environments. 
The air flow measurement method proposed in this paper is 
based on the interaction of the air flow with the end of the 
fiber waveguide located in the flow [8]. As a result of this 
interaction, random high frequency vibrations are 
generated in the fiber waveguide. The intensity of high 
frequency vibrations depends on the air flow velocity. The 
stochastic transducers are created for the realization of this 
method. 
The purpose of this work is to propose an air flow 
measurement method, to create a measurement transducer 
and to investigate its metrological characteristics. 
The structure and working principle of the stochastic 
transducer 
 
The stochastic transducer consists of the fiber 
waveguide, the piezoceramic element and the preamplifier. 
The fiber waveguide can be made from various materials. 
In our case the waveguide is composed of a set of thin 
copper wires. Several fiber waveguides of different length 
were produced and analyzed.  
The working principle of the stochastic transducer is 
based on the fact that air whirls are generated when air 
flow moves past the end of the fiber waveguide. They 
cause high frequency vibrations (fluctuations of the 
pressure) and their propagation in the waveguide. Random 
high frequency vibrations )(tξ  with power spectrum ξG  
are generated in the end of the waveguide. High frequency 
vibrations propagated along the waveguide are converted 
into voltage with the help of piezoceramic element. Then 
this voltage is amplified with a preamplifier. The block 
diagram of the stochastic transducer is shown in Fig. 1.  
The power spectrum of the signal of the transducer 
output is: 
 
×⋅⋅=
22 )()(),,,()( ωωωω ξ WOpT KKTVPGG  
22 )()( ωω AP KK ⋅× ,                                                      (1) 
 
where ),,,( TVPG pωξ  is the power spectrum of high 
frequency vibrations; pP  is the pressure fluctuation; V is 
 360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2 
 
 
 VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
204 
air flow velocity; T is the temperature; )(ωOK  is the 
modulus of the acoustical transfer function of the space 
between the end of the fiber waveguide and the inner 
surface of the pipe. It depends on the diameter of the pipe, 
the pressure of the air, the sound speed in the air, and the 
diameter of the end of the fiber waveguide; )(ωWK  is the 
modulus of the transfer function of the fiber waveguide; 
)(ωPK  is the modulus of the transfer function of the 
piezoceramic element; )(ωAK  is the modulus of the 
transfer function of the preamplifier.  
 
 
 
 
Fig. 1. Block diagram of the stochastic transducer: 
ST – stochastic transducer; A – preamplifier; P – piezoceramic 
element; FW – fiber waveguide; OK  – acoustical transfer 
function of the space between the end of the fiber waveguide and 
the inner surface of the pipe; WK  – transfer function of the fiber 
waveguide; PK  – transfer function of the piezoceramic element; 
AK  –  transfer function of the preamplifier; PU  – voltage of the 
output of the piezoceramic element; TU  – voltage of the output 
of the stochastic transducer 
 
Experimental results and discussion 
 
It can be assumed that the resulting signal at the 
transducer output is random and has a Gaussian 
distribution because the elements of fiber waveguide 
interact with the flow and create elementary random 
signals at the transducer output. Propagation channel and 
air flow velocity will determine the power spectrum of this 
signal. A measurement system shown in Fig. 2 is formed in 
order to check this assumption.  
A stable air flow is generated supplying air by the air 
compressor. This air flow is measured simultaneously 
using the stochastic transducer and the flow meter. A 
calibrated Venturi nozzle is used for flow measurement. 
The signals are amplified and visualized in the 
oscilloscope. Then the signals are measured using the 
Agilent Technologies digital oscilloscope 54622A with the 
sampling frequency 200 MHz and the 8-bit analog/digital 
converter. Afterwards the signals are fed to a computer. 
The Matlab software was used for data analysis.  
 
