Page 1

1294 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010

Separation of Gas–Liquid Two-Phase Flow Through

Independent Component Analysis

Yanbin Xu, Huaxiang Wang, Senior Member, IEEE, Ziqiang Cui,

Feng Dong, Senior Member, IEEE, and Yong Yan, Senior Member, IEEE

Abstract—Two-phase flow measurement has attracted a major

interest in the past four decades due to its wide range of ap-

plications in industry. This paper introduces a new method to

separate the gas phase from the liquid phase through a blind

source separation algorithm, without a separate device, based

on the assumption that the two phases are separated and their

independence is reflected in the statistical relation between the

electrical signals generated by the process. Experimental data are

obtained from a gas–liquid two-phase flow rig through electrical

resistance tomography (ERT). An independent component analy-

sis (ICA) method is applied to separate the gas phase from the

liquid phase. The efficiency of the ICA method with the ERT data

is assessed through experiments. The independent components

(ICs) are interpreted by comparing them with the reconstructed

images byERT.Thecomparative studiesshowthatICAiseffective

in extracting phase information of gas–liquid two-phase flow, par-

ticularlyforstratified,slug,andwaveflows.Basedontheextracted

ICs, the cross-correlation technique is adopted to estimate the

mean velocity of the liquid phase in the central area, the gas phase

at the interface, and the liquid phase around the pipe wall and the

liquid slug. Through correlating ICs representing different spa-

tially independent processes from the upstream and downstream

planes after the elimination of cyclostationary characteristics of

ICs, the mean velocity of different spatially processes is obtained.

Index Terms—Cross-correlation technique, cyclostationary

characteristics, electrical resistance tomography (ERT), indepen-

dent component analysis (ICA), two-phase flow.

I. INTRODUCTION

T

as chemical processes and nuclear systems, to microscale ap-

plications, such as electronics cooling. The general two-phase

flow measurement method is a separating method that separates

the two phases first and then measures the single-phase flows

individually. This method requires expensive facilities and

WO-PHASE flow is widely seen in many industrial

processes. These range from large-scale applications, such

Manuscript received June 30, 2009; revised December 17, 2009. Current

version published April 7, 2010. This work was supported by the National

Natural Science Foundation of China under Grants 60532020, 50776063,

60820106002, and 60910001. The Associate Editor coordinating the review

process for this paper was Dr. Juha Kostamovaara.

Y. Xu, H. Wang, and F. Dong are with Tianjin Key Laboratory of Process

Measurement and Control, School of Electrical Engineering and Automation,

Tianjin University, Tianjin 300072, China (e-mail: xuyanbin@tju.edu.cn).

Z. Cui was with Tianjin Key Laboratory of Process Measurement and

Control, School of Electrical Engineering and Automation, Tianjin University,

Tianjin 300072, China. He is now with the Department of Automation, Nankai

University, Tianjin 300071, China.

Y. Yan is with the Department of Electronics, University of Kent, CT2 7NT

Canterbury, U.K. (e-mail: y.yan@kent.ac.uk).

Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIM.2010.2044077

will result in the interruption of the industrial process, which

sometime is not allowed. This paper introduces a new method

to separate the gas phase from the liquid phase through an

algorithm, without a separate device, based on the assumption

that the two phases are separated and their independence is

reflected in the statistical relation between the electrical signals

generated by the process.

Blind source separation (BSS) [1] is a general signal process-

ing method that consists of recovering, from a finite set of

observations recorded by sensors, the contributions of different

physical sources independently from the propagation medium

without any specific knowledge of the sources. The underlying

principle in solving this problem is independent component

analysis (ICA) [2]. ICA is a statistical technique for transfor-

mation of multidimensional vectors into components that are

statistically as independent from each other as possible [3]–

[5]. ICA is widely used for data analysis and decomposition

to solve the BSS problem. It has successfully been used in

many fields of applied sciences and engineering, including

BSS [6]–[8], biomedical [9]–[11], feature extraction [12]–[14],

speech recognition [15]–[17], image processing [18]–[20], face

recognition [21]–[24], and so on. Until now, BSS methods

have seldom been used for the information extraction of two-

phase flow. Xu et al. [25] have applied the ICA method to

extract the flow regime information from the data, as well as the

interface fluctuation of the two-phase flow. This paper, which is

substantially extended from its conference version [25], focuses

on the application of ICA to gas–liquid two-phase flow in a

horizontal pipeline to extract phase information. Additionally,

cross-correlation techniques are adopted to estimate the mean

velocity of different spatial processes based on the extracted

independent components (ICs). Several researchers have as-

sumed that separated two-phase flow can be represented by the

superimposition of two single-phase flows [26]–[28]. In some

horizontal flows such as stratified, wave, and slug flows due to

the gravitational effect, the gas–liquid separation phenomenon

exists, and accordingly, the independence assumption is only

partially met.

