Plug Regime Flow Velocity Measurement Problem Based on Correlability Notion and Twin Plane Electrical Capacitance Tomography: Use Case - MDPI
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sensors Article Plug Regime Flow Velocity Measurement Problem Based on Correlability Notion and Twin Plane Electrical Capacitance Tomography: Use Case Volodymyr Mosorov * , Grzegorz Rybak and Dominik Sankowski Institute of Applied Computer Science, Lodz University of Technology, 90-537 Łódź, Poland; grzegorz.rybak@p.lodz.pl (G.R.); dsan@kis.p.lodz.pl (D.S.) * Correspondence: volodymyr.mosorov@p.lodz.pl Abstract: In this paper, the authors present the flow velocity measurement based on twin plane sensor electrical capacitance tomography and the cross-correlation method. It is shown that such a technique has a significant restriction for its use, particularly for the plug regime of a flow. The major issue is with the irregular regime of the flow when portions of propagated material appear in different time moments. Thus, the requirement of correlability of analyzed input signal patterns should be met. Therefore, the checking of the correlability should be considered by such a technique. The article presents a study of the efficiency of the original algorithm of automatic extraction of the suitable signal patterns which has been recently proposed, to calculate flow velocity. The obtained results allow for choosing in practice the required parameters of the algorithm to correct the extraction of signal patterns in a proper and accurate way. Various examples of the application of the discussed algorithm were presented, along with the analysis of the influence of the parameters used on the Citation: Mosorov, V.; Rybak, G.; Sankowski, D. Plug Regime Flow quality of plugs identification and determination of material flow. Velocity Measurement Problem Based on Correlability Notion and Twin Keywords: electrical capacitance tomography; pattern; correlability; multiphase flow Plane Electrical Capacitance Tomography: Use Case. Sensors 2021, 21, 2189. https://doi.org/10.3390/ s21062189 1. Introduction The flow velocity measurements are often applied to many industrial processes, Academic Editors: Kenneth Loh and such as food, mineral, chemical, and pharmaceutical production [1–5]. For one phase Ruben Specogna flow, velocity measurement is a relatively simple task. However, it is still challenged in multiphase flow applications when the velocity measurement of the chosen phase is Received: 22 January 2021 required. One of the concrete applications is plastic bottle production, where a pneumatic Accepted: 16 March 2021 transport system transports granular material. One of the basic efficiency criteria for such Published: 21 March 2021 a transport system is the maintenance of low air pressure during material propagation. Thus, continuous measurement of solid material velocity is necessary for estimating the Publisher’s Note: MDPI stays neutral transportation efficiency of such a system. Nowadays, in practice, different techniques for with regard to jurisdictional claims in published maps and institutional affil- the flow velocity measurement are used, although they are still not perfect. Sometimes, iations. invasive techniques are used. They require sensors inserted into the pipe, and as a result, they disturb the material propagation and are exposed to abrasion over time. There are also laser methods and other optical methods, but they have a limited scope of application related to its radiation issues. One of the techniques that are not invasive is process tomography. The electrical Copyright: © 2021 by the authors. capacitance tomography (ECT) technique is successfully applied when flow phases are not Licensee MDPI, Basel, Switzerland. electrically conductive. In the mentioned pneumatic transport, this situation occurs. Such a This article is an open access article distributed under the terms and technique is relatively low-cost and safe, especially its measurement sensor part. The classi- conditions of the Creative Commons cal tomographic image velocimeter (TIV) includes twin sensor planes mounted around an Attribution (CC BY) license (https:// investigated pipe/vessel/column. Each sensor consists of electrodes (typically, the number creativecommons.org/licenses/by/ of the electrodes is 8, 12 rarely) and it is used to measure the electrical capacitance between 4.0/). any pairs. Based on these capacitance measurements, an image reconstruction algorithm is Sensors 2021, 21, 2189. https://doi.org/10.3390/s21062189 https://www.mdpi.com/journal/sensors
Sensors 2021, 21, 2189 2 of 13 next utilized to reconstruct the material distribution inside the investigated volume of inter- est. To calculate the material velocity between the sensors’ planes, a series of reconstructed images are required. The correctness and reliability of a particle velocity measurement of multiphase flow are still a key challenge, despite the fact that currently there are many published elaborations related to this research scope [6–8]. Excluding the problems concerning the time stability of the measured capacitances and calibration limitations, the main problem is how to correctly calculate flow velocity based on reconstructed images. Although different techniques are proposed, for instance, the method based on the computation of the sensitivity matrix spatial gradient [9,10], the main method of velocity calculation is still a classical cross-correlation one [11–16]. To estimate flow velocity in the chosen pixel of the volume of interest, first, the cross-correlation function of signals representing material distribution changes within the pixel of the first and second plane of the tomographic unit is calculated. It is assumed that the global maximum of the calculated function corresponds to a transit time of material propagation between two sensor planes. Moreover, it is important to mention that the transit time is calculated for a time window. Therefore, this calculated velocity corresponds to the average material velocity between two sensor planes. The signal correlation function is based on the