- Email: [email protected]
Optical fibre sensor for proses tomography
Copyright to IFAC Artificial Intelligence in Real-Time Control, Kuala Lumpur, Malaysia, 1997
Optical fibre sensor for proses tomography R Abdul Rahim 1, R G Green 2 1.
2.
Applied Control Panel., Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Locked Bag 791, 80990 lohor Bahru, lohor, Malaysia. Fax 075566272. Email : [email protected] School of Engineering IT, Sheffield Hallam University, Pond Street, Sheffield, SI 1WB, England.
~~
-
-,-=-
~-" " -
-
-
-
. . .,. - == --====- --
Abstract This paper describes an investigation into the use of optical fibre sensors in a tomographic measurement system designed to measure the flow of dry solids in gravity drop and pneumatic conveyors. A simple model of the system is provided and used to predict the response of individual sensors and the full system. Results are provided which show the model is acceptable. The system is used to provide tomographic images of solid concentration within a gravity conveyor.
Figure 1. The arrangement of optical fibres to provide a projection In the experiments reported in this paper two orthogonal projections are used (figure 2)
Copyright © 1998 IFAC
1 Introduction Process tomography [1] is a measurement technique that is being developed for measurement in two and multicomponent flows . These measurement systems use distributed groups of identical sensors, termed arrays, to investigate the physical properties of the material and its distribution within a container, e.g. a pneumatic conveyor, in real time [2] . Most of the tomography systems being investigated aim to provide concentration distributions of moving components of interest within the measurement section in the form of a visual image, much like an x-ray picture of hand for example, which is updated at a refresh rate dependent upon the process being investigated [3]. However, the long term aim is to provide flow information such as mass flow rate, which will be calculated by combining both concentration and velocity profiles.
Figure 2 Two orthogonal projections across the pipe cross-section The pipe in which the sensors are mounted has a nominal bore of 81 mm with a sensor spacing of 5 mm. This spacing means, with an optical fibre diameter of 1 mm, that approximately one fifth of the cross-section is directly interrogated, the remaining four fifths not being in a direct path between a source and its receiver, though there may be some output due to the beam spreading out from the transmitter fibre due to its optical aperture and light scattering by the particles. The effects of diffraction and scattering are ignored, because the primary effect is attenuation of optical energy by particles intercepting the beam. Thus each fibre is taking only a sample measurement of the particles flowing in the pipe. However, it is assumed that each fibre produces readings which represent a realistic sample of the solids passing through the space at each side of the fibre.
2 System model The measurement system (section 3) uses thirty-two optical fibre transmitters and receivers. Each transmitter is aligned with a specific receiver and the resulting sensor is tenned a transmitter/receiver pair. A sensor interrogates a finite section of the measurement section as shown in figure 1. Each sensor provides a view. Parallel sensors provide a projection.
To be able to predict the output of any sensor it is necessary to detennine the amount of the
531
pipe cross-section it interrogates. Also, the total volume interrogated by all the fibres determines the percentage cross-section of the conveyor which is being sampled. The volume sampled by a fibre is its area (diameter 1 mm) multiplied by the optical path length within the conveyor. From figures 1 and 2, it is obvious that individual path lengths are a function of the sensor position within the measurement section. The path lengths are determined from scale drawings. The volume being monitored by each projection of sixteen views, V 16 is
VT = =
" Jr-
Figure 4. The effect of baffle position on the predicted optical path length These calculations determine the voltage profile that should arise from sensors arranged around the circumference of the conveyor. The aim of the project described in this paper is to use these voltages to generate tomographic images of the cross-section of the conveyor. This is achieved using a simple back projection algorithm based on sensitivity maps.
15 (Lpath length)
4 0 796 mm'
And the total volume monitored by both 3 projections is 1600 mm . The vertical flow pipe (figure 8) has a bore of 81 mm, so approximately 30% of the pipe cross section is monitored.
For a collimated optical system, the sensitivity map is related to the beam path within the pipe. The pipe is projected onto a rectangular array of 32x32 pixels. Pixels outside the pipe will not contribute to the measurement so have a sensitivity value of zero. If the beam of the sensor being considered passes through a pixel within the pipe the pixel has sensitivity one, otherwise zero. For example the sensitivity or matrix map for sensor 2 is shown in figure 5. For the system described within this paper there are thirty two sensitivity maps. This neglects that some pixels are not completely square (should contribute less than unity) and the effects of beam scattering contributing to the outputs of neighbouring sensors, however, the results from these effects are small [9] .