Electrical tomography (ET) is based on the use of an array

of sensing elements located around the circumference of a

pipe or a vessel. For electrical resistance tomography (ERT),

different excitation schemes or current patterns can be ap-

plied to the electrodes, and the resulting changes in voltage

are measured. Based on the current–voltage relationship, the

electrical properties of the internal distribution, i.e., the phase

distribution, can be reconstructed. When ERT is used to obtain

data of gas–liquid two-phase flow in a horizontal pipe, the

0018-9456/$26.00 © 2010 IEEE

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.

Page 2

XU et al.: SEPARATION OF GAS–LIQUID TWO-PHASE FLOW THROUGH ICA1295

ICA method can be applied to separate the gas phase from the

liquid phase. In this paper, the physical interpretation of the

ICs is carefully achieved by comparing them with the results

from reconstructed ERT images. The mean velocity of different

components in the pipe is estimated through cross-correlation

processing.

II. ICA

BSS is a class of signal processing methods by which un-

observed signals, also called sources, are recovered from the

observation of several mixtures of them. Typically, the obser-

vations are obtained as the output of a set of sensors, where

each sensor receives a different combination of source signals.

The adjective “blind” indicates that the source signals are not

observed and, also, that no information is available about the

mixture. The lack of knowledge about the mixture and the

sources is compensated by assuming the mutual independence

of the sources. This assumption allows exploitation of the

spatial diversity provided by many sensors. When this is the

case, the corresponding solutions belong to the area of ICA. For

the process of using ERT to measure multiphase flow, the flow

activity from each different phase is observed (i.e., measured)

by sensors. Each sensor responds to a mixture of the signals

generated by individual phase sources. For stratified, wave, and

slug flows in a horizontal pipe, because of the gravitational

effect, there exists the gas–liquid separation phenomenon, and

thereby, the independence assumption is satisfied.

In this paper, the ICA method is incorporated into ERT data

analysis to separate the gas-phase information from the liquid-

phase information. The approach is based on the assumption

that the gas- and liquid-phase activities are separate processes

and their independence is reflected in the statistical relation

between the electrical signals generated from the processes,

namely, one phase has no or little influence on the other in

the gas–liquid two-phase flow. In other words, the measured

data from sensors are the linear sum of the contributions from

several spatially independent processes corresponding to gas

and liquid phases separately. If ERT data are expressed as a

time-series matrix X, the data can be modeled as

X =AS

(1)

X =[x1,...,xi,...,xn]T

S = [s1,...,sj...,sm]T

(2)

where xiis the time series measured from the ith sensor; n is

the sensor number; S is the IC matrix, sjis the jth IC, i.e., ICj;

m is the number of ICs; and A is an n ∗ m scalar matrix, which

is called mixing matrix. The goal of ICA is to determine the

unmixing matrix W to achieve the IC estimation

˜S =WX

˜S =[˜ s1,..., ˜ sj,..., ˜ sm]T

(3)

(4)

where˜S is the estimated IC matrix, and ˜ sj is the estimated

jth IC, i.e., ICj. The estimation usually chooses a suitable

objection function and then minimizes or maximizes it.

There are various algorithms to find the unmixing matrix W.

Infomax ICA and FastICA are two of the algorithms that are of-

ten applied in the implementation of spatial ICA. Infomax ICA

has advantages in global estimation and noise reduction [29]

and is hence employed in this paper. The algorithm is based on

the Infomax principle [30], which is a self-organizing learning

algorithm that maximizes the information transferred in a net-

work of nonlinear units. The mutual information maximization

between inputs and outputs can be achieved by maximizing the

Shannon (joint) entropy of the outputs, and thus, the learning

algorithm of the unmixing matrix W can be derived using the

maximum-likelihood estimation [30]. Infomax ICA initializes

W to the identity matrix I and then iteratively attempts to

maximize the joint entropy of the outputs passed through a

set of nonlinear functions, i.e., f(·). The nonlinear function,

which provides necessary higher order statistical information,

is chosen to be the logistic function

f(si) =

1

1 + e−˜ si

(5)

where˜S = WZ = WV X, and V = 2(XXT)−1/2. The use of

the whitening matrix Z instead of X aims to constrain the

matrix W to be symmetric [31]. The entropy in discrete form is

?

where pkis the probability of the kth event. The elements of

W are updated using small batches of data vectors randomly

drawn from Z without substitution, according to

⎛

∂W

H(·) = −

k

pklog pk

(6)

ΔW = −η

⎝∂H

?

f(˜S)

?

