artificial neural network approach for flow regime classification in gas–liquid–fiber flows...

Chemical Engineering Science 59 (2004) 2241–2251www.elsevier.com/locate/ces

Arti�cial neural network approach for $ow regime classi�cation ingas–liquid–�ber $ows based on frequency domain analysis

of pressure signals

T. Xiea, S.M. Ghiaasiaana ;∗, S. Karrilab

aG.W. Woodur� School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USAbInstitute of Paper Science and Technology at Georgia Tech, Atlanta, GA 30318-5794, USA

Received 8 December 2003; received in revised form 1 February 2004; accepted 3 February 2004

Abstract

The feasibility of a transportable arti�cial neural network (ANN)-based technique for the classi�cation of $ow regimes in three phasegas/liquid/pulp �ber systems by using pressure signals as input was examined. Experimental data obtained in a vertical, circular column1:8 m in height and 5:08 cm in diameter, with air/water/Kraft softwood paper pulp, were used. The pulp consistency (weight percentof dry pulp in the pulp–water mixture) was varied in the 0.0–1.5% range. Local pressure $uctuations were recorded at three di:erentstations along the column using three independent but principally similar transducers. An ANN was designed, trained and tested for theclassi�cation of the $ow regimes using as input some density characteristics of the power spectrum for one of the normalized pressuresignals (from Sensor 1), and was shown to predict the $ow regimes with good accuracy. A voting scheme was also examined in whichthe three sensors fed separately trained ANNs, and a correct $ow regime would require a vote from at least two of the three ANNs. Thisscheme improved the agreement between the model predictions and the data.

The ANN trained and tested for Sensor 1 predicted the $ow regimes reasonably well when applied directly to the normalized pressurepower spectrum density characteristics of the other two sensors, indicating a good deal of transportability. For further improvement oftransportability, an ANN-based method was also developed, whereby the power spectrum density characteristics of other sensors wereadjusted before they were used as input to the ANN that was based on Sensor 1 alone. The method was shown to improve the accuracy of the$ow regime predictions. This method requires in practice, that the “replacement” sensor to which regime identi�cation is transported willbe, for some while, in simultaneous use with the sensor to be replaced; then the training of the “input-adjusting” ANN would be possiblein industry practice. Such a situation is realistic for sensitive processes, where redundant sensors are implemented for fault tolerance.? 2004 Elsevier Ltd. All rights reserved.

Keywords: Flow regimes; Three-phase; Power spectrum density; Pressure $uctuation; Arti�cial neural network; Transportability

1. Introduction

Objective $ow regime identi�cation in multi-phase $owprocess systems using minimally intrusive sensors is ofgreat interest to various branches of industry. In papermaking and recycling, in particular, opaque gas–liquid–pulp �ber three-phase mixtures are encountered in largedeligni�cation, bleaching, and deinking devices. An objec-tive and minimally intrusive regime classi�cation techniquecan help the development of online diagnostic or controlmethods for such systems. Hydrodynamic characteristics of

∗ Corresponding author. Tel.: 404-894-3746; fax: 404-894-8496.E-mail address: [email protected] (S.M. Ghiaasiaan).

gas–liquid–pulp �ber slurry $ows have been investigatedin the past (Du:y and Titchener, 1975; Du:y et al.,1976; Bennington et al., 1995; etc), and more recentlytheir $ow regimes and gas holdup characteristics have beenstudied (Lindsay et al., 1995; Reese et al., 1996; Heindel,1999; Heindel and Garner, 1999; Xie et al., 2003a,b).Brief reviews of the recent studies can be found inXie et al. (2003a,b).Attempts at the characterization of two-phase $ow pat-

terns based on a combination of subjective judgments andobjective methods have also been made in the past (Hubbardand Dukler, 1966; Mandhane et al., 1974; Jones andZuber, 1975; Merilo et al., 1977; Weisman et al., 1979;Taitel et al., 1980; Mishima and Ishii, 1983; Matsumi,

0009-2509/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2004.02.017

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2242 T. Xie et al. / Chemical Engineering Science 59 (2004) 2241–2251

