Flow pattern recognition is necessary to select design equations for finding operating details of the process and to perform computational simulations. Visual image processing can be used to automate the interpretation of patterns in two-phase flow. In this paper, an attempt has been made to improve the classification accuracy of the flow pattern of gas/ liquid two- phase flow using fuzzy logic and Support Vector Machine (SVM) with Principal Component Analysis (PCA). The videos of six different types of flow patterns namely, annular flow, bubble flow, churn flow, plug flow, slug flow and stratified flow are re- corded for a period and converted to 2D images for processing. The textural and shape features extracted using image processing are applied as inputs to various classification schemes namely fuzzy logic, SVM and SVM with PCA in order to identify the type of flow pattern. The results obtained are compared and it is observed that SVM with features reduced using PCA gives the better classification accuracy and computationally less intensive than other two existing schemes. This study results cover industrial application needs including oil and gas and any other gas-liquid two-phase flows.

1. Research article
An artificial intelligence based improved classification of two-phase
flow patterns with feature extracted from acquired images
C. Shanthi n
, N. Pappa
Department of Instrumentation Engineering, MIT Campus, Anna University, Chennai, India
a r t i c l e i n f o
Available online 13 February 2017
Keywords:
Gas-liquid flow pattern
Image processing
Fuzzy logic
Support vector machine
Principal component analysis
a b s t r a c t
Flow pattern recognition is necessary to select design equations for finding operating details of the
process and to perform computational simulations. Visual image processing can be used to automate the
interpretation of patterns in two-phase flow. In this paper, an attempt has been made to improve the
classification accuracy of the flow pattern of gas/ liquid two- phase flow using fuzzy logic and Support
Vector Machine (SVM) with Principal Component Analysis (PCA). The videos of six different types of flow
patterns namely, annular flow, bubble flow, churn flow, plug flow, slug flow and stratified flow are re-
corded for a period and converted to 2D images for processing. The textural and shape features extracted
using image processing are applied as inputs to various classification schemes namely fuzzy logic, SVM
and SVM with PCA in order to identify the type of flow pattern. The results obtained are compared and it
is observed that SVM with features reduced using PCA gives the better classification accuracy and
computationally less intensive than other two existing schemes. This study results cover industrial ap-
plication needs including oil and gas and any other gas-liquid two-phase flows.
& 2017 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Gas/liquid flow is a type of flow encountered in applications
such as oil and gas, power plant and chemical industries etc. Many
researchers have carried out flow pattern identification work on
two-phase flow in pipelines [1–3]. The detection of two-phase
flow patterns is mainly performed by either visual observation or
flow signals processing. The flow signals include pressure and
velocity variations within the flow. Visual observation is the most
preferred method for gas-liquid flow pattern identification. This
method of flow pattern classification purely depends upon in-
dividual's interpretation of images. Hence there are numerous
methods for classification followed for these flows. In a horizontal
pipe, phase separation occurs when gravity acts perpendicular to
the tube axis. Typical flow patterns observed in industries are
annular flow, bubbly flow, churn flow, plug flow, slug flow and
stratified flow.
Annular flow is a flow pattern where liquid flows on the wall of
the pipe and gas flows in the centre. In bubbly flow, liquid is
continuous and there is a dispersion of bubbles within the liquid.
Churn flow is a kind of flow pattern where the liquid is unstable or
oscillating. In Plug flow pattern, the bubbles have coalesced to
make a larger bubble which approaches the diameter of the pipe.
Slug flow finds its application in oil industry in pipelines carrying
oil and natural gas. In stratified pattern, the horizontal interface is
smooth. Hence the liquid and gas are completely stratified in this
regime.
There are difficulties on flow pattern maps with most of the
existing literature. These maps are dimensional dependent and
therefore apply only to the specific pipe sizes and fluids employed
by the investigator. It is difficult to have a generalized flow pattern
map for different set of fluids and pipe sizes. Because one transi-
tion might occur at a Weber number whereas another boundary
may occur at a Reynolds number. Hence, there exist no universal
dimensionless flow pattern maps for fluids. Fig. 1 shows the oc-
currence of different flow patterns for the flow of air/water two-
phase flow in a horizontal 5 cm pipe.