⎞

⎠WTW = η(I + Y˜STW)

(7)

where η is the learning rate (gradually reduced until W stops

changing appreciably), and the vector Y has elements

?∂f(˜ sj)

A more detailed discussion of the training process can be

found in the literature [30].

According to (3), estimated ICs can be obtained. The source

signals could be obtained up to their permutation, sign, and

amplitude only, that is, the order and variances of ICs cannot be

determined. These indeterminacies are, however, insignificant

in most of the applications.

yi=∂

∂ln

∂

?

= 1 − 2f(˜ sj).

(8)

III. ERT SYSTEM AND EXPERIMENTS

The dual-plane ERT system is applied. Each plane com-

prises eight titanium electrodes, equispaced around the internal

circumference of a Perspex pipe with an internal diameter of

85 mm, as shown in Fig. 1. Each electrode is 6 mm high and

4 mm wide. The axial distance L between the upstream and

downstream planes is 170 mm. Details of the data acquisition

unit are reported elsewhere [32]. The measured data are sent

to the computer via a Universal Serial Bus interface. Cross-

sectional images of the phase distribution are reconstructed

using an image reconstruction algorithm at 50 frames/s with

28 data in each frame.

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.

Page 3

1296 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010

Fig. 1.Mounting of the electrodes on the pipe wall.

Fig. 2.Experiment setup.

The gas–water two-phase flow rig on which the experiments

were conducted is shown in Fig. 2. The flow rates of gas and

water were controlled by adjusting the valves and measured

by Vortex and Roots flowmeters, respectively. The measured

data were recorded and displayed on the computer. During the

experiments, the following conditions are maintained:

1) gas temperature: 27◦C;

2) gas pressure: 0.54–0.70 MPa;

3) gas flow rate: between 4.84 and 13.4 m3/h;

4) water temperature: 32◦C;

5) water pressure: 0.19–0.22 MPa;

6) water flow rate: 3.45–22.02 m3/h.

IV. RESULTS AND ANALYSIS

Experiments were carried out in ten groups. In each group,

the water flow rate was fixed, and the gas flow rate was adjusted

from small to large and then to small again. The water flow

rate was different in different groups, which was gradually

decreased. For the same water and gas flow rates, 2000 frame

ERT data were sampled for a duration of 40 s. The measured

signals under 200 different flow conditions were acquired. Slug

and stratified-wavy flows were generated. The measured data

were transformed into time series from the eight sensors. The

data acquisition rate in ICA calculation is 350 Hz.

The time series, which demonstrate the instantaneous fluc-

tuation characteristic of a flow, are very different from those

obtained by the traditional time-averaged approach and by the

lower order statistical method. However, it is still difficult to

interpret the physical meaning of each IC. It has been observed

that ICs seem to “split” a true signal into several artificial

signals, as mentioned by McKeown et al. [33]. Therefore, it

Fig. 3.

images for a stratified/slug flow. (a) ICs with principal components 6.

(b) Reconstructed imageseries for 20 s fromside view. (c) Reconstructed image

series for 20 s from top view.

Comparison between the estimated ICs and the reconstructed ERT

is essential to reduce the dimension of the observed data (the

time-series matrix X) to avoid artifacts of ICA. In this paper,

principle component analysis is used not only for preprocessing

to make the signals uncorrelated but also for reducing the

dimensions of the observed data. In the ERT system, each

sensing plane has eight electrodes, i.e., the dimension of the

observed data is eight.

Three typical flow regimes are presented as follows: The ICs

can be interpreted by comparing them with the reconstructed

ERT images.

A. Stratified/Slug Flow

For a stratified/slug flow (USW= 1.06 m/s,

0.31 m/s), the number of principal components is selected as

six. Fig. 3(a) presents the ICA result, and Fig. 3(b) and (c)

shows the images reconstructed using the sensitivity algorithm

for 20 s from the side view and from the top view, respectively.

It can be seen that IC5 and IC6 correspond to the intermittent

dark blue part in Fig. 3(b) and (c), which shows the impulsive

motion characterized by a sharp rise in the liquid height in

the front and a sharp drop in height in the back. That is, IC5

and IC6 represent the liquid slug information. IC2 and IC4

correspond to the red part (i.e., the gas phase) interfacing with

USG=

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.

Page 4

XU et al.: SEPARATION OF GAS–LIQUID TWO-PHASE FLOW THROUGH ICA1297

Fig. 4.

images for a wavy/slug flow. (a) ICs with principal components 6. (b) Recon-

structed image series for 20 s from side view. (c) Reconstructed image series

for 20 s from top view.