indicated time intervals, in which the range of measurements used in the calculations is determined. The indicated time intervals constitute time windows for the measurement data. Most often, such a window is set as a constant value before performing the calculations and its scope does not change during the analysis. Unfortunately, there are no hints or information on what basis the parameters were determined [16–20]. On the other hand, it turns out that the window width parameter is important in the context of ensuring the effectiveness of the algorithm. Due to this fact, it is obvious that the pattern should be computed based on the signal that is processed. Warsito and Fan 2008 [21] proposed the technique of tracing flow structures but without indicating the mechanism of time window selection. Fuchs et al. [22] described a method based on determining the length of a plug, but without explaining how to determine the length of time windows for the flow velocity estimation algorithm. The problem is still omitted by the researchers, for instance, in the articles published in the last years [4,23,24]. The existing gap has recently been filled up by developing a new concept for an appropriate algorithm allowing the automatic determination of the time window (Mosorov et al. 2020) [11]. The authors propose automatically detecting signal patterns to measure the particle velocity based on the obtained series of tomographic images. However, the proposed algorithm uses arbitrary chosen parameters, and their choices have not been justified. There is no study presenting the dependence between the accuracy of flow velocity measurement and parameter values. Therefore, the article has several aims: • Justification of the choice of parameters to detect signal patterns to measure flow velocity. • Determination of the problems for utilization of the proposed approach in real-case- studies. The authors suppose that the obtained results of the conducted study can be success- fully utilized in many applications that use the cross-correlation method to calculate time parameters of flow measurements, where the plug regime occurs. 2. Theoretical Considerations An ECT tomography system to determine a velocity profile in the region of interest should consist of at least two plane sensors mounted around a pipe (see Figure 1). To ensure fulfilling the assumption on the laminar character of the investigated flow, a distance between the two planes should be chosen, as short as possible. Such an ECT tomographic velocimeter provides the constant speed of imagining, representing the distribution of the material concentrations in cross-sections of both planes.
ensure fulfilling the assumption on the laminar character of the investigated flow, a dis- tance between the two planes should be chosen, as short as possible. Such an ECT tomo- Sensors 2021, 21, 2189 3 of 13 graphic velocimeter provides the constant speed of imagining, representing the distribu- tion of the material concentrations in cross-sections of both planes. Diagram Figure 1.Figure 1. of flow velocity Diagram measurement of flow realized by a two-plane-sensor velocity measurement electrical capacitance realized by a two-plane-sensor tomography electrical capaci-(ECT) tanced is tomography, the distance (ECT) tomography between the two planes. tomography, d is the distance between the two planes. Material concentrations are represented as images reconstructed based on raw mea- Material concentrations are represented as images reconstructed based on raw meas- surement. The typical image resolution is 32 × 32 pixels. To calculate the flow velocity urement. The typical image resolution is 32 × 32 pixels. To calculate the flow velocity pro- profile, the cross-correlation method is utilized. First, the cross-correlation function is file, the cross-correlation calculated methodbetween is utilized. changes First, in the the cross-correlation corresponding pixel values function is calcu- of the images, and then, lated between changes the maximumin the of corresponding the cross-correlationpixel values of isthe function images, and determined. Suchthen, the max- a founded maximum imum of the cross-correlation determines the time function delay of is material determined. Such abetween propagation founded themaximum two planes.deter- Let x mines the time delay of material i,j ( nT ) and y ( propagation i,j nT ) define the material distribution between the two planes. changes for (i, j) pixel of the Let , ( nth) and ( ) defineimage I × J , tomographic (see Figure the material 1) captured distribution with the changes ( , ) rate forframe pixelresolution of T obtained from planes X and Y of the twin plane the th I × J tomographic image (see Figure 1) captured with the frame rate resolution tomograph, respectively. As mentioned before, it is assumed that flow has a laminar character. Therefore, obtained from planes and of the twin plane tomograph, respectively. a strong relationship between the material distribution changes coming from the As mentioned before, it isand assumed that flow has a laminar character. Therefore, a X plane and Y one exists, the cross-correlation function R i,j ( kT ) of the two time series xi,j (nT ) strong relationship and between yi,j (nT ) ,the n =material N, . . . N +distribution M − 1 can bechanges applied: coming from the X plane and Y one exists, and the cross-correlation function , ( ) of the two time series , ( ) and , ( ) , n = N, … N +1MN + − M1−can 1 be applied: Ri,j (kT ) = M ∑ xi,j (nT )yi,j ((n − k ) T ), k = . . . , −1, 0, 1 . . . (1) 1 −1 n= N ,( )= ∑ = ,( ) , (( − ) ), = ⋯ , −1,0,1 … (1) where M is the number of frames determining the time window considered in the calculations. where M is the number of frames The founded determining maximum of thethe time window cross-correlation considered Rmax inthe determines thetime calcu- delay τ0 in lations. a frame rate between the two signals representing material change distributions. Then, The foundeda velocity maximumVi,j of of the theflow in (i, j) pixel of cross-correlation thedetermines Rmax cross-section calculated the in timeinwindow time delay [N, N +the a frame rate between M] two is given by the signals formula: representing material change distributions. Then, a d velocity , of the flow in (i, j) pixel of the cross-section Vi,j =calculated in time window [N, N (2) τ0 + M] is given by the formula: It is worth nothing that it is an average velocity of material propagation in the time , = window, for instance, in the frame [N, N + M]. (2) The changes in the concentration of the pneumatic flow material measured in the It is worth vertical nothingpipethatsection it is anhave a characteristic average velocity ofshape, namely material quasi-regular propagation pulses in the timesimilar to rectangular ones. In terms window, for instance, in the frame [N, N + M]. of fluid mechanics, plug flow is a basic model describing a material flowing in a pipe. In plug flow, the velocity of the The changes in the concentration of the pneumatic flow material measured in the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe. Such a plug vertical pipe section have a characteristic shape, namely quasi-regular pulses similar to flow model assumes that there is no boundary layer adjacent to the inner wall of the pipe. rectangular ones. In terms of fluid mechanics, plug flow is a basic model describing a ma- For instance, Figure 2 shows the chosen time interval of typical normalized concentration terial flowing inchanges a pipe.inIntheplug chosenflow, the pixel of velocity of the fluid the tomographic images isfor assumed to beconveying, a pneumatic constant where 0 across any cross-section corresponds of the to anpipe perpendicular empty pipe and 1 meansto the theaxis of the highest pipe. concentration material Such a plug flow (to normalize model assumes material that there is no boundary concentration, layer adjacent the calibration to the procedure inner wall of the pipe. For is required). instance, Figure 2 shows the chosen time interval of typical normalized concentration changes in the chosen pixel of the tomographic images for a pneumatic conveying, where
signal patterns. Hence, the velocity calculation should consider choosing the appropriate signal patterns of time series , ( ) and , ( ), i.e., determination of a time window. Since the plug propagation time is not constant, the choice of a time window with a fixed length M is not possible. In addition, plugs appear irregularly, therefore, there is a Sensors 2021, 21, 2189 problem: How to automatically determine the time of appearance of the plug and its4 fin-of 13 ishing. Hence, the algorithm for determining the velocity based on Equation (1) should automatically detect the moments of plug occurrence. (a) (b) Figure Figure2.2.Normalized Normalized concentration concentration changes within aa chosen changes within chosenpixel pixel(15,15) (15,15)ofofthe thetomographic tomographicimages im- ages (a) and the image captured by a high speed camera (#220–#320) (b); s0—some threshold level (a) and the image captured by a high speed camera (#220–#320) (b); s0 —some threshold level and and m0—the arbitrarily chosen number of frames. m0 —the arbitrarily chosen number of frames. Applying simple As mentioned thresholding in Mosorov et al. to determine 2020 [11], thethe time moments estimation is not of the time possible delay betweenduetwo to the fact that there can be a high probability of short pulses which are not suitable time signals requires fulfilling the condition of their correlability. The notion of correlability for de- termining the material of input signals means velocity that the by the correlation calculated method due cross-correlation to their function willshort duration. allow Such determining aacase can be described dependency between as theimpulsive analyzednoise in terms signals. of signal processing The correlability is strictly notions. connected with a In Mosorov problem et al. 2020 determining [11],window the time the algorithm to determine to the calculation of the the time interval is proposed. cross-correlation function. ItThis includes the following steps: means that the choice of the time window depends on the considered signal patterns. 1.Hence, the velocity Choose arbitrarilycalculation shouldvalue the threshold consider choosing the appropriate s0 experimentally signal and an interval patterns of of confidence timemseries xi,j (nTm)0 and 0T, where yi,j (arbitrarily is the nT ), i.e., determination chosen number of aoftime window. frames. It is assumed that the Since the values threshold plug propagation must be above time is known the not constant, the choice of a time window with noise level. a fixed length M is 2. Waiting when the signal ,not possible. (In ) addition, or , ( ) plugs appear is is below irregularly, therefore, the threshold value sthere 0. is 3. If the signal value , ( ) or , ( ) exceeds the threshold value s0 during the con- a problem: How to automatically determine the time of appearance of the plug and its finishing. fidence Hence, intervalthe[Nalgorithm bT, NbT +for determining m0T], then moment the velocity NbT − mbased on Equation 0T determines (1) should the beginning automatically of the signal detect the moments of plug occurrence. pattern. 4. If the signal value thresholding Applying simple , ( ) to determine , ( ) is below the thetime moments threshold is not values possible due 0 during the in- to the terval of confidence [NeT, NeT + m0T], then moment NeT + m0T is chosen assuitable fact that there can be a high probability of short pulses which are not the endfor of determining the the signal pattern.material velocity by the correlation method due to their short duration. 5.SuchThe a case cancorrelation cross be described as impulsive function noise as is calculated in follows: terms of signal processing notions. In Mosorov et al. 2020 [11], the algorithm to determine the time interval is proposed. It includes the following steps: 1. Choose arbitrarily the threshold value s0 experimentally and an interval of confidence m0 T, where m0 is the arbitrarily chosen number of frames. It is assumed that the threshold values must be above the known noise level. 2. Waiting when the signal xi,j (nT ) or yi,j (nT ) is below the threshold value s0 . 3. If the signal value xi,j (nT ) or yi,j (nT ) exceeds the threshold value s0 during the confidence interval [Nb T, Nb T + m0 T], then moment Nb T − m0 T determines the beginning of the signal pattern. 4. If the signal value xi,j (nT ) or yi,j (nT ) is below the threshold value s0 during the interval of confidence [Ne T, Ne T + m0 T], then moment Ne T + m0 T is chosen as the end of the signal pattern. 5. The cross correlation function is calculated as follows: Ne + M0 1 Ri,j (kT ) = Ne − Nb + 2M0 ∑ xi,j (nT )yi,j ((n − k) T ), k = . . . , −1, 0, 1 . . . (3) n= Nb − M0