1984; Lin and Hanratty, 1986; Fang et al., 1986; Francaet al., 1991; Drahos et al., 1991; Spedding and Spence,1993; Lindsay et al., 1995; Cai et al., 1996; Zhang et al.,1997; Heindel and Monefeldt, 1997; Shim and Jo, 2000).Pressure $uctuations that result from the passage of gasand liquid pockets, and their statistical characteristics, areparticularly attractive for objective characterization of $owregimes because the required sensors are robust, inexpensiveand relatively well-developed, and therefore more likely tobe applied in the industrial systems (Drahos et al., 1991).Power spectral density (PSD) and probability density func-tion (PDF) of pressure drop $uctuations recorded by twopressure transducers were studied by Franca et al. (1991),and more recently by Shim and Jo (2000), for regimeidenti�cation in gas–liquid two-phase $ows. Based on theanalysis of experimental data in a horizontal tube, Francaet al. (1991) noted that, although PSD and PDF could noteasily be used for regime identi�cation, objective discrim-ination between separated and intermittent regimes mightbe possible by fractal techniques. Based on PSD and PDFanalyses, Shim and Jo could characterize bubbly, churn,and slug $ow patterns in low-$ow experiments in a verticaltube. At high $ow rates, however, their technique couldonly distinguish the bubbly $ow regime.To avoid subjective judgment, arti�cial neural network

(ANN) modeling and frequency estimation methods havebeen employed to implement non-linear mappings frommeasurable physical parameters to $ow regimes (Cai et al.,1994; Mi et al., 1998; Mi et al., 2001). Arti�cial neural net-works are analytical tools that imitate the neural aspect of thehuman brain, whereby learning is based on experience andrepetition rather than the application of rule-based principlesand formulas. An ANN (in its most typical form, so-calledfeed-forward network) consists of a layered network of neu-rons (nodes), with each neuron connected to a large numberof others. The input signal to the network is passed amongthe neurons, with each neuron calculating its own outputusing weighting associated with connections. Learning isachieved by the adjustment of the weights associated withinter-neuron connections. ANNs provide capabilities suchas learning, self-organization, generalization (response tonew problems using incomplete information), and training;and are excellent for pattern recognition and trend predic-tion for processes that are non-linear, poorly-understood,and/or too complex for accurate �rst-principle mathematicalmodeling. They seem ideal for applications to multiphase$ow systems, and when properly designed and trained, canpotentially improve on-line monitoring and diagnostics.ANNs have recently been applied for the prediction of

complex thermal systems rather extensively. Although theapplication of neural networks to multiphase $ow prob-lems has started only recently, the published studies haveclearly demonstrated their enormous potential. Mi et al.(1998, 2001) applied a neural network for two-phase $owregime identi�cation in a vertical channel using signals fromelectric capacitance probes with excellent results. Gupta

et al. (1999) successfully applied a hybrid method based onfour neural networks along with simple �rst-principle mod-els (the latter intended to render the model independent ofspeci�c device geometry), for prediction of the attachmentrate constant in $otation columns.This paper follows our previous investigations (Xie et al.,

2003a,b). Xie et al. (2003a) reported on a detailed inves-tigation of the $ow patterns and gas holdup of gas–water–pulp three-phase $ows in a vertical, upward column. Therange of pulp consistency (i.e., weight fraction of dry pulpin the pulp-water mixture) in the experiments was varied inthe 0.0–1.5% range, which represents the low consistency(LC) pulp suspension range. The aforementioned test facil-ity, with some modi�cations, was subsequently used (Xieet al., 2003b), whereby local pressure $uctuations recordedby a single high-sensitivity pressure transducer at a par-ticular location on the test section wall (1:2 m above thetest section inlet) were measured and utilized for the de-velopment of an ANN-based method for $ow regime iden-ti�cation. Two feed-forward back-propagation ANNs weredeveloped, each having a single hidden layer, and they wereshown to predict the $ow regimes well using inputs basedon the pressure signal: the standard deviation, coeLcientsof skewness and kurtosis, and several time shift autocorre-lations of normalized signals.Although the aforementioned studies have shown that