Comparison between the estimated ICs and the reconstructed ERT

the adjoining phases in Fig. 3(b), which represents the gas-

phase fluctuation, particularly at the interface, but excluding the

interface information of the impulsive motion. IC3 corresponds

to the blue part in Fig. 3(c), which represents the liquid-phase

fluctuation around the pipe wall. IC1 corresponds to the light

blue part in Fig. 3(c), which represents the liquid phase in the

central region of the pipe.

B. Wavy/Slug Flow

For a wavy/slug flow (USW= 0.20 m/s, USG= 0.18 m/s),

Fig. 4(a) presents the ICA result, and Fig. 4(b) and (c) shows

the reconstructed image series.

In Fig. 4, IC5 and IC6 represent the impulsive motion,

which represents the liquid slug information. IC2 and IC4

represent the gas-phase fluctuation at the interface, excluding

the interface information of the impulsive motion. A wave can

be observed after the liquid height drops behind the first slug

tail and before the height rises back to the original one shown

in red and dotted lines, as shown in Fig. 4(a). The size of waves

can directly be found from the curve. IC3 represents the liquid

phase on the pipe wall. IC1 represents the gas phase in the

central region of the pipe.

C. Stratified-Wavy Flow

For a stratified-wavy flow (USW= 0.21 m/s,

0.22 m/s), Fig. 5(a) shows the ICA result, and Fig. 5(b) and

(c) shows the reconstructed image series.

In Fig. 5, IC5 and IC6 represent the large waves of the liquid

phase, which presents a gradual decrease in the liquid height

in their tail profile. IC1 represents the gas phase in the central

region of the pipe. IC2 represents the fluctuation of the gas

USG=

Fig. 5.

images for a stratified-wavy flow. (a) ICs with principal components 6.

(b)Reconstructed image series for20 s fromside view. (c) Reconstructed image

series for 20 s from top view.

Comparison between the estimated ICs and the reconstructed ERT

phase at the interface, excluding the impulsive motion from

large waves. IC3 represents the fluctuation of the liquid phase at

the interface, excluding the impulsive motion from large waves.

IC4 represents the liquid phase on the pipe wall projecting on

the axis parallel to the horizontal direction.

D. Velocity Estimation

By cross correlating the signals representing the gas and

liquid phases separately from the upstream and downstream

planes, the transit time between the two sensor arrays can be

measured; this, together with the distance between the sensor

planes, enables us to calculate the velocity of the gas and liquid

phases in the flow.

ICs obtained from the ERT data are verified to be second-

order cyclostationary signals, whose cyclic autocorrelation

functionsdetectsecond-orderperiodicities[34].Itisinducedby

the cycle-exciting–cycle-measurement strategy of the adjacent

data collection protocol adopted by the ERT system [34].

According to this strategy, currents are applied to the adjacent

electrode pair, and the voltage measurements are successively

preformed on all other electrode pairs. This procedure is re-

peated until all possible combinations have been completed.

In the time series measured from the ith sensor xi, there

are consecutive (n − 1) data corresponding to an excitation

cycle (n is the sensor number), which causes cyclostationary

characteristics. This also results in that the power spectra of the

ICs show peaks at harmonics of the fundamental characteristic

frequency, exhibiting narrow-band characteristics, as shown as

Fig. 6. However, for the cross-correlation method, if data have a

wide frequency spectrum, the flowmeter measurement accuracy

will increase in general [35]. In this paper, the cyclostationary

characteristics have been eliminated by taking the time average

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.

Page 5

1298 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010

Fig. 6. Power spectral density of ICs for the aforementioned stratified/slug flow.

Fig. 7.Power spectral density of ICs for the stratified/slug flow after the elimination of cyclostationary characteristics.

of consecutive (n − 1) data under one excitation cycle instead

of the (n − 1) data. After the elimination of the cyclostationary

characteristics, the power spectrum of the signal appears to be

broad-band (Fig. 7).

A typical example dealing with the velocity estimation of

different components from the stratified/slug flow (USW=

1.06 m/s, USG= 0.31 m/s), as shown in Section IV-A, is de-

scribed here. Based on the extracted ICs, the cross-correlation

technique was adopted to estimate the mean velocity of the

liquid phase in the central area, the gas phase at the interface,

and the liquid phase around the pipe wall and the liquid slug.

Figs. 8–11 demonstrate the ICs representing different spatially

independent processes before and after the elimination of cy-

clostationary characteristics, respectively, from the upstream

and downstream planes for the stratified/slug flow, as shown

in Fig. 3(a).

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.