 
 
Fig. 2. The experimental measurement system: 
C – air compressor; ST – stochastic transducer; FM – flow meter; 
AM – amplifier; O – oscilloscope; PC – computer; F – air flap; 
CB – control block; TU  – voltage of the output of the stochastic 
transducer 
 
To test whether a single distribution function obtained 
from an experiment is Gaussian, we run the Jarque-Bera 
test (Matlab, Statistics Toolbox) for goodness-of-fit at a 
significance level of 0.01 (99 % confidence level). The 
Jarque-Bera test evaluates the null hypothesis that the 
given sample data has the Gaussian distribution, against 
the alternative hypothesis that the same sample data does 
not have a Gaussian distribution. The distribution of the 
output signal of the stochastic transducer is presented in 
Fig. 3.  
 
 
-0.4 -0.2 0 0.2 0.4 
0 
2 
4 
6 
8 
x 10 4 
Amplitude, V 
N
u
m
be
r 
o
f v
al
u
e 
2 
1 
 
Fig. 3. The distribution of the output signal of the stochastic 
transducer – 1; the Gaussian distribution – 2. Results are obtained 
for the stable air flow velocity 
 
 
The signal characteristics at the transducer output in the 
frequency domain as well as in the time domain are 
important. This paper presents the characteristics of the 
four created stochastic transducers. The calculated power 
spectrum densities for different stochastic transducers are 
given in Fig. 4 and Fig. 6. The signals of the stochastic 
transducers have resonance character and different shapes 
of the power spectrum densities as illustrated in Fig. 4 and 
Fig. 6. They depend upon the parameters of the stochastic 
transducers.  
 360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2 
 
 
 VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
205
The relationship between the calculated power 
spectrum density and air flow velocity is presented in Fig. 
4. It is demonstrated that the positions of the frequency 
band resonances do not depend upon the air flow velocity. 
 
 
Fig. 4. The relationship between power spectrum density of the 
stochastic transducer signals and air flow velocity (the parameters 
of the stochastic transducer are presented in the Table 1 – 1) 
 
Each stochastic transducer has analogous structure but 
different parameters. The structures of the stochastic 
transducers are presented in Fig. 6 (b,d,f) and Fig. 8. The 
values and the parameters of the stochastic transducers are 
presented in Table 1, Fig. 5 and Fig. 6. 
 
 
Table 1. The parameters and values of the stochastic transducers  
Notations d, 
mm 
Shape 
and a, 
mm 
m, 
mm 
s, 
mm 
l, 
mm 
Characteristics 
1 4 □     6 6 0.4 40 Figs. 4, 8, 
2 1 ○  2.5 2.5 0.1 130 Figs. 6(a), 6(b) 
3 4 ○     4 2.5 0.1 90 Figs. 6(c), 6(d) 
4 4 □     6 5 0.1 80 Figs. 6(e), 6(f) 
 
 
 
 
Fig. 5.  Stochastic transducers 
 
In order to evaluate the maximum speed of 
measurement it is necessary to establish the quadratic 
correlation interval. The measurement duration should be 
longer than the quadratic correlation interval [9]. For this 
reason the autocorrelation is calculated and it allows to 
estimate the necessary minimum measurement duration. 
The minimum measurement duration ensures statistically 
reliable and non-correlated measurement result.  
The minimum measurement duration (the quadratic 
correlation interval) is evaluated according to the following 
equation: 
 
∫
∞
=
0
2
.
)( ττρτ dqk ,                                                   (2) 
 
where qk.τ  is the quadratic correlation interval; 
)0(
)()(
R
R τ
τρ =  is the standard autocorrelation function. In 
our case 3
.
105.0 −⋅≈qkτ s. It can be noted that signals, 
obtained by dividing the measured signal into time 
intervals of a length qk.τ , do not correlate with each other 
[9-10]. The standard autocorrelation function of the 
stochastic transducer signal is presented in Fig. 7. 
The measured output signal of the stochastic transducer 
is a noise type non-stationary signal. It can be described by 
the root mean square (RMS) value and the envelope [11]. 
RMS value of the stochastic transducer signal is calculated 
according to the following equation: 
 