, ( )= ∑ , ( ) , (( − ) ), = ⋯ , −1,0,1 … (3) 6. Finally, the velocity of the flow in (I,j) pixel is calculated according to Equation (2), during the interval [NeT, NeT + m0T]: Sensors 2021, 21, 2189 5 of 13 , |[ , ] = (4) 7. Return to step 2 where n = Ne, i.e., starting from the moment of the interval when the signal , ( ) , ( ) is below the threshold value s0. 6. Finally, the velocity of the flow in (I,j) pixel is calculated according to Equation (2), In practice, during it is unnecessary the interval [Ne T, Ne Tto +m combine 0 T]: two signal values , or , and it has to choose one of them. In the article, such a basic signal is , . However, there are no studies showing how the rightness of the velocity Vi,j|[ Ne T,calculation willd depend on the choice of s0 and Ne T + M0 T ] = (4) m0 parameters. Therefore, the next section describes the carried τ0 out studies regarding the estimation of influence of these parameters on the rightness of velocity calculation and 7. Return finding to step the best 2 where values for the n =calculation Ne , i.e., starting from the moment of the interval when the procedure. signal xi,j ( Ne T ) or yi,j ( Ne T ) is below the threshold value s0 . 3. Experiments In practice,and unnecessary to combine two signal values xi,j or yi,j and it has to it isDiscussion choose The measurementthe one of them. In article, is made such with ana electrical basic signal is xi,j . However, capacitance there are tomography unitno bystudies meas- showing how the rightness of the velocity calculation will depend on the choice of s0 and uring the value of the electric capacity between successive pairs of electrodes Nel. Elec- m0 parameters. Therefore, the next section describes the carried out studies regarding the trodes are placed around the pipe at an equal distance, as shown in Figure 3. The meas- estimation of influence of these parameters on the rightness of velocity calculation and urement output has the form of the vector where its elements stand for consecutive elec- finding the best values for the calculation procedure. trode pairs: 3. Experiments and Discussion V = [ 1.0073 … 1.0114]. The measurement is made with an electrical capacitance tomography unit by measuring The number of electrode pairs Nel can be calculated as follows: the value of the electric capacity between successive pairs of electrodes Nel . Electrodes are ( ) placed around the pipe at an equal distance, =as shown in Figure 3. The measurement output(5) has the form of the vector where its elements stand for consecutive electrode pairs: where ne is the number of electrodes. V = of1.0073 In our experiment, the number . . .ne is electrodes 1.0114 . 8 and hence, the number of electrode pairs Nel is 28. (a) (b) Figure 3. Figure 3. Electrical Electrical capacitance capacitance tomography tomographymeasurement measurementunitunitand andsensor sensorplacing placingon onthe thepipe pipe(a). (a). On the right hand, the cross-section of the pipe is presented with electrodes (e1, e2 …) mounted On the right hand, the cross-section of the pipe is presented with electrodes (e1, e2 . . . ) mounted around the pipe (b). around the pipe (b). The number The process of of obtaining a tomogram, electrode pairs thecalculated Nel can be graphicalasrepresentation follows: of reconstructed tomographic data requires several stages, which include: Data acquisition from tomo- graphic sensors, device calibration (determining − 1range ne (ne the ) of the minimum and maximum Nel = (5) value for the process, normalization of measurement 2 data, preparation of the sensitivity matrix, and reconstruction of the tomographic image). where ne is the number of electrodes. One of the ECT data processing stages is to perform an image reconstruction algo- In our experiment, the number of electrodes ne is 8 and hence, the number of electrode rithm that allows preparing the pipe cross-section view. There are many such methods. pairs Nel is 28. However, despite the lower quality, the most frequently used method in real-time systems The process of obtaining a tomogram, the graphical representation of reconstructed to- mographic data requires several stages, which include: Data acquisition from tomographic sensors, device calibration (determining the range of the minimum and maximum value for the process, normalization of measurement data, preparation of the sensitivity matrix, and reconstruction of the tomographic image). One of the ECT data processing stages is to perform an image reconstruction algorithm that allows preparing the pipe cross-section view. There are many such methods. However, despite the lower quality, the most frequently used method in real-time systems is the linear