Page 6

XU et al.: SEPARATION OF GAS–LIQUID TWO-PHASE FLOW THROUGH ICA1299

Fig. 8.

of the pipe. (a) From the upstream and downstream planes. (b) After the

elimination of cyclostationary characteristics.

ICs representing the liquid-phase fluctuation in the central region

Fig. 9.

(a) From the upstream and downstream planes. (b) After the elimination of

cyclostationary characteristics.

ICs representing the gas-phase fluctuation, particularly at the interface.

Fig. 8(a) shows the ICs representing the liquid phase in the

central region of the pipe from the upstream and downstream

planes. Fig. 8(b) presents the ICs in Fig. 8(a) after the elimi-

nation of cyclostationary characteristics. Plane 1 and Plane 2

mean the upstream and downstream sensor planes, respectively.

It can be seen that the signals from the two planes have a

Fig. 10.

(a) From the upstream and downstream planes. (b) After the elimination of

cyclostationary characteristics.

ICs representing the liquid-phase fluctuation around the pipe wall.

Fig. 11.

stream and downstream planes. (b) After the elimination of cyclostationary

characteristics.

ICs representing the liquid slug fluctuation. (a) From the up-

similarity to a certain extent, with the downstream signal being

a time-delayed but corrupted version of the upstream signal.

The time lag between the two signals represents the transit

time. The mean velocity is equal to the distance between the

measurement planes divided by this transmit time.

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.

Page 7

1300 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010

TABLE I

COMPARISON BETWEEN THE MEAN VELOCITY OF ICS WITH LIQUID AND GAS SLUGS GOING THROUGH

BY TURNS AND THOSE WITHOUT LIQUID SLUG GOING THROUGH

The ICs from the dual planes, representing the gas-phase

fluctuation at the interface, are given in Fig. 9(a). The ICs in

Fig. 9(a) after the elimination of cyclostationary characteristics

are plotted in Fig. 9(b). Again, the signals from the dual planes

exhibit a good similarity between them.

Fig. 10 depicts the original ICs representing the liquid film

fluctuation and after the elimination of cyclostationary charac-

teristics. It is evident that the liquid film has smaller energy.

When it moves from the upstream plane to the downstream

plane, a larger change may occur. Accordingly, the similarity

of the ICs representing the liquid film fluctuation from the two

planesisweakerthanthoserepresentingotherspatialprocesses.

Fig. 11 presents the original ICs representing the liquid slug

and after the elimination of cyclostationary characteristics. It

can be seen that the signals from the downstream and upstream

planes have a good similarity, which allows the reliable mea-

surement of the cross-correlation velocity.

It can be seen from Fig. 3 that, from 6 to 10 s, liquid and gas

slugs go through by turns, and from 10 to 12 s, there is no liquid

slug going through. Table I presents the comparison between

the mean velocity of different spatially independent compo-

nents with liquid and gas slugs going through by turns and

those without liquid slug going through. The mean velocity of

all spatially independent components with liquid and gas slugs

going through by turns is greater than those without liquid slug

going through. As expected, the liquid velocity increases with

the introduction of slug. Without liquid slug going through,

the liquid phase has a low velocity, particularly for the liquid

phase around the pipe wall (liquid film). With liquid slug going

through, the liquid phase is accelerated. This result agrees with

the findings of previous studies [36]. The increase in the gas-

phase velocity is related to the initiation process of slug flow.

The gas flows above the liquid in parallel streams, and slugs

originate from waves at the gas–liquid interface that grow to

fill the pipe cross section. Wave growth can be described by

Kelvin–Helmholtz instability. Long wavelength disturbances

on a stratified layer develop into growing waves until eventually

one of the waves grows to block the pipe. This restricts the

flow of gas, and thus, pressure builds up behind the blockage,

causing it to be accelerated to the gas velocity, forming a slug.

The mean velocity of the liquid phase in the central region is

greater than that of the gas phase at the interface, which is

consistent with the flow condition (USW= 1.06 m/s,USG=

0.31 m/s; the superficial velocity of the liquid phase is larger

than that of the gas phase). The central region velocity

(3.60 m/s) is close to the slug velocity (3.96 m/s). This result

supports the assumptions made by Dukler et al. [37]. Without

liquid slug going through, the liquid film velocity is lower than

that in the central region. This is because, without liquid slug

going through, there is relatively larger friction between the

liquid phase near the wall and the pipe wall, which results in

the lower mean velocity near the pipe wall than that in the

centralregion.Withliquidandgasslugsgoingthroughbyturns,

the liquid slug with fast velocity drives the liquid phase near

the pipe wall to move forward, which leads to the faster mean

velocitynearthepipewall.Theaforementionedresultsfromthe

novel method have a good agreement with the actual physical

processes, which indirectly validate the effectiveness of this

approach.