Signal processing of the received beams results in a voltage which increases with increased solid flow rate, i.e. the more particles that intersect a beam the greater the Voltage. The assumption made in this paper is that the relationship between solid concentration passing through a beam and the corresponding sensor output voltage is linear. Thus the total mass flow rate is given by equation 1. 3 I
V Tolal =
L
31
V
k
i "" 0
m L P i ::: 0
eq(l) Continuing with this assumption, for a given uniform flow rate the output voltage from each sensor will be directly proportional to it's optical path length. The theoretically predicted sensor outputs for a uniformly distributed solid flow are shown in figure 3.
-
s.... or'1
x _ 0 0 o 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0
0
0
1
1
1
1
1
0 0 0 0 0 0 0
o
0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
00 0 0 0 0 o 0 0 0 0 0 o 0 0 0 o 0 0 0 0 0 o 0 o 0 0 0 0 0 0 0 o 0 0 o 0 0 o 0 0 o 0 0 o 0 0 0
0 0 0 0 0 0 00 0 0 0 o o 0 o 0 0 0
0 o 0 0 o 0 0 o 0 0 0 0 o
0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 T\tIOK*
1
0 1
1
000 0 0 0
0 0 0 0 0 0 0 0 0 0 o 0
"enslMty mllP (Senior 2)
Figure 5. Sensitivity map for sensor number 2
Figure 3. The predicted sensor readings for
For the back projection calculation [10] the sensor voltage Vi is multiplied by its sensitivity matrix. Corresponding elements of the images arising from the thirty two calculations are summed and the combined value provides the output concentration
uniform flow If the effective path length is reduced, say by a baffle as shown in figure 4, the method described above may be used to predict the expected sensor output voltages.
532
matrix. In practice, there are only two sensor voltages which contribute to the final , individual pixels' values. These correspond to the pixel at the intersection of the X and Y sensor beams.
has little effect on the velocity of the particles when they arrive at the measurement section. However, due to particle-particle and particlewall collisions, the particles are not excluded completely from the areas masked by the bafile.
3 The measurement system The measurement system consists of thirty two transmitter-receiver pairs. Light from a halogen bulb is conducted into the measurement cross-section via an optical fibre. The optical axis of the transmitter fibre is aligned with the optical axis of the receiving fibre. Light energy from the receiving fibre is converted into electrical energy by a current to voltage converter. The voltage is amplified and conditioned to produce a linear response between solids concentration and voltage. The conditioned signal is sampled to produce a digital signal in a form suitable for further processing in the personal computer.
screw feeder
+- positimof bolBe bolBe inser1ed fr(ltl this dir~on
positim ofopticaJ 6bre
140 an
J---'-r-'/ U .... IX 31
tx 16 IX 15
txo
sensa
Figure 8 The gravity flow rig The position and direction of rotation of the feeder relative to the bafile position are shown in figure 9. The arrangement means that even with no bafile the solids are not uniformly distributed over the measurement crosssection.
Sixteen of these transmitter-receiver pairs are mounted around the measurement section (figure 7). All the transmitter fibres are illuminated by the same light source, however, each receiver has a dedicated amplifier and conditioning circuit.
--
III
11 5
_at
;r;::rcl
." r-'------'---'----, ::w~-=-c <_ro..,ia
'-r----.....,---'
---
dind:io.
..
~
Figure 9. Position of screw feeder relative to the optical fibre sensors
&
....
Tests were carried out by setting the screw feeder to provide the required mass flow rate and then recording the outputs from the sensor arrays for several seconds. This was repeated for different flow rates and for the two types of material. The measured data was then processed in several ways.
Figure 7. Schematic diagram of measurement system All tests on the system were carried out on a gravity drop system with an 81 mm diameter down pipe (figure 8). The solids, either sand or 3 mm plastic chips, were fed at a controlled rate from the storage hopper into the pipe via a screw feeder. The feeder feed rate is controlled electrically.
4 Results
The average reading at a given flow rate was determined for each sensor to investigate the linearity between flow rate and output voltage. A typical result is shown in figure 10.
The down pipe of the conveyor is fitted with an adjustable bafile. The position of the bafile is used to control the distribution of the solids in the down pipe and hence within the measurement cross section. The bafile is placed just below the screw feeder so that it
533
31 25
~
2
'§
15
i
i
"
1
05
mass to.nt.1 gmIs
Figurel3 . Concentration profile for sand as three dimensional surface: quarter flow at 200 gmIs
Figure 10. A typical optical fibre calibration The averaged output from each sensor was determined for a given flow rate and compared with the predicted response at the specified flow rate and flow distribution (figure 11).