SensorsSensors 2021, 21, x FOR 2021, 21, x PEER REVIEW FOR PEER REVIEW 6 of 13 6 of 13 Sensors 2021, 21, 2189 6 of 13 is the is the linear linear backprojection back projection (LBP) (LBP) method method[25,26] [25,26]due dueto to thethelowlow costcost of computing. of computing.The The back methodprojection of linear(LBP) back method projection[25,26] is a due to the method low costtoofthe belonging computing. group of The method inverse of problem method of linear back projection is a method belonging to the group of inverse problem linear back solution projection [27], allowing is to a method calculatebelonging to the more result group data thanofthe inverse amountproblem solution of input data. [27], This solution [27], allowing to calculate more result data than the amount of input data. This allowing to calculate method includes more result calculating data than all points thetomogram of the amount ofusing input thedata. This method so-called includes sensitivity ma- method includes calculating all calculating points of the all pointsusing tomogram of the thetomogram so-called using thematrix. sensitivity so-called Thissensitivity structure ma- trix. This structure is based on a predefined N-element image table, where each element trix. is This structure based on a to corresponds is based predefined on ofa predefined N-element the distribution N-element imagecapacitance electric table, where eachimage between elementtable, where corresponds two sensor each electrodes. element to Part the corresponds distribution to the distribution of electric of the sensitivity matrix capacitanceof electric with examplebetween capacitance pairs two between sensor electrodes. of electrodes two are shownPart sensor electrodes. sensitivity Part of the 4. in Figure of matrix the sensitivity matrix with example pairswith example pairs of electrodes of electrodes are shown in Figure 4.are shown in Figure 4. Figure 4. Visualization of sensitivity matrix parts, an example. The red color stands for amplified values between pairs of electrodes. Figure Figure 4. Visualization 4. Visualization of sensitivity of sensitivity matrix matrix parts,an parts, anexample. example. The The red red color color stands standsfor foramplified amplifiedvalues between values pairs between pairs of of electrodes. electrodes. The sensitivity matrix is a graphical representation of the electric capacitance distri- bution between the electrodes, which results in the amplification effect of the values be- The sensitivity matrix is a graphical representation of the electric capacitance dis- The the tween sensitivity matrix electrodes, whileisweakening a graphicaltherepresentation signal’s influence of theon electric the central capacitance area of thedistri- tribution between the electrodes, which results in the amplification effect of the values analyzed bution betweenplane.theTheelectrodes, size of eachwhichsensitivity resultsmatrix in image the is equal to 32 amplification × 32 of effect pixels theofof the values between the electrodes, while weakening the signal’s influence on the central area the be- same tween dimensions, the electrodes, as a result, while a reconstructed weakening the image. signal’s The output influence is obtained on32the thanks central area to analyzed plane. The size of each sensitivity matrix image is equal to × 32 pixels of theof the Equation analyzed (6): plane. Theassize of each sensitivity matrix same dimensions, a result, a reconstructed image.image is equal The output to 32 × 32 is obtained pixels thanks to of the same dimensions, Equation (6): as a result, a reconstructed = × image. ∗ The output is obtained thanks (6) to Equation (6): I MG Mx1 = S− 1 ×M ∗ C Lx1 (6) where M is the ECT image resolution, L is theLvector size of one ECT measurement, CLx1 is where the ECT M is the ECT image measurement resolution, vector, L is SL×M is thesensitivity the vector = × ∗of one ECT size matrix, and measurement, CLx1 is the IMG is the tomographic (6) ECT image. measurement vector, SL×M is the sensitivity matrix, and IMG is the tomographic image. where ThereM is the There areECT are many many image numerical resolution, numerical problems problems Lassociated isassociated the vectorwith size thethe with ofsensitivity one ECT sensitivity measurement, matrix. This matrix. ma-CLx1 is matrix This theistrix notisanot ECT square matrix. measurement Its dimensions vector, S depend is the on the sensitivitynumber of matrix, independent a square matrix. Its dimensions depend on the number of independent meas- L×M and IMG measurements is the tomographic and image. from aand urements significantly greater number from a significantly greaterof image number points. of imageHence, it is impossible points. Hence, it isto calculate impossible the inverse to There calculate of arethe matrices inverse many and in various of matrices numerical known and in various problems methods associatedknown the with pseudo-reverse methods of the the pseudo-reverse the sensitivity matrix. image of ma- This reconstruction the image is used. reconstruction The isproblem used. is The considered problem is as ill-conditioned. considered as In the ill-conditioned.LBP algorithm, In the LBP trix is not a square matrix. Its dimensions depend on the number of independent meas- the pseudo-inverse algorithm, the sensitivity matrix pseudo-inverse is computedisthrough sensitivity its transpositions. urements After and from a significantly greatermatrix number computed of image through points. its transpositions. Hence, it is impossible After performing the image reconstruction algorithm, the cross-section image performing the image reconstruction algorithm, the cross-section image is is ob- ob- to tained calculate the inverse (Figure 5a). of matrices and in various known methods the pseudo-reverse of tained (Figure 5a). the image reconstruction is used. The problem is considered as ill-conditioned. In the LBP algorithm, the pseudo-inverse sensitivity matrix is computed through its transpositions. After performing the image reconstruction algorithm, the cross-section image is ob- tained (Figure 5a). (a) (b) Figure 5. Figure 5. Reconstructed Reconstructed ECT ECT image image (a) (a) and and the the photography photographythat thatpresents presentsthe thematerial materialinside insidethe the pipe. (b) The red color shows the material inside the pipe, and the black color represents an empty pipe. (b) The red color shows the material inside the pipe, and the black color represents an empty part of the pipe. On the right hand, (b) the image of the pipe section is presented. part of the pipe. On the right hand, (b) the image of the pipe section is presented. (a) (b) Figure 5. Reconstructed ECT image (a) and the photography that presents the material inside the pipe. (b) The red color shows the material inside the pipe, and the black color represents an empty part of the pipe. On the right hand, (b) the image of the pipe section is presented.