ANNs are capable of learning to recognize $ow regimesbased on pressure $uctuation and some other $ow-inducedsignals, a number of important issues need to be resolved be-fore they can �nd widespread industrial applications. Prac-tical functional transportability of trained ANNs is amongthese crucial issues. This transportability is de4ned here asthe capability of a single ANN to function with several sen-sors in the following sense: trained with a sensor, and/ora scaled-down system, it performs acceptably with anotherreasonably similar sensor and/or a prototypical-scale sys-tem. The ANNmust then use somewhat sensor-independent,invariant characteristics of the input signal; we will help italong by preprocessing these signals to promote such invari-ance in the inputs.In this paper, using the data obtained with the aforemen-

tioned test facility (Xie et al., 2003b), the transportabil-ity of an ANN trained for regime classi�cation, betweenpressure signals from three separate but in principle similarsensors, is addressed. The sensors represent di:erent obser-vation points in $ow that is not fully developed, and theirsignal characteristics are therefore somewhat di:erent in ad-dition to di:erences in calibration (zero, gain, and linearity)—also minor di:erences in the physical installation of thesensors can a:ect their signals. Transportability with respectto multiple similar sensors applied to the same system scale(i.e., no scale-change di:erence) is considered here. Thistype of transportability is important since small di:erencesamong similar sensors (caused by sensor drift, for exam-ple) are often inevitable. An ANN is developed that usesthe power spectral characteristics of the normalized pressure

T. Xie et al. / Chemical Engineering Science 59 (2004) 2241–2251 2243

$uctuations as input, and is shown to have good transporta-bility. An ANN-based method is furthermore developed thatenhances the transportability of the aforementioned ANNs.While a redundant system with multiple sensors is an ob-vious target application, such robustness of algorithms thatprovides transportability will also contribute to performancewith a single sensor, shielding against e:ects of calibrationchanges or sensor replacements.

2. Experiments

The experimental test loop has been described in de-tail by Xie et al. (2003a,b), and will be reviewed herebrie$y. A schematic of the experimental facility is shown inFig. 1. The main components of the loop include a feedtank, a receiving tank, a circulation pump (1 hp, 1725 rpmDisc$o pump), a Hydrosonic pump (also known as a ShockPulse Generator or SPG), and the test section. The $ow inthe test loop was established by the circulation pump in thesetests, and the Hydrosonic pump was not used except as apassive component in the loop. Pulp of the proper consis-tency was �rst loaded into the feed tank and the receivingtank, both 0:144 m3 in volume. The pulp used in this studywas washed, unbleached Kraft softwood. The average �berlength was measured to be 2:45 mm. Kraft softwood pulp�bers are typically about 30 �m in diameter. Filtered airfrom the building at measured $ow rates was injected into

Fig. 1. Schematic of the test loop.

Silicon

diaphragm

Test

section

Fig. 2. Typical installation of dynamic pressure transducer.

the $owing liquid-pulp mixture in a 2:5 cm diameter tubeprior to the Hydrosonic pump. The gas/liquid/�ber mixtureexiting from the column was channeled into the receivingtank via a series of �ttings. Among the instruments are dif-ferential pressure transducers, a high-speed video camera,an X-ray $ash photography system, and a Gamma-ray den-sitometer. The test section was a PVC schedule 40 pipethat was 1:8 m in length and has a 5:08 cm inner diame-ter. The geometric con�guration of industrial systems pre-cludes fully developed $ow conditions. The unavailabilityof general scaling laws for multiphase $ows renders the ex-perimental simulation of prototypical systems diLcult. Thisexperimental study was thus meant to shed light on funda-mental hydrodynamic issues, rather than directly simulatingprototypical systems.The principal objective of the experiments in this study

was to record and analyze the pressure $uctuations for var-ious $ow regimes in the column. For this purpose, threepiezoresistive dynamic pressure sensors (Model 8510B-2,ENDEVCO Corp.), which are designed for measurementsrequiring a combination of small size, high sensitivity(10:878 mV=kPa or 150 mV=psi), and wideband frequencyresponse (resonance frequency of 70; 000 Hz), were in-stalled in the bubble column wall. Fig. 2 depicts howthe pressure sensors were installed: nearly $ush �tting isintended to minimize the $ow disturbance. The pressuretransducers have a 10-32 mounting thread, and 3:8 mm facediameter. The output signals of the pressure sensors, whichare proportional to the dynamic component of pressure, arefed to a signal conditioner for A/D conversion and �lter-ing. A Labview application was programmed to control thelogging frequency and collect the data.In the experiments, tests were carried out over 216