The flow regime identification of gas/liquid flow in vertical pipe
was carried out using feature extraction based Support Vector
Machine and Neural network [4]. The two-phase gas-liquid flow
pattern in an upriser pipe of an airlift pump has been investigated
using image processing techniques.Four patterns bubbly, slug,
churn and annular flow were recognized. The performance of the
airlift pump in different submergence ratios was measured [5] and
compared with the flow pattern map of Hewitt and Roberts [6].
Based on the textural features and SVM, flow classification was
proposed in [7]. The flow parameters are measured by image
analysis and the uncertainty associated with the measured para-
meters also calculated [8]. Flow pattern identification was carried
out using distance evaluation method and Support Vector Machine
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/isatrans
ISA Transactions
http://dx.doi.org/10.1016/j.isatra.2016.10.021
0019-0578/& 2017 ISA. Published by Elsevier Ltd. All rights reserved.
n
Corresponding author.
E-mail address: cgshanthi@gmail.com (C. Shanthi).
ISA Transactions 68 (2017) 425–432

2. [9]. Fuzzy Neural Network was used to identify the flow pattern of
bubbly, slug and plug flow [10]. Experimental study was carried
out to identify the flow patterns in the wake of a Taylor bubble
rising through vertical columns of stagnant and flowing liquids
[11]. The flow images are visualized and the patterns were clas-
sified using different techniques [12–17]. Gas/liquid two-phase
flow pattern identification is done in order to improve the flow
performance and flow parameter measurement. Three major flow
patterns namely, bubbly, slug and churn were identified using the
data collected from Electrode Resistance Tomography (ERT) sys-
tem. 1D and 2D wavelet transform has been used to extract fea-
tures from ERT data [18]. Acoustic Emission (AE) system combined
with artificial neural network was used to recognize the flow
patterns in an air-water vertical two-phase flow column [19]. A
study of the evolution of slug flow parameters was carried out in
vertical pipe. The local void fraction was measured using fibre
optic probes [20]. A flow regime map for the flow of air-water
mixture in a horizontal pipe has been discussed [21]. In the pre-
sent work, a fuzzy logic system and SVM with PCA is proposed to
identify the gas-liquid flow patterns.
2. Experimental setup
The experimental setup of liquid-gas flow measurement is gi-
ven in Fig. 2. Atmospheric air is compressed and passed through
the air flow meter (Process Line size:2”,Flow rate: 0.1–16 m3
/h.)
with the regulated valve in the air line. At the same time water
from overhead tank is regulated and is sent through the flow
meter (Process Line size:2”,Flow rate: 1–80 m3
/h.) to the water
line. At the T-joint air and water gets mixed together and is al-
lowed to flow through the transparent glass pipe. Depending upon
the different air flow rates, different flow patterns are obtained
with constant water flow rate of 150lpm and are tabulated in
Table 1. Since there is possibility of liquid pressure to be higher
than the air pressure, there is a non-return valve connected to the
air flow side to prevent the liquid from entering the air flow side.
The rotameter for measuring liquid flow rate is acrylic type. Both
flow meters are at ambient temperature and have no pressure loss.
Digital camera Nikon Coolpix p5.10 is used for capturing the videos
at a speed of 25 frames per second of liquid/gas two-phase flow
patterns. The six different types of flow patterns identified in this
paper are given in Fig. 3.
3. Image processing
Inferential measurement based on image analysis is a powerful
technique to identify the flow patterns of gas-liquid flow. There
are a number of techniques in digital image processing which can
be used to obtain desired results. The images of the six different
flow patterns taken under study are acquired. The frames are
loaded in such a way that they are available continuously one after
the other for the successive processing techniques. The frames of
Red Green Blue (RGB) images of the six different types of flow
patterns loaded are shown in Fig. 2. The RGB images are converted
to gray scale images (0 to 255) using weighted or luminosity
method. This method converts RGB to gray images by eliminating
the hue and saturation while retaining the luminance. Gray images
are then converted into black and white images by global
thresholding that classifies pixels into two categories (black and
white). Binary images contain numerous imperfections. In parti-
cular, binary regions produced by thresholding are distorted by
Fig. 1. Flow pattern map for the gas /liquid flow in a horizontal 5 cm pipe.