stances in the transport route or the distribution of material concentration in the cross- section of the tank during industrial processes. Despite the low quality, the accuracy of concentration changes is determined at the level of about 3%. The research was based on a two-phase pneumatic gas-bulk material flow. The Sensors 2021, 21, 2189 equipment configuration includes two 100 L tanks placed one below the other, 7 of 13a rotary feeder, a pump, piping in the horizontal section (2 × 7 m ) and vertical (approx. 3 m), as 2 shown in Figure 6. Stainless steel piping was used with a diameter of Ø1 = 57 mm (inner). In the uppertopart Thanks ECT,ofusing the installation, there itisisa possible the LBP method, filter that to separates determine the the phase number ofofthe loose material from the gaseous medium. A polymer granulate with a size substances in the transport route or the distribution of material concentration in the cross-of 3 mm × 3 mm × 1 mm and section of athe dielectric tank duringpermittivity industrial of approximately processes. Despite the 2.1 low wasquality, adopted the as the transported accuracy of substance concentration(Jaworski changesand Dyakowski is determined 2001) at the [28]. level of about 3%. The research As seen was based in Figure on tomographic 6, the a two-phase pneumatic sensors gas-bulk have been material flow.inThe installed theequip- vertical sec- mentEach tion. configuration of them includes consiststwo 100 Lelectrodes of eight tanks placed one below placed the other, at equal a rotary intervals feeder, on the outer wall a pump, piping in the horizontal section (2 × 7 m 2 ) and vertical (approx. 3 m), as shown in (electrode width 30 mm). The distance between them is constant and was d = 130 mm. The Figure 6. Stainless steel piping was used with a diameter of Ø1 = 57 mm (inner). In the measurement was made using the mentioned tomographic unit with a sampling fre- upper part of the installation, there is a filter that separates the phase of the loose material quency from the of 100 Hz. gaseous The gas medium. velocity A polymer (for anwith granulate empty pipe) a size can ×vary of 3 mm 3 mm from 1.0 to × 1 mm and 5 m/s by inserting three different nozzles and the pressure control. It follows a dielectric permittivity of approximately 2.1 was adopted as the transported substance from the above that the highest (Jaworski and achievable Dyakowskimaterial velocity is 5 m/s. 2001) [28]. Figure 6. Pneumatic Figure 6. Pneumaticmaterial material conveying conveying system system schema schema withwith tomography tomography sensors sensors andcam- and video video cam- era era placement. placement. As seen in Figure 6, the tomographic sensors have been installed in the vertical section. Each of them consists of eight electrodes placed at equal intervals on the outer wall (electrode width 30 mm). The distance between them is constant and was d = 130 mm. The measurement was made using the mentioned tomographic unit with a sampling frequency of 100 Hz. The gas velocity (for an empty pipe) can vary from 1.0 to 5 m/s by
Sensors Sensors 21, x21, 2021,2021, FOR2189 PEER REVIEW 8 of 13 8 of 13 inserting As part three different of the nozzles the experiment, andacquisition the pressureofcontrol. It followsvalues measurement from thewasabove that performed us- the highest achievable material velocity is 5 m/s. ing a tomographic sensor from two planes, and then the data were processed according As part of the experiment, the acquisition of measurement values was performed tousing the steps shown in sensor a tomographic Figurefrom 1. The twomain parts planes, andofthen thethe algorithm data were are the plugs processed identification according section and the to the steps cross-correlation shown in Figure 1. The module. main partsWhen the measurement of the algorithm are the plugssamples arrive at the identification plug identification module, the s section and the cross-correlation module. When the measurement samples arrive at the Then, 0 threshold is used to determine if the plug appears. if plug the higher material identification concentration module, the s0 thresholdis recorded is used in the periodif greater to determine the plug than m0 (confidence appears. Then, if the higher threshold), thematerial concentration plug beginning is recorded is indicated. Thein the opposite greater thanismperformed periodprocedure 0 (confidencefor plug threshold), the plug beginning is indicated. The opposite procedure end determination. Figure 7 presents example graphs showing changes in the concentra- is performed for plug endvalue tion determination. in the pipe Figure 7 presents example cross-section based on graphs a 15showing × 15 pixelchanges in the concentration of tomographic images from value in the pipe cross-section based on a 15 × 15 pixel of tomographic images from two two planes and the result of the discussed plug identification algorithm to parameters s0, planes and the result of the discussed plug identification algorithm to parameters s0 , m0 . m0As. As can be seen, the pattern of the time range (dotted red line) covers the time range of can be seen, the pattern of the time range (dotted red line) covers the time range of plug plug appearance appearance (blue(blue line) completely. line) completely. Figure 7. Plug Figure identification 7. Plug identification algorithm algorithmoutput output for severalcases. for several cases.The Thesignal signal from from thethe second second planeplane is presented is presented with an with an orange color. orange TheThe color. dotted dotted lines linespresent presentranges of computed ranges of computedpatterns: patterns: (a)(a) Shows Shows patterns patterns where where s0 =and s0 = 0.1 0.1mand m0 = 20; (b–d) 0 = 20; (b–d) shows patterns shows with patterns s0 =s00.6 with and = 0.6 andm0m=0 30. = 30. Thediscussed The discussed algorithm, algorithm, together withwith together arbitrarily set parameters, arbitrarily apparently set parameters, indicates indi- apparently the correct speed estimates. However, there are situations when the obtained cates the correct speed estimates. However, there are situations when the obtained values arevalues inconsistent with reality. One of the reasons for the occurrence of inappropriate estimates are inconsistent with reality. One of the reasons for the occurrence of inappropriate esti- is the reliance on incorrect algorithm arguments. The analysis of the plug registration mates is the reliance on incorrect algorithm arguments. The analysis of the plug registra- threshold s0 impact on the plugs identification algorithm effectiveness was performed. tion Thethreshold s0 impactinon results are presented the 8a,b. Figure plugs identification algorithm effectiveness was per- formed. Using the parameters s0 = 0.35inand The results are presented Figure m0 =8a,b. 5, an additional wrong plug is detected (Figure 8a). It results from the occurrence of situations where the instantaneous fluctua- tions of the concentration level exceed the indicated threshold and remain above m0 = 5 units. In such a situation, a signal pattern is generated, where the maximum correlation reaches the value of n = 21 (wrong velocity value eq. 0.62 m/s). The plug identification algorithm requires proper parameter setting that would enable the correct speed estima- tion. The authors conducted a series of experiments that allow indicating the right values. The results are shown in Figure 9.