ULS6 51 cm=s and 06UGS6 26 cm=s super�cial veloc-ity ranges for the pulp-liquid slurry and the gas phase,


respectively. Flow regimes were identi�ed in the tests fol-lowing the procedures described in Xie et al. (2003b). Thetypical and maximum uncertainties associated with phasesuper�cial velocities were ±3:0% and ±4:5% for ULS ; and±9:6% and ±33:0% for UGS , respectively. In every test,the pressure $uctuations were recorded using the afore-mentioned dynamic pressure sensors, located at heights of120 cm (Sensor 1), 130 cm (Sensor 2), and 140 cm (Sen-sor 3) from the inlet of the bubble column. Acquisitionfrequency and length of time series data are important fac-tors for the estimation of statistical properties of randomdata. The former was selected as 100 samples=s so thatthe Nyquist rate exceeded the maximum frequency con-tained in the data, as prior literature suggests that the mostinformative pressure $uctuations in the bubble columnsoccur in the range from 0 to 20 Hz (Drahos et al., 1991).The record length of 2000 data points (20 s duration) waschosen on the basis of preliminary experiments to satisfywide-sense stationarity. Further details about the test appa-ratus, schematics of the major $ow regimes, typical pressuretraces for each $ow regime, and experimental $ow regimemaps, can be found in Xie et al. (2003b).

3. Spectral analysis

Periodic phenomena pervade in engineering systems, andthe hydrodynamic processes in bubble columns are no ex-ception. Spectral analysis is commonly used to reveal theperiodicity in a time-series. The power spectral density is afrequency domain characteristic of a time series and is ap-propriate for the detection of frequency composition in astochastic process (Matsumoto and Suzuki, 1984). Assum-ing the process to be stationary and ergodic, the power spec-tral density function Px(f) of a discrete-time signal x(n) isde�ned as the Fourier transform of the autocorrelation se-quence Rx(k)

Px(f) =∞∑

k=−∞Rx(k)e−i2�kf=fs ; (1)

where, fs is the sampling frequency.For an autocorrelation-ergodic real-valued process and an

unlimited amount of data, the autocorrelation sequence mayin theory be approached by a time-average

Rx(k) = limN→∞

12N + 1

N∑n=−N

x(n+ k)x(n): (2)

The record length of the signal we actually work with isof course limited. To diminish the distortion of the spectrumdue to �nite length of data record, the averaged modi�edperiodogrammethod (Welch’s method) was adopted. If x(n)is only measured over a �nite interval, say n=0; 1; : : : ; N −1, then periodogram method estimates the power spectral

density as

P̂x(f) =N−1∑

k=−N+1

R̂x(k)e−i2�kf=fs ; (3)

where, the autocorrelation is given as

R̂x(k) =1N

N−1−k∑n=0

x(n+ k)x(n): (4)

Welch (1967) modi�ed the periodogram method by sub-dividing the N-point sequence into overlapping segments.He then applied window function to each data segment andcomputed the corresponding periodograms for each seg-ment. Finally, he averaged the periodograms to obtain thepower spectrum estimate. More details of this method areavailable in Proakis and Manolakis (1996).

In our study, the normalized pressure $uctuations, de�nedbelow, were the time series of interest

p∗ = (p− Sp)=√

(p− Sp)2: (5)

The power spectrum was estimated using segments witha length of 256 points and a Hanning window of the samesize in order to lower the variance of the estimate. All thepower spectrum analyses were performed using the signalprocessing toolbox of Matlab 6.1 (MATLABJ6.1 Release12.1).Examples of power spectra for all the major $ow regimes

are shown in Fig. 3(a)–(d). The power spectrum in the bub-bly $ow regime exhibits two clear peaks (approximately at13 and 27 Hz for the depicted case), which may correspondto the frequency of gas bubbles of two major di:erent sizegroups. In the plug $ow regime, the lower-frequency peakbecomes more dominant. This may represent the passing-byof large gas plugs with dimensions comparable to the chan-nel diameter. The power spectrum of churn $ow regimeshows several peaks spread over a wide frequency rangefrom 0 to 15 Hz except for strong peaks at the small fre-quency range (less than about 3 Hz). The peaks may rep-resent the coalescence and collisions of gas pockets. Theslug $ow regime has a very strong spike (at about 2 Hz inthe displayed case). It is also noted that the frequency com-ponents over 30 Hz do not contribute much to the powerspectral density.The above examples indicate that the power spectral struc-