A third visual image, not shown here, is as a concentration contour map, which is a vertical projection of figure 13 .
5 Conclusions Tests on linearity showed straight line relationships between sensor output and mass flow rate, with no sign of saturation over the range of flows used: up to 4% vol.lvol. The model based on the optical path length of each transmitter receiver pair seems compatible with the measured accuracy of the system. For flow measurement the system results should be independent of how the solids are distributed in the flow cross-section (flow profile). The system appears to achieve this requirement, because all the measured flow rates were within 11.3 % of the set feeder rate for all the flow distributions investigated.
Figure 11 . Comparison of predicted and measured responses The solids concentration was determined using the back projection algorithm described earlier. Results from this can be presented in a variety of ways. If further calculations are required the data may be left in the form of a matrix. As an aid to visualisation the solid distribution within the conveyor may be presented as a concentration map (figure 12) or as a three dimensional image (figure 13).
The overall accuracy of the measurement can be improved by in two ways. Firstly, by increasing the number of optical fibre sensors so that more of the conveyor is interrogated. The number of fibres can easily be doubled, increasing the sampled volume to 62%. Secondly, by using a longer averaging time constant to reduce the rapid fluctuations arising from the individual particles, which could be provided either in hardware or software.
1I 102tlU11515l1t'D2221:aDI' 11 "M
Optical tomography systems have been relatively neglected. This paper, however, demonstrates that they work in the laboratory. They have several advantages over other sensing systems. They are linear in their response to increases in concentration and the optical beams travel in straight lines. This simplifies the reconstruction of tomograrns, which should also be provided at high speed. The high resolution (better than 2%) and
Figure 12. Concentration profile for sand as two dimensional map: quarter flow at 320 gm/s
534
frequency bandwidth associated with these sensors should enable velocity profiles to be obtained. The major problem is in keeping the optics clean. However, many industrial processes make use of air purge systems and this may be a suitable case. 6 References [l) C G Xie, (1993) "Review of image reconstruction methods for process tomography." Process Tomography - A Strategy for Industrial Exploitation, Ed M S Beck et al., Pub by UMIST.
[2) Process Tomography: Principles, Techniques and Applications, Ed R.A.Williams and M.S.Beck, ButterworthHeinemann, 1995, 101-118. [3) Wiegand, F. and Hoyle, B.S. (1991) Development and implementation of real-time ultrasound process tomography using a transputer network. Parallel Computing, 17, 791-807.
535
Optical fibre sensor for proses tomography R Abdul Rahim 1, R G Green 2 1.
2.
Applied Control Panel., Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Locked Bag 791, 80990 lohor Bahru, lohor, Malaysia. Fax 075566272. Email : [email protected] School of Engineering IT, Sheffield Hallam University, Pond Street, Sheffield, SI 1WB, England.
~~
-
-,-=-
~-" " -
-
-
-
. . .,. - == --====- --
Abstract This paper describes an investigation into the use of optical fibre sensors in a tomographic measurement system designed to measure the flow of dry solids in gravity drop and pneumatic conveyors. A simple model of the system is provided and used to predict the response of individual sensors and the full system. Results are provided which show the model is acceptable. The system is used to provide tomographic images of solid concentration within a gravity conveyor.
Figure 1. The arrangement of optical fibres to provide a projection In the experiments reported in this paper two orthogonal projections are used (figure 2)
Copyright © 1998 IFAC
1 Introduction Process tomography [1] is a measurement technique that is being developed for measurement in two and multicomponent flows . These measurement systems use distributed groups of identical sensors, termed arrays, to investigate the physical properties of the material and its distribution within a container, e.g. a pneumatic conveyor, in real time [2] . Most of the tomography systems being investigated aim to provide concentration distributions of moving components of interest within the measurement section in the form of a visual image, much like an x-ray picture of hand for example, which is updated at a refresh rate dependent upon the process being investigated [3]. However, the long term aim is to provide flow information such as mass flow rate, which will be calculated by combining both concentration and velocity profiles.
Figure 2 Two orthogonal projections across the pipe cross-section The pipe in which the sensors are mounted has a nominal bore of 81 mm with a sensor spacing of 5 mm. This spacing means, with an optical fibre diameter of 1 mm, that approximately one fifth of the cross-section is directly interrogated, the remaining four fifths not being in a direct path between a source and its receiver, though there may be some output due to the beam spreading out from the transmitter fibre due to its optical aperture and light scattering by the particles. The effects of diffraction and scattering are ignored, because the primary effect is attenuation of optical energy by particles intercepting the beam. Thus each fibre is taking only a sample measurement of the particles flowing in the pipe. However, it is assumed that each fibre produces readings which represent a realistic sample of the solids passing through the space at each side of the fibre.