SensorsSensors 2021, 2021, 21, 21, 2189 x FOR PEER REVIEW 9 of 139 of 13 (a) (a) (b) Material velocity estimation chart in relation to the parameter s0 for each plug. The different colors represent 0: (a) Full data, (b) removed data for s0 = 0.35 m, and plug number 9. Using the parameters s0 = 0.35 and m0 = 5, an additional wrong plug is detected (Fig- ure 8a). It results from the occurrence of situations where the instantaneous fluctuations of the concentration level exceed the indicated threshold and remain above m0 = 5 units. In such a situation, a signal pattern is generated, where the maximum correlation reaches the value of n = 21 (wrong velocity value eq. (b)0.62 m/s). The plug identification algorithm 8.requires FigureFigure Material proper velocity 8. Material parameter estimation velocity estimation setting chart chart that would ininrelation relation toto the enable sthe parameter the parameter 0s0for correct for each each speed plug. plug. estimation. TheThe different different Therepresent colors colors represent parameter authors parameter conducted s0: (a)s0Full : (a) data,data, Full (b) (b)a removed seriesdata removed ofdata experiments fors0s0= =0.35 for 0.35m,that m,and allow and plug indicating number plug number 9.9. the right values. The re- sults are shown in Figure 9. Using the parameters s0 = 0.35 and m0 = 5, an additional wrong plug is detected (Fig- ure 8a). It results from the occurrence of situations where the instantaneous fluctuations of the concentration level exceed the indicated threshold and remain above m0 = 5 units. In such a situation, a signal pattern is generated, where the maximum correlation reaches the value of n = 21 (wrong velocity value eq. 0.62 m/s). The plug identification algorithm requires proper parameter setting that would enable the correct speed estimation. The authors conducted a series of experiments that allow indicating the right values. The re- sults are shown in Figure 9. (a) (b) Figure Figure 9. (a)9.Analysis (a) Analysis of the influence of the influence of parameters of parameters s0 , m0 on thes0number , m0 on of theidentifiable number of identifiable plugs plugs (red (red line—expected value); line—expected (b) absolute value); error for the (b) absolute correlation function error for thetocorrelation with respect parameters s0function withof , m0 . The color respect to parameters circles indicates s0,of m0 the value m0. The(the parameter color scaleofiscircles shown indicates on the rightthe value of m0 parameter (the scale is shown on the right hand). hand). (a) (b) Figure 9. (a) Analysis of the influence of parameters s0, m0 on the number of identifiable plugs (red line—expected value); (b) absolute error for the correlation function with respect to parameters s0,
Sensors 2021, 21, 2189 10 of 13 The conducted experiments show unequivocally that the use of the right algorithm parameters is crucial when assessing its effectiveness. For the real data series, which shows the passage of 20 plugs (Figure 9a red line), it is noticeable that for the threshold s0 ≥ 0.75 the number of identified plugs does not reach the expected value and additionally shows an extreme influence of the m0 parameter. Moreover, for a value of s0 ≤ 1, a similar situation exists. On the other hand, if there is a higher s0 threshold, then a lower m0 parameter should be set to return the required number of plugs. Additionally, reducing the m0 allows identifying more plugs. The second experiment was performed in order to visually estimate the signal time shifts (p) for successive plugs. Then, results were taken as reference values to calculate the root of mean square error (RMSE); Equation (7)) for the algorithm with respect to s0 , m0 . s 2 ∑nPn=1 ( p̂ − p(n)) RMSE = , (7) Pn where Pn is the plug count; n is the plug number; p(n) is the time shift for n-th plug between planes; p̂ is the expected time shift (visual analysis). As a result of the analysis, the diagram (see Figure 9b) was obtained. The reference data (visual analysis) may be inaccurate. Therefore, the values on the graph fluctuate around RMSE = 1. It is noticeable that for low m0 and high s0 values, the estimation error is lower. Based on the above analyses, it can be assumed that the best parameters of the discussed algorithm are s0 = 0.6 and m0 = 10. Another aspect of the algorithm’s efficiency is the speed estimation error based on the correlation result resolution. The maximum speed that can be obtained with the indicated measurement parameters of the system equals n1 = 13 m/s (where n = 1 indicates the number of units of shifting the signals between two measurement planes). The follow- ing values are: n1 = 13 m/s, n2 = 6.5 m/s, n3 = 4.3 m/s, n4 = 3.25 m/s, n5 = 2.6 m/s, n6 = 2.17 m/s, n7 = 1.86 m/s, etc. Hence, the speed estimation error resulting from the erroneous calculation of the maximum value of the correlation increases with the increase in speed, reaching the maximum absolute value equal to v > 13 m/s (100%). In the current experiment, where the velocity of the medium is known, it is expected to obtain the plug velocity v < 6.5 m/s, which gives an error of 51%, and for the value of v = 2.17 m/s (n = 6), respectively 17%. The authors conducted an algorithm accuracy analysis. The first step was to check the changes in the estimated velocity to the parameter s0 . It was expected to show that different velocity estimates were obtained for different threshold values. In the second step, an error resulting from the estimation using of the considered algorithm to visual measurements was demonstrated. The results of the experiments are presented in Figure 10. The top chart (a) shows the relative error from the elaborated algorithm. The analysis proves that for a low threshold (smaller than 0.4) and higher than 0.7 results are not stable. Contrary, the center values give constant velocity estimation that allows us to assume this range as correct. On the lower plot, the error rate was calculated based on the reference measurement performed as a visual analysis. Same as above, a threshold greater than 0.4 gives better results. For the discussed case, the average error oscillates around 13.3% and the maximum error reaches up to 33.3%.