ture of each hydrodynamic regime in a gas–liquid pulp mix-ture $ow is distinct, and therefore it may be possible toidentify the hydrodynamic regimes of the gas–liquid–pulpslurry �ber $ow in a bubble column based on their estimatedpressure power spectral characteristics.

4. Neural network model for regime identi cation usingthe power spectral characteristics of pressure

The principles of ANNs have been described in numer-ous publications, and will not be repeated here, and only


Fig. 3. Examples of the power spectral density functions of pressure $uctuation: (a) bubbly $ow; (b) plug $ow; (c) churn-turbulent $ow; (d) slug $ow.

the major characteristics of the designed ANNs are pre-sented. ANNs represent a class of algorithms that can bedesigned and trained to perform $ow regime identi�cation.To some extent, an ANN pattern recognition approach in-volves a trainable black box (Tsoukalas and Uhrig, 1997).An ANN can be trained to learn the correct output or classi-�cation for each of the training samples. After training, the�xed neural network will interpolate or extrapolate with newinputs, and can perform well if the training data “taught”patterns essential to the current case (Mi et al., 2001). Thefeasibility of an ANN for regime identi�cation was demon-strated by Xie et al. (2003b), using as inputs the standarddeviation, coeLcients of skewness and kurtosis, and severalsecond-order correlation terms of the normalized pressuresignals recorded by a single sensor. The feasibility of usingnormalized pressure power spectral characteristics is nowexamined, as our current goal is to promote a certain typeof invariance (indi:erence to zero and gain at least).

To characterize the hydrodynamics of the $ow based onthe power spectral density function, it is necessary to �rstimplement parameterization of the information contained inthe spectral patterns. Based on the recorded power spectra,we focus on a frequency range up to 30 Hz. Each spec-trum is normalized to one in its integral over the 0–30 Hzrange (which provides invariance against changes in gain).The frequency range over 0–30 Hz is then divided into �vebandwidths: 0–3, 3–8, 8–13, 13–25, and 25–30 Hz. Ac-cording to Parseval’s relation, the integral of the power spec-tral density across the entire band is a measure of the totalenergy of the signal. To approximate the percentage of en-ergy the signal has in a given frequency band, we need tosum the estimated average power spectral density over thedesired frequency band. The mean value of power in eachof the aforementioned bands, denoted as P∗

0–3 Hz, P∗3–8 Hz,

P∗8–13 Hz, P

∗13–25 Hz, and P

∗25–30 Hz, respectively, is then used

as representative of the individual band. Other parameters


InputLayer

Output Layer

Hidden Layer

*83 HzP −

*30 HzP −

*2513 HzP −

f

*3025 HzP −

2fσ

�

*138 hzP −

indicator

regime

flow

Fig. 4. Schematic of the con�guration of ANN-1.

of interest are mean frequency, Sf, given by

Sf =∑

i fiPx(fi)∑i Px(fi)

; (6)

and spectrum variance �2f, estimated from

�2f =∑

i(fi − Sf)2Px(fi)∑i Px(fi)

: (7)

The above 7 discrete parameters, suggested by Drahos andCermak (1989), were selected to represent the characteris-tics of power spectrum of pressure $uctuations. Along withthe �ber consistency of the three-phase $ow �, they consti-tute the inputs to the forthcoming neural networks—the con-sistency is regulated and known in real process applications,and provides essential prior information. The output of theneural network is an indicator of $ow regimes. The com-mercial software package (NeuroShell 2) was used for thedesign and training of the neural network models. Based onthe experience described in Xie et al. (2003b), the targetedoutput values were designated to 0.3, 0.5, 0.7, and 0.9 cor-responding to bubbly $ow, plug $ow, churn-turbulent $ow,and slug $ow, respectively. The $ow regime is thereforetreated like an ordinal variable in the neural network, havinga natural ordering based on the observed typical sequenceof regime transitions. The output value from the ANN iscontinuous, and 0.4, 0.6, and 0.8 were set a priori as thedecision boundaries between the $ow regimes. This designwas consistent with the nearly linear transition boundariesin the (log–log plotted) $ow regime maps reported earlier(Xie et al., 2003b).A three-neuron-layer ANN was designed. The neurons in