2 System model The measurement system (section 3) uses thirty-two optical fibre transmitters and receivers. Each transmitter is aligned with a specific receiver and the resulting sensor is tenned a transmitter/receiver pair. A sensor interrogates a finite section of the measurement section as shown in figure 1. Each sensor provides a view. Parallel sensors provide a projection.
To be able to predict the output of any sensor it is necessary to detennine the amount of the
531
pipe cross-section it interrogates. Also, the total volume interrogated by all the fibres determines the percentage cross-section of the conveyor which is being sampled. The volume sampled by a fibre is its area (diameter 1 mm) multiplied by the optical path length within the conveyor. From figures 1 and 2, it is obvious that individual path lengths are a function of the sensor position within the measurement section. The path lengths are determined from scale drawings. The volume being monitored by each projection of sixteen views, V 16 is
VT = =
" Jr-
Figure 4. The effect of baffle position on the predicted optical path length These calculations determine the voltage profile that should arise from sensors arranged around the circumference of the conveyor. The aim of the project described in this paper is to use these voltages to generate tomographic images of the cross-section of the conveyor. This is achieved using a simple back projection algorithm based on sensitivity maps.
15 (Lpath length)
4 0 796 mm'
And the total volume monitored by both 3 projections is 1600 mm . The vertical flow pipe (figure 8) has a bore of 81 mm, so approximately 30% of the pipe cross section is monitored.
For a collimated optical system, the sensitivity map is related to the beam path within the pipe. The pipe is projected onto a rectangular array of 32x32 pixels. Pixels outside the pipe will not contribute to the measurement so have a sensitivity value of zero. If the beam of the sensor being considered passes through a pixel within the pipe the pixel has sensitivity one, otherwise zero. For example the sensitivity or matrix map for sensor 2 is shown in figure 5. For the system described within this paper there are thirty two sensitivity maps. This neglects that some pixels are not completely square (should contribute less than unity) and the effects of beam scattering contributing to the outputs of neighbouring sensors, however, the results from these effects are small [9] .
Signal processing of the received beams results in a voltage which increases with increased solid flow rate, i.e. the more particles that intersect a beam the greater the Voltage. The assumption made in this paper is that the relationship between solid concentration passing through a beam and the corresponding sensor output voltage is linear. Thus the total mass flow rate is given by equation 1. 3 I
V Tolal =
L
31
V
k
i "" 0
m L P i ::: 0
eq(l) Continuing with this assumption, for a given uniform flow rate the output voltage from each sensor will be directly proportional to it's optical path length. The theoretically predicted sensor outputs for a uniformly distributed solid flow are shown in figure 3.
-
s.... or'1
x _ 0 0 o 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0
0
0
1
1
1
1
1
0 0 0 0 0 0 0
o
0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
00 0 0 0 0 o 0 0 0 0 0 o 0 0 0 o 0 0 0 0 0 o 0 o 0 0 0 0 0 0 0 o 0 0 o 0 0 o 0 0 o 0 0 o 0 0 0
0 0 0 0 0 0 00 0 0 0 o o 0 o 0 0 0
0 o 0 0 o 0 0 o 0 0 0 0 o
0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 T\tIOK*
1
0 1
1
000 0 0 0
0 0 0 0 0 0 0 0 0 0 o 0
"enslMty mllP (Senior 2)
Figure 5. Sensitivity map for sensor number 2
Figure 3. The predicted sensor readings for
For the back projection calculation [10] the sensor voltage Vi is multiplied by its sensitivity matrix. Corresponding elements of the images arising from the thirty two calculations are summed and the combined value provides the output concentration
uniform flow If the effective path length is reduced, say by a baffle as shown in figure 4, the method described above may be used to predict the expected sensor output voltages.
532
matrix. In practice, there are only two sensor voltages which contribute to the final , individual pixels' values. These correspond to the pixel at the intersection of the X and Y sensor beams.
has little effect on the velocity of the particles when they arrive at the measurement section. However, due to particle-particle and particlewall collisions, the particles are not excluded completely from the areas masked by the bafile.