∑
=
−
=
N
n
T nUN
RMS
1
2 )(
1
1
,                                              (3) 
 
where )(nUT  is the digitized time signal of the stochastic 
transducer; N is a number of points.  
The signal envelope is a slowly varying function, 
which can be estimated by using various algorithms [11]. 
The signal envelope is calculated by dividing the output 
signal of the stochastic transducer into overlapping M-
length segments and calculating their RMS: 
 
,)(
1
1)( 2∑
+
=
−
=
Mr
rn
T nUM
rENV ),1(,...,2,1 −−= mNr      (4) 
 
where M is the length of a segment; )(nUT  is the digitized 
time signal of the stochastic transducer. 
The calibration of the stochastic transducer showing the 
dependence of the output signal RMS of the stochastic 
transducer on the air flow velocity has been performed. 
The relationship between measured RMS values of the 
stochastic transducer signals and air flow velocity is 
presented in Fig. 8. The RMS values are measured 10 
times at the each point of the calibration curve. The 
measurement duration for each RMS value is 5 ms. The 
averages of the RMS values ( AVERMS ) are used for the 
calibration curve (Fig. 8). 
 
 360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2 
 
 
 VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
206 
 
(a) 
 
 
(b) 
 
 
(c) 
 
 
(d) 
 
 
(e) 
 
 
(f) 
 
Fig. 6. (a), (c), (e) The power spectrum densities for different 
stochastic transducers; (b), (d), (f) the relationships between 
measured RMS values of the different stochastic transducers 
signals and air flow velocities; (a), (b) first stochastic transducer 
(Table 1 – 2); (c), (d) second stochastic transducer (Table 1 – 3); 
(e), (f) third stochastic transducer (Table 1 – 4) 
 
 
 
 
 
Fig. 7. The standard autocorrelation function of the stochastic 
transducer signal (the parameters of the stochastic transducer are 
presented in Table 1 – 1) 
 
 360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2 
 
 
 VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
207
 
 
Fig. 8. The relationship between measured RMS values (with the 
uncertainties) of the output signals of the stochastic transducer 
and air flow velocity (the parameters of the stochastic transducer 
are presented in Table 1 – 1) 
 
 
 
The uncertainties are estimated experimentally and 
calculated for each point of this curve. The RMS values at 
each point of the calibration curve are calculated according 
to: 
 
∑
=
=
N
n
AVE nRMSN
RMS
1
)(1 ,                                           (5) 
 
where AVERMS is the average of the RMS values at each 
point; N is the number of the RMS values. 
 
The standard uncertainty of the measured signal RMS 
values is calculated in the following way:  
 
∑
=
−
−
=
N
n
AVERMS RMSnRMSNN
u
1
2))(()1(
1
.            (6) 
 
The expanded uncertainty of the measured signal RMS 
values can be obtained: 
 
RMSEXP uku ⋅= ,                                                        (7) 
 
 
 
where k is the coverage factor. 
The coverage factor will be k =2, providing a level of 
confidence of approximately 95%. The results of the 
calculated uncertainties of the RMS values are presented in 
Table 2 and in Fig. 8. 
One of the most important transducer properties is its 
dynamics. The measurement system shown in Fig. 2 is 
used in order to evaluate the transient response of the 
stochastic transducer. The air flap opens and closes the 
pipe (it is used to change the air flow). Fig. 9 shows the 
transient response of the stochastic transducer. This 
transient response enables to define a settling time st . The 
settling time is used to evaluate the transient response 
characteristic of the stochastic transducer. It is defined as 
the time for RMS value to vary from 0 – 90 % of steady-
state value. For the present stochastic transducer st  is 
approximately 20 ms as is indicated in Fig. 9. The transient 
change in the air flow velocity is shorter than the settling 
time of the stochastic transducer.  
A filter that distinguishes a certain frequency band can 
be used in order to increase signal-to-noise ratio. In the 
case of the analyzed transducer (Fig. 4), the best signal-to-
noise ratio is equal to 39 if the filter of 30 kHz – 60 kHz 
frequency band is used. 
 
 
 
 
Fig. 9. Dynamic characteristic of the stochastic transducer (white 
line indicates the envelope of the measured signal; the parameters 
of the stochastic transducer are presented in Table 1 – 1). 
 