the input layer had a piecewise linear activation function,while the neurons in the hidden and the output layers used thelogistic activation function. The back-propagation learningparadigm was used. The number of neurons in the hiddenlayer was experimented with, and the optimal number ofnodes was found to be 5. The con�guration of this neuralnetwork (referred to as ANN-1) is shown in Fig. 4.The pressure data measured by Sensor 1 were used �rst. A

total of 197 data records were available. Following commonpractice, a fraction of the obtained data (77%, or 152 data

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Fig. 5. Comparison between the predictions of ANN-1 and the test subsetof the data: (a) 0.5% pulp consistency; (b) 1.0% pulp consistency;(c) 1.5% pulp consistency. Transition lines are experimental and symbolsare ANN predictions. Dashed lines are from the previous experiments (Xieet al., 2003a).

records) was selected for training ANN-1, which constitutedthe so-called ‘calibration data’. The remainder of the data(45 data records), which the network had never ‘seen’ dur-ing the training process, was used to test the network. Thetest set of data was of course randomly chosen to avoid amemorized-patterns e:ect. During training, to prevent in-cipient over-training, the process was stopped when 20,000training events since the minimum average error for the cal-ibration data set were reached.The predictions of the designed and trained ANN are

compared with the test subset of the experimental data inFig. 5(a)–(c), for the three consistencies of 0.5%, 1% and1.5%, respectively. In these �gures the depicted regime tran-sition lines are experimental. The data points, however, arewhat the ANN predicts. The solid lines in these �gures rep-resent the observed $ow regime transitions in the experi-ments where the aforementioned pressure signals were alsorecorded (Xie et al., 2003b). The dashed lines are the regimetransitions observed in an earlier series of experiments us-ing essentially the same test facility (Xie et al., 2003a).


With the exception of bubbly-plug transition in Fig. 5(a),the two sets of regime transition lines are in agreement.In the analysis of the data associated with the latter tests,three di:erent bubbly $ow patterns (dispersed bubbly, lay-ered bubbly, and incipient bubbly) were reported (Xie et al.,2003a). Analysis with ANNs, however, indicated that these$ow patterns had similar pressure $uctuation characteris-tics (Xie et al., 2003b). The apparent discrepancy betweenthe bubbly-plug transition lines in Fig. 5(a) is likely due todiLculty associated with distinction between incipient plugand plug $ow patterns in our earlier experiments (Xie et al.,2003a). The experimental regime transition lines depicted inall the forthcoming �gures are the same as the solid lines inFig. 5(a)–(c).As noted in Fig. 5(a)–(c), the neural network ANN-1 pre-

dicts the $ow regimes successfully, misclassifying only 5 outof the 45 test data records. Only neighboring $ow regimeswere confused: the misclassi�ed cases in fact all representnear-transition conditions. It is also worth noting that mostof the misclassi�cation cases occur in experiments with thehighest consistency (1.5%), which may indicate that the datawith 1.5% consistency were contaminated with an interfer-ing signal, and that the noise level in the pressure signalscan be signi�cantly boosted by the presence of more �ber.The interfering noise displayed low frequency characteris-tics and could not be fully eliminated by low-pass �lteringduring signal processing.The above results further support the feasibility of using a

single, minimum-intrusive pressure sensor for $ow regimeidenti�cation. However, more experiments are needed. Inparticular, the feasibility of this method for much largerindustrial systems needs experimental veri�cation.Using the ANN-1 design, a voting scheme was developed

and tested with the objective of improving the regime pre-dictions by taking advantage of the multiplicity of the pres-sure sensors. Accordingly, three separate ANNs, all havingthe con�guration depicted in Fig. 4, were used, each trainedusing the signals recorded by one of the three sensors. Thetraining was done using a common set of 158 data points.The signals recorded by each sensor for the remainder of thedata points (the test data) were then used as input for thatparticular sensor. The correct $ow regime associated witheach test data would then depend on the majority vote amongthe three ANNs. The results of this method are comparedwith the test data in Fig. 6(a)–(c). Overall, these predictionsshow an improvement over those depicted in Fig. 5(a)–(c),as expected. The relatively high confusion rates associatedwith the �= 1:5% consistency persist, however, con�rmingthat these confusions may be caused by noise signals.