3 The measurement system The measurement system consists of thirty two transmitter-receiver pairs. Light from a halogen bulb is conducted into the measurement cross-section via an optical fibre. The optical axis of the transmitter fibre is aligned with the optical axis of the receiving fibre. Light energy from the receiving fibre is converted into electrical energy by a current to voltage converter. The voltage is amplified and conditioned to produce a linear response between solids concentration and voltage. The conditioned signal is sampled to produce a digital signal in a form suitable for further processing in the personal computer.
screw feeder
+- positimof bolBe bolBe inser1ed fr(ltl this dir~on
positim ofopticaJ 6bre
140 an
J---'-r-'/ U .... IX 31
tx 16 IX 15
txo
sensa
Figure 8 The gravity flow rig The position and direction of rotation of the feeder relative to the bafile position are shown in figure 9. The arrangement means that even with no bafile the solids are not uniformly distributed over the measurement crosssection.
Sixteen of these transmitter-receiver pairs are mounted around the measurement section (figure 7). All the transmitter fibres are illuminated by the same light source, however, each receiver has a dedicated amplifier and conditioning circuit.
--
III
11 5
_at
;r;::rcl
." r-'------'---'----, ::w~-=-c <_ro..,ia
'-r----.....,---'
---
dind:io.
..
~
Figure 9. Position of screw feeder relative to the optical fibre sensors
&
....
Tests were carried out by setting the screw feeder to provide the required mass flow rate and then recording the outputs from the sensor arrays for several seconds. This was repeated for different flow rates and for the two types of material. The measured data was then processed in several ways.
Figure 7. Schematic diagram of measurement system All tests on the system were carried out on a gravity drop system with an 81 mm diameter down pipe (figure 8). The solids, either sand or 3 mm plastic chips, were fed at a controlled rate from the storage hopper into the pipe via a screw feeder. The feeder feed rate is controlled electrically.
4 Results
The average reading at a given flow rate was determined for each sensor to investigate the linearity between flow rate and output voltage. A typical result is shown in figure 10.
The down pipe of the conveyor is fitted with an adjustable bafile. The position of the bafile is used to control the distribution of the solids in the down pipe and hence within the measurement cross section. The bafile is placed just below the screw feeder so that it
533
31 25
~
2
'§
15
i
i
"
1
05
mass to.nt.1 gmIs
Figurel3 . Concentration profile for sand as three dimensional surface: quarter flow at 200 gmIs
Figure 10. A typical optical fibre calibration The averaged output from each sensor was determined for a given flow rate and compared with the predicted response at the specified flow rate and flow distribution (figure 11).
A third visual image, not shown here, is as a concentration contour map, which is a vertical projection of figure 13 .
5 Conclusions Tests on linearity showed straight line relationships between sensor output and mass flow rate, with no sign of saturation over the range of flows used: up to 4% vol.lvol. The model based on the optical path length of each transmitter receiver pair seems compatible with the measured accuracy of the system. For flow measurement the system results should be independent of how the solids are distributed in the flow cross-section (flow profile). The system appears to achieve this requirement, because all the measured flow rates were within 11.3 % of the set feeder rate for all the flow distributions investigated.
Figure 11 . Comparison of predicted and measured responses The solids concentration was determined using the back projection algorithm described earlier. Results from this can be presented in a variety of ways. If further calculations are required the data may be left in the form of a matrix. As an aid to visualisation the solid distribution within the conveyor may be presented as a concentration map (figure 12) or as a three dimensional image (figure 13).
The overall accuracy of the measurement can be improved by in two ways. Firstly, by increasing the number of optical fibre sensors so that more of the conveyor is interrogated. The number of fibres can easily be doubled, increasing the sampled volume to 62%. Secondly, by using a longer averaging time constant to reduce the rapid fluctuations arising from the individual particles, which could be provided either in hardware or software.
1I 102tlU11515l1t'D2221:aDI' 11 "M
Optical tomography systems have been relatively neglected. This paper, however, demonstrates that they work in the laboratory. They have several advantages over other sensing systems. They are linear in their response to increases in concentration and the optical beams travel in straight lines. This simplifies the reconstruction of tomograrns, which should also be provided at high speed. The high resolution (better than 2%) and
Figure 12. Concentration profile for sand as two dimensional map: quarter flow at 320 gm/s
534
frequency bandwidth associated with these sensors should enable velocity profiles to be obtained. The major problem is in keeping the optics clean. However, many industrial processes make use of air purge systems and this may be a suitable case. 6 References [l) C G Xie, (1993) "Review of image reconstruction methods for process tomography." Process Tomography - A Strategy for Industrial Exploitation, Ed M S Beck et al., Pub by UMIST.
[2) Process Tomography: Principles, Techniques and Applications, Ed R.A.Williams and M.S.Beck, ButterworthHeinemann, 1995, 101-118. [3) Wiegand, F. and Hoyle, B.S. (1991) Development and implementation of real-time ultrasound process tomography using a transputer network. Parallel Computing, 17, 791-807.
535