V. CONCLUSION

From the comparisons between the ICs and the reconstructed

ERT images, the ICs have been given good interpretations, and

ICA has been verified to be an effective method for extracting

phase informationofgas–liquidtwo-phaseflow, particularlyfor

stratified, slug, and wave flows. The ICs have physically been

interpreted by comparing the obtained ICs with the results from

the reconstructed ERT images.

Through correlating ICs representing different spatially in-

dependent processes from the upstream and downstream planes

after the elimination of cyclostationary characteristics of ICs,

the mean velocity of different spatial processes were obtained.

The experimental results obtained using the novel method

have demonstrated a good agreement with the actual physical

processes.

The results presented in this paper have shown that BSS

is a promising tool for extracting phase information for two-

phase flow measurement. Combined with the phase distribution

information obtained from the ERT, the flow rates of different

physical phases can be estimated. However, there is still a lot

of work to be done in the future, for instance, extending and

studying the nonlinear ICA (or BSS) method to take account of

more complicated physical models.

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.

Page 8

XU et al.: SEPARATION OF GAS–LIQUID TWO-PHASE FLOW THROUGH ICA1301

REFERENCES

[1] S. Haykin, Ed., “Unsupervised adaptive filtering,” in Blind Source Sepa-

ration. New York: Wiley, 2000.

[2] S. Choi, A. Cichocki, H. M. Park, and S. Y. Lee, “Blind source separation

andindependentcomponentanalysis:Areview,”NeuralInf.Process.Lett.

Rev., vol. 6, no. 1, pp. 1–57, Jan. 2005.

[3] P. Comon, “Independent component analysis: A new concept?” Signal

Process., vol. 36, no. 3, pp. 11–20, 1994.

[4] T. W. Lee, Independent Component Analysis: Theory and Applications.

Boston, MA: Kluwer, 1998.

[5] A. Hyvärinen and E. Oja, “Independent component analysis: Algo-

rithms and applications,” Neural Netw., vol. 13, no. 4/5, pp. 411–430,

May/Jun. 2000.

[6] M. B. Zadeh and C. Jutten, “A general approach for mutual informa-

tion minimization and its application to blind source separation,” Signal

Process., vol. 85, no. 5, pp. 975–995, May 2005.

[7] S. Dodel, J. M. Herrmann, and T. Geisel, “Localization of brain

activity—Blind separation for fMRI data,” Neurocomputing, vol. 32/33,

pp. 701–708, 2000.

[8] V. D. Calhoun, T. A. Dali, M. C. Stevens, K. A. Kiehl, and J. J. Pekar,

“Semi-blind ICA of fMRI—A method for utilizing hypothesis-derived

time courses in a spatial ICA analysis,” NeuroImage, vol. 25, no. 2,

pp. 527–538, Apr. 2005.

[9] T. P. Jung, C. Humphries, T.-W. Lee, S. Makeig, M. J. McKeown,

V. Iragui, and T. J. Sejnowski, “Removing electroencephalographic arti-

facts: Comparison between ICA and PCA,” in Proc. Neural Netw. Signal

Process. VIII, 1998, pp. 63–72.

[10] C. J. Jame and O. J. Gibson, “Temporally constrained ICA: An applica-

tion to artifacts rejection in electromagnetic brain signal analysis,” IEEE

Trans. Biomed. Eng., vol. 50, no. 9, pp. 1008–1116, Sep. 2003.

[11] C. J. James and C. W. Hesse, “Independent component analysis for bio-

medical signals (Topical review),” Physiol. Meas., vol. 26, no. 1, pp. R15–

R39, Feb. 2005.

[12] S. Akaho, “Conditionally independent component analysis for super-

vised feature extraction,” Neurocomputing, vol. 49, no. 1, pp. 139–150,

Dec. 2002.

[13] J. Lin and A. Zhang, “Fault feature separation using wavelet–ICA filter,”

NDT&E Int., vol. 38, no. 6, pp. 421–427, Sep. 2005.

[14] N. Kwak, C. H. Choi, and J. Choi, “Feature extraction using ICA,” in

Proc. ICANN, vol. 2130, LNCS, 2001, pp. 568–573.

[15] K. Torkkola, “Blind separation for audio signals—Are we there yet?” in

Proc ICA, Aussiois, France, 1999, pp. 239–244 .

[16] T. Kim and S. Y. Lee, “Learning self-organized topology-preserving

complex speech features at primary auditory cortex,” Neurocomputing,

vol. 65, pp. 793–800, Jun. 2005.