The authors conducted an algorithm accuracy analysis. The first step was to check the changes in the estimated velocity to the parameter s0. It was expected to show that different velocity estimates were obtained for different threshold values. In the second step, an error resulting from the estimation using of the considered algorithm to visual Sensors 2021, 21, 2189 measurements was demonstrated. 11 of 13 The results of the experiments are presented in Figure 10. The top chart (a) shows the relative error from the elaborated algorithm. Sensors 2021, 21, x FOR PEER REVIEW 11 of 13 (a) (b) Figure 10.10. Figure Plug identification Plug identificationalgorithm algorithmthreshold thresholdvalue value impact on the impact on the velocity velocityestimation estimationaccuracy. accuracy. The The plot plot onon thethe toptop (a) (a) shows the relative error for s0 = 0.7 as a reference (expected value). The relative error based on the visual analysis as a shows the relative error for s0 = 0.7 as a reference (expected value). The relative error based on the visual analysis as a reference is shown beneath (b). reference is shown beneath (b). The analysis proves that for a low threshold (smaller than 0.4) and higher than 0.7 4. Conclusions results are not stable. Contrary, the center values give constant velocity estimation that allowsAlthough us to assumean ECTthistomograph range as correct. system Oncanthe lower plot, the be successfully errortorate utilized was calculated determine a ve- locityon based profile in multiphase the reference flow, however, measurement there still performed as is a lack of a visual the efficient analysis. Same algorithms as above, a implemented threshold in such greater thana 0.4 system givesto better calculate the velocity results. For the profile in the right discussed case, way. It is shown the average error that the key factor is the choice of appropriate time oscillates around 13.3% and the maximum error reaches up to 33.3%. intervals for velocity calculations. This carried out research concerns the study of dependence between the threshold level 4.parameters Conclusions of signal pattern detection and rightness of the calculated velocity values. It is shown that these threshold level parameters have a major influence on the appropriate plugAlthough detection, anasECT welltomograph system can be successfully as on the cross-correlation utilized result that stands fortoaccurate determine a ve- veloc- locity profile in multiphase flow, however, there still is a lack of the efficient ity estimation. In this article, a use case is presented which proves the relation between algorithms implemented in such the s0 threshold and athesystem to calculate m0 parameter thein given velocity profile inalgorithm. the elaborated the right way. It is shown The larger s0 , that the then key factor smaller m0 mustis thebechoice of appropriate to obtain a valid counttime intervals of plugs. for velocity Additionally, the calculations. correlation out- This carried out determined put is also research concerns the study by a threshold of For value. dependence the range between of s0 = , threshold level pa- the algorithm rameters gives theoflowest signalerror pattern detection referring to theand rightness visual analysis.of the calculated velocity values. It is shownAlthough that thesethethreshold conducted level study parameters was obtainedhave for gravity flowinfluence a major experiments onand the pneumatic appropriate conveying, plug otherasstudies detection, well as can onalso thebecross-correlation valuable for flowsresult with different tomographic that stands modalities. for accurate velocity estimation. In this article, a use case is presented which proves the relation between the s0 Author Contributions: Investigation, V.M. and G.R.; project administration, D.S.; resources, V.M.; threshold and the m0 parameter given in the elaborated algorithm. The larger s0, then writing—original draft, V.M. and G.R. All authors have read and agreed to the published version of smaller m 0 must be to obtain a valid count of plugs. Additionally, the correlation output the manuscript. is also determined by a threshold value. For the range of s0 = , the algorithm gives lowestThis Funding: the work error was partly referring funded to the by the visual Intelligent Development Operational Program 2014– analysis. 2020 co-financed by the European Regional Development Fund, project POIR.04.01.02-00-0089/17-00. Although the conducted study was obtained for gravity flow experiments and pneu- Institutional matic conveying,Review Board other Statement: studies Not applicable. can also be valuable for flows with different tomographic modalities. Informed Consent Statement: Not applicable. Author Contributions: Investigation, V.M. and G.R.; project administration, D.S.; resources, V.M.; writing—original draft, V.M. and G.R. All authors have read and agreed to the published version of the manuscript. Funding: This work was partly funded by the Intelligent Development Operational Program 2014-
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