5. Transportability

Transportability of a model is often de�ned as the capa-bility to produce accurate predictions of data not included inthe development of the prediction model, and drawn from

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Fig. 6. Comparison between the predictions based on the voting schemeand experiment (regime boundaries are from experiments; symbols aremodel predictions).

a di:erent but plausible related population (Justice et al.,1999). For ANNs of interest in $ow regime classi�cation,where the system scale and the characteristics of the sensorare also important, the transportability concept needs to beextended to not only address a di:erent but plausible pop-ulation, but the system scale and sensors as well. A trans-portable ANN-based method should ideally be trained ona reference system using a set of reference sensors, and beable to correctly classify the $ow regimes when applied toa system with a signi�cantly di:erent scale and using some-what di:erent sensors, but subject to a similar $ow �eld.The signals recorded in the latter (prototypical) system mayevidently need to be manipulated before they can be usedas input to the trained reference ANN. The development ofa method appropriate for this manipulation is a crucial steptowards transportability.As a �rst step, the transportability of the ANN-1 for the

interpretation of the signals recorded by Sensors 2 and 3without any manipulation of the ANN and data, was exam-ined. Accordingly, the pressure signals recorded by Sensors2 and 3 were normalized and were directly (without any


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Fig. 7. Comparison between the predictions of ANN-1 and the experi-mental data when pressure signals of Sensor 2 are directly used for thecalculation of NN input parameters (regime boundaries are from experi-ments; symbols are model predictions).

manipulation) used for the calculation of input parametersfor ANN-1. The predictions of ANN-1 are compared withthe entire experimental data in Fig. 7(a)–(c) and Fig. 8(a)–(c) for Sensors 2 and 3, respectively. The agreement is en-couraging, and only about 13% of the data are misclassi�ed,with the misclassi�ed data points all representing conditionsclose to regime transition.A similar test was performed using the ANN discussed

in Xie et al. (2003b). The latter ANN, as mentioned earlier,uses the standard deviation, coeLcients of skewness andkurtosis, and several time-shift auto correlations of normal-ized pressure signals from a sensor as input. The result ob-tained by directly applying the ANN trained and tested forSensor 1 to the data recorded by Sensors 2 and 3 (not shownhere for brevity) were inferior to those depicted in Figs. 7and 8, and led to about 16% mismatches. This particular netwas using inputs that were not indi:erent to gain and shiftof zero point: the standard deviation is proportional to gain.To further improve the transportability of ANN-1 to Sen-

sors 2 and 3, a method similar to the one proposed by Bala-ban et al. (2000) was attempted. The pressure signals fromSensors 2 and 3 were normalized and their power spectra

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Fig. 8. Comparison between the predictions of ANN-1 and the experi-mental data when pressure signals of Sensor 3 are directly used for thecalculation of NN input parameters (regime boundaries are from experi-ments; symbols are model predictions).

*83 HzP −

*30 HzP −

*2513 HzP −

*3025 HzP −

*138 hzP −

Input Layer (sensor 2 or 3)

Output Layer (sensor 1)

Hidden Layer

f2fσ

f2fσ

*83 HzP −

*30 HzP −

*2513 HzP −

*3025 HzP −

*138 hzP −

Fig. 9. Representation of the con�guration of ANN-2. For training, inputparameters are from either Sensor 2 or Sensor 3, while output parametersare from Sensor 1.

were obtained. The three-layer back-propagation ANN de-picted in Fig. 9 (hereafter referred to as ANN-2) was thendeveloped. ANN-2 was meant to be trained in order to con-vert all the input parameters needed by ANN-1 that repre-sent either Sensor 2 or Sensor 3, such that they could becorrectly interpreted by ANN-1. An ANN similar to ANN-2


(a)

(b)

(c)