Table 2. The results of the calculated uncertainties of the RMS values at each point of the calibration curve (Fig. 8) 
Flow velocity, m/s 4.69 6.48 8.29 8.96 9.77 10.44 10.86 
AVERMS , mV 6.10 8.61 23.25 32.52 46.81 67.14 81.26 
RMSu ,mV 0.0467 0.1961 0.78 0.87 1.02 1.70 1.86 
Coverage factor 2 2 2 2 2 2 2 
EXPu , mV 0.0935 0.3922 1.56 1.74 2.05 3.40 3.73 
EXPu , % 1.53 4.55 6.71 5.35 4.38 5.06 4.59 
  
 360. A METHOD FOR AIR FLOW MEASUREMENT USING HIGH FREQUENCY VIBRATIONS. V. AUGUTIS1,  M. SAUNORIS2 
 
 
 VIBROMECHANIKA.  JOURNAL OF  VIBROENGINEERING.  JUNE   2008,   VOLUME  10,  ISSUE  2,  ISSN 1392-8716 
 
208 
Concluding remarks 
 
A new air flow measurement method was proposed as 
well as stochastic transducers for air flow measurement 
were developed. Transducers are based on high-frequency 
vibrations measurement. It is demonstrated that these 
stochastic transducers have a simple construction and their 
working principle is based on the generation of high- 
frequency vibrations in the fiber waveguide. The stochastic 
transducers can be used for high-pressure, high 
temperature environments since fiber waveguide is made 
from copper. It is estimated that the settling time of 
stochastic transducer is approximately 20 ms and the 
accuracy of the measurement of air flow velocity is 
approximately 7 %. 
Further work will be devoted to investigate the 
application of the stochastic transducer for the 
measurement of the different ranges of air flow velocity. 
Investigation of the application of the stochastic transducer 
under different environmental conditions is also in the 
scope of our future research. 
 
References 
 
[1] Flow Sensors, Available: 
http://www.sensorsportal.com/HTML/SENSORS/Flow.htm 
 
[2] Upp E. L. and LaNasa P. J. Fluid flow measurement. 2nd 
ed, Gulf Professional Publishing, 2002. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
[3] Baker R. C. Flow measurement handbook: industrial 
designs, operating principles, performance, and 
applications. Cambridge University Press, New York, 2005. 
 
[4] Spitzer D. W. Industrial Flow Measurement. 3rd Edition, 
ISA-Instrumentation, Systems, and Automation, 2004. 
 
[5] Popa N. C., Potencz I. and Vekas L. Magnetic fluid flow 
meter for gases. Magnetics, IEEE Transactions on, vol. 30, 
issue 2, part 1-2, 1994, p. 936–938.  
 
[6] Liptak B. G. Instrument Engineers Handbook, 4th Edition 
- Process Measurement and Analysis, Vol. 1, ISA/CRC 
Press, 2003. 
 
[7] Fujita H., Ohhashi T., Asakura M., Yamada M. and 
Watanabe K. A thermistor anemometer for low-flow-rate 
measurements. Instrumentation and Measurement, IEEE 
Transactions on, vol. 44, issue 3, 1995, p. 779–782. 
 
[8] Augutis V. and Saunoris M. The Application of a 
Stochastic Transducer for Air Flow Measurement. 
IMTC/06. Proceedings of the 23rd IEEE, 2006, p. 1999–
2002. 
 
[9] Mirskij G. J. Estimation of the characteristics of the 
stochastic processes. Energija, Moscow, 1972. [In Russian]. 
 
[10] Bendat J. S. and Piersol A. G. Random Data Analysis and 
Measurement Procedures. 2nd ed, John Wiley & Sons, New 
York, 1986. 
 
[11] Augutis V. and Nakutis Z. Measurement of 
quasistacionary random signal envelope. Proceedings of 
XVI IMEKO World Congress, Viena, vol. VI, 2000, p. 
129-134. 


Journal of Mechanical Engineering, Automation and Control Systems

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A method for air flow measurement using high frequency vibrations

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