[17] D. E. Callan, A. M. Callan, C. Kroos, and E. Vatikiotis-Bateson, “Multi-

modal contribution to speech perception revealed by independent compo-

nent analysis: A single-sweep EEG case study,” Cogn. Brain Res., vol. 10,

no. 3, pp. 349–353, Jan. 2001.

[18] D. R. Tailor, L. H. Finkel, and G. Buchsbaum, “Color-opponent receptive

fields derived from independent component analysis of natural images,”

Vis. Res., vol. 40, no. 19, pp. 2671–2676, Sep. 2005.

[19] Z. Wang, C. S. Leung, Y.-S. Zhu, and T.-T. Wong, “Data compression on

the illumination adjustable images by PCA and ICA,” Signal Process.:

Image Commun., vol. 19, no. 10, pp. 939–954, Nov. 2004.

[20] N. Katsumata and Y. Matsuyama, “Database retrieval for similar images

using ICA and PCA bases,” Eng. Appl. Artif. Intell., vol. 18, no. 6,

pp. 705–717, Sep. 2005.

[21] P. C. Yuen and J. H. Lai, “Face representation using independent com-

ponent analysis,” Pattern Recognit., vol. 35, no. 6, pp. 1247–1257,

Jun. 2002.

[22] O. Déniz, M. Castrillón, and M. Hernández, “Face recognition using

independent component analysis and support vector machines,” Pattern

Recognit. Lett., vol. 24, no. 13, pp. 2153–2157, Sep. 2003.

[23] H. K. Ekenel and B. Sankur, “Feature selection in the independent com-

ponent subspace for face recognition,” Pattern Recognit. Lett., vol. 25,

no. 12, pp. 1377–1388, Sep. 2004.

[24] B. A. Drapter, K. Baek, M. S. Bartlett, and J. R. Beveridge, “Recognizing

faces with PCA and ICA,” Comput. Vis. Image Underst., vol. 91, no. 1/2,

pp. 115–137, Jul./Aug. 2003.

[25] Y. Xu, H. Wang, Z. Cui, F. Dong, and Y. Yan, “Independent component

analysis of the interface fluctuations of gas/liquid two-phase flow,” in

Proc.Int.Conf.IEEEInstrum.Meas.Technol.,Singapore,May5–7,2009,

pp. 1725–1729.

[26] M. Akai, A. Inoue, and S. Aokis, “The prediction of stratified two-phase

flow with two-equation model of turbulence,” Int. J. Multiphase Flow,

vol. 7, no. 1, pp. 21–29, Feb. 1981.

[27] R. I. Issa, “Prediction of turbulent, stratified, two-phase flow in inclined

pipes and channel,” Int. J. Multiphase Flow, vol. 14, no. 2, pp. 141–154,

Mar./Apr. 1988.

[28] A. Liné, L. Masbernat, and A. Soualmia, “Interfacial interactions and

secondary flows in stratified two-phase flow,” Chem. Eng. Commun.,

vol. 141, no. 1, pp. 303–329, Nov. 1996.

[29] F. Esposito, E. Formisano, E. Seifritz, R. Goebel, R. Morrone,

G. Tedeschi, and F. D. Salle, “Spatial independent component analysis

of functional MRI time-series: To what extent do results depend on

the algorithm used?” Hum. Brain Mapp., vol. 16, no. 3, pp. 146–157,

Jul. 2002 .

[30] A. J. Bell and T. J. Sejnowski, “An information-maximization approach to

blind separation and blind deconvolution,” Neural. Comput., vol. 7, no. 6,

pp. 1129–1159, Nov. 1995.

[31] T. P. Jung, S. Makeig, M. J. McKeown, A. J. Bell, T. W. Lee, and

T. J. Sejnowski, “Imaging brain dynamics using independent component

analysis,” Proc. IEEE, vol. 89, no. 7, pp. 1107–1122, Jul. 2001.

[32] Z. Q. Cui, H. X. Wang, L. Tang, L. F. Zhang, X. Y. Chen, and Y. Yan,

“A specific data acquisition scheme for electrical tomography,” in Proc.

Int. Conf. IEEE Instrum. Meas. Technol., Vancouver Island, BC, Canada,

May 12–15, 2008, pp. 726–729.

[33] M. J. McKeown, S. Makeig, G. G. Brown, T. P. Jung, S. S. Kindermann,

and A. J. Bell, “Analysis of fMRI data by blind separation into indepen-

dent spatial components,” Hum. Brain. Map., vol. 6, no. 3, pp. 160–188,

1998.

[34] Y. Xu, “Research on gas/liquid two-phase flow measurement in horizontal

pipeline based on electrical resistance tomography,” Ph.D. dissertation,

Tianjin Univ., Tianjin, China, 2008.