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Fig. 10. Comparison between the prediction of the ANN and the testsubset of data for Sensor 2: (a) 0.5% pulp consistency; (b) 1.0% pulpconsistency; (c) 1.5% pulp consistency (regime boundaries are fromexperiments; symbols are model predictions).

was trained for each of Sensor 2 and Sensor 3. For train-ing ANN-2 with respect to Sensor 2, the 7 parameters rep-resenting the power spectral density characteristics associ-ated with 152 data points (‘calibration data’ subset) obtainedwith Sensor 2 were used as input to ANN-2, while the corre-sponding parameters obtained with Sensor 1 constituted theoutputs. Once trained in this way, ANN-2 was then utilizedfor the conversion of the 45 unseen Sensor 2 data records,and the output parameters generated by ANN-2 were thenused as input for ANN-1. The predictions of ANN-1 for thelatter 45 data records are compared with the experimentaldata in Fig. 10(a)–(c). A similar procedure for Sensor 3 ledto Fig. 11(a)–(c). The results, as noted, are encouraging.The misclassi�cations are few, and represent relatively mi-nor confusion for data points associated with regime tran-sition zones. It is also worth emphasizing that mismatchesassociated with � = 1:5% are more severe, con�rming theadded complexity of the $ow �eld due to higher consistency.Our investigation thus con�rms the feasibility of the de-

velopment of transportable ANNs that use pressure signalcharacteristics, at least with respect to similar pressure sen-

(a)

(b)

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Fig. 11. Comparison between the prediction of the ANN and the testsubset of data for Sensor 3: (a) 0.5% pulp consistency; (b) 1.0% pulpconsistency; (c) 1.5% pulp consistency (regime boundaries are fromexperiments; symbols are model predictions).

sors in systems that are of the same size scale. Further inves-tigations are evidently needed. Transportability with respectto system size scales, in particular, needs to be investigated.

6. Conclusions

In this paper, the feasibility of using a transportable arti�-cial neural network (ANN)-based technique for the identi�-cation of $ow regimes in a gas/liquid/pulp �ber three-phase$ow systemwas examined. Experimental data were obtainedusing an instrumented test loop that included a transpar-ent vertical column (test section) that was 1:8 m long andhad an inner diameter of 5:08 cm. Flow regimes, includingbubbly, plug, churn and slug, were identi�ed visually. Mea-surements included pressure $uctuations recorded by threesimilar highly sensitive sensors. A three-layer, feed-forwardANN was designed that used seven input parameters all rep-resenting the characteristics of the spectral power densitydistributions of normalized pressure $uctuations associatedwith a single pressure sensor, and was shown to perform


well. A voting scheme, whereby ANNs trained for the threesensors would be used for regime identi�cation for an un-seen data set based on the majority vote, resulted in an im-provement in the accuracy of the predictions. The ANN thathad been trained based on signals recorded by one of thesensors (Sensor 1), furthermore, was directly applied to thesignals recorded by the other two sensors, and was shownto predict the $ow regimes reasonably well. An ANN-basedmethod was then developed for the conversion of the spec-tral power density characteristics of one sensor such thatthey approximated similar characteristics obtained with an-other sensor, to enable the use of a classi�cation algorithmcreated for the latter sensor. The results were good, and con-�rmed the suitability of the proposed method for improvingtransportability.The results of this investigation indicate that the devel-

oped ANN-based regime classi�cation method that uses thenormalized pressure power spectral density characteristics isreasonably transportable when high-sensitivity sensors areused on analogous systems of the same size scale. Trans-portability with respect to sensors that are signi�cantly dif-ferent, and with respect to systems with di:erent size scalesremains to be resolved, however, and further investigationsare recommended.

Notation

f frequency (Hz)fs sampling frequency (Hz)k discrete time shiftN �nite length of a discrete time signalp pressure (Pa)p∗ normalized pressure signalPx power spectral density function (dB)Rx autocorrelation functionUGS super�cial gas velocity (cm/s)ULS super�cial pulp–water mixture velocity (cm/s)x(n) discrete time signal�2f variance of spectrum� �ber consistency in mixture (%)

Superscripts

∧ estimated- time average

Acknowledgements

This work was partially supported by DOE grantDE-FC07-00ID13871, which is gratefully acknowledged.

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