[35] M. S. Beck and A. Plaskowski, Cross Correlation Flowmeters: Their

Design and Application. Bristol, PA: Adam Hilger, 1987.

[36] O. Kvernvold, V. Vindoy, T. Sontvedt, A. Saasen, and S. Selmen-Olsen,

“Velocity distribution in horizontal slug flow,” Int. J. Multiphase Flow,

vol. 10, no. 4, pp. 441–457, Aug. 1984.

[37] A. E. Dukler, D. M. Maron, and N. Brauner, “A physical model for

predicting the minimum stable slug length,” Chem. Eng. Sci., vol. 40,

p. 1379, 1985.

Yanbin Xu received the B.S., M.S., and Ph.D. de-

grees from Tianjin University, Tianjin, China, in

2001, 2004, and 2009, respectively, all in control

science and engineering.

She is currently a Lecturer with the School of

Electrical Engineering and Automation, Tianjin Uni-

versity. Her research interests include industrial

process tomography, multiphase flow measurement,

biomedical measurement, process parameter detec-

tion, and information processing.

Huaxiang Wang (SM’06) received the M.S. degree

in detecting technique and automation from Tianjin

University, Tianjin, China, in 1982.

He is currently a Professor with the School of

Electrical Engineering and Automation, Tianjin Uni-

versity. His main research interests are in the field of

detecting technique and signal processing, as well as

process tomography.

Ziqiang Cui received the B.S. degree in electrical

engineering and automation from Hebei University

of Technology, Tianjin, China, in 2004 and the M.S.

and Ph.D. degrees in control science and engineering

from Tianjin University, Tianjin, in 2006 and 2009,

respectively.

He is currently a Postdoctoral Fellow with

the Department of Automation, Nankai University,

Tianjin, China. His research interests include indus-

trial process tomography and signal processing.

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.

Page 9

1302 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 5, MAY 2010

Feng Dong (S’01–M’04–SM’06) received the B.S.,

M.S., and Ph.D. degrees from Tianjin University,

Tianjin, China, in 1988, 1996, and 2002, respec-

tively, all in control science and engineering.

He is currently a Professor with the School of

Electrical Engineering and Automation, Tianjin Uni-

versity. During his career, he has published more

than 80 technical papers. He is the holder of two

patents. His research interests include process pa-

rameter detection and control system, industrial

process tomography, multiphase flow measurement,

and intelligent information processing.

Dr. Dong is a Committeeman of the International Steering Committee for

the International Society for Industrial Process Tomography, a Committeeman

of the China National Technical Committee of Standardization for Industrial

Process Measurement and Control (SAC/TC124), a Vice-Chairman of the En-

ergy Saving Applied Technology Committee of China Instrument and Control

Society, andaCommitteemanoftheMultiphaseFlowMeasurementCommittee

of China Metrological Measuring Institute. He was the recipient of the Tianjin

Municipality Natural Science Award in 2002 and 2009.

Yong Yan (M’04–SM’04) received the B.Eng. and M.Sc. degrees in instru-

mentation and control engineering from Tsinghua University, Beijing, China, in

1985 and 1988, respectively, and the Ph.D. degree in solids flow measurement

and instrumentation from the University of Teesside, Middlesbrough, U.K.,

in 1992.

He started his academic career as an Assistant Lecturer with Tsinghua

University in 1988. In 1989, he joined the University of Teesside as a Research

Assistant. After a short period of postdoctoral research, he initially worked as a

Lecturer with the University of Teesside during 1993–1996 and then as a Senior

Lecturer, Reader,and Professor, respectively, with the University of Greenwich,

London, U.K., during 1996–2004. He is currently a Professor of electronic

instrumentation, the Head of Instrumentation, Control and Embedded Systems

Research Group, and the Director of Research with the School of Engineering

and Digital Arts, University of Kent, Canterbury, U.K. He serves as a member

oftheEditorialBoardsforFlowMeasurementandInstrumentationandChinese

Journal of Scientific Instruments. He has published more than 250 research

papers in archived journals and conference proceedings.

Dr. Yan is a Fellow of the Institution of Engineering Technology [IET;

formerly Institution of Electrical Engineers (IEE)], the Institute of Physics, and

the Institute of Measurement and Control, U.K. He is a member of five U.K.

national technical committees and expert panels. He was the recipient of the

Achievement Medal from IEE in 2003 and the Engineering Innovation Prize

from IET in 2006, in recognition of his outstanding contributions in gas–solid

flow measurement and combustion flame imaging.

Authorized licensed use limited to: IEEE Xplore. Downloaded on April 23,2010 at 01:45:23 UTC from IEEE Xplore. Restrictions apply.