Fig. 2. Experimental set up. (a) Schematic diagram of the experimental set up. (b)
Photo of the experimental set up.
Table 1
Nominal air flow rates for flow patterns.
S.No. Type of flow pattern Flow rate of Air (lpm)
1. Bubbly flow 20
2. Plug flow 22
3. Slug flow 30
4. Churn flow 35
5. Annular flow 40
6. Stratified flow 45
C. Shanthi, N. Pappa / ISA Transactions 68 (2017) 425–432426

3. noise and texture. Morphological image processing operations
(Erosion and dilation) are used to remove these imperfections.
4. Fuzzy logic
Fuzzy logic converts linguistic strategy to automatic control
strategy based on expert knowledge. The fuzzy logic system
comprises of four components; Fuzzification, Knowledge Base,
Decision making logic and Defuzzification. From the morpholo-
gically processed images, the maximum and minimum object
width is calculated by finding the longest and the shortest dis-
tance between two white pixels. The obtained values for the re-
corded images acquired as video for 5 sec. time period are given
in Table 2. These values are used to design the fuzzy logic system.
Fuzzification converts the input data to linguistic variables. In
this work, fuzzification is performed for the maximum and
minimum widths denoted by W1 and W2. Triangular membership
functions are used. Fig. 4. shows the input membership functions
for W1 and W2. Five different linguistic variables namely Very
Small (VS), Small(S), Medium (M), Large (L), Very Large (VL) are
assigned for each membership function. The knowledge base is a
rule base. The rules are expressed with syntax like: IFofuzzy
proposition4THEN o fuzzy proposition4.
The Knowledge base is modelled for the fuzzified values of W1
and W2. Twenty five rules are framed to identify the six different
flow patterns. The rule base thus created is given in Table 3. Once
the rules are framed a rule base matrix is obtained. From this
matrix it can be seen that each output depends on number of
rules. This gives rise to ambiguity which can be avoided by deci-
sion making. In decision making all the possible combinations of
inputs for each output are grouped together to form a single rule.
Thus decision making is the process of obtaining a single truth
value. The number of rules obtained as a result of decision making
is equal to the number of output. Decision making is the process of
considering the input value and all rules including the aggregation
of their output into a single output value. Thus six set of rules were
formulated for the six different flow patterns as shown in Table 4.
Defuzzification results a crisp, non-fuzzy parameter from an in-
ferred fuzzy value. In this paper, the centre of area method is
considered as the defuzzification strategy. Defuzzification is per-
formed for each membership function to convert the values of the
linguistic variables into crisp values. Fig. 5 shows the defuzzified
output. The fuzzy logic system is validated with 20 frames of
Fig. 3. Sample images extracted from video for six different flow patterns.
Table 2
Ranges of Maximum and Minimum object widths (W1 and W2).
S.No. Type of flow
pattern
Maximum object width
W1 ( pixels)
Minimum object width
W2 ( pixels)
1. Bubbly Flow 10–38 5–15
2. Plug Flow 36–60 26–38
3. Slug Flow 70–92 35–48
4. Churn Flow 58–74 28–38
5. Annular Flow 60–90 15–25
6. Stratified Flow 40–60 40–60
Fig. 4. Input membership functions. (a). Membership functions for Maximum
width (W1). (b). Membership functions for Minimum width (W2).
Table 3
Formulated rule base for different flow patterns.
W2 W1
Very Small Small Medium Large Very Large
Very Small Bubbly Bubbly Annular Annular Annular
Small Bubbly Bubbly/Slug Annular Annular Annular
Medium Bubbly Plug Stratified Churn Slug
Large Bubbly Plug/ Slug Stratified Churn Slug
Very Large Bubbly Slug Stratified/
Annular
Churn/slug Slug
C. Shanthi, N. Pappa / ISA Transactions 68 (2017) 425–432 427

4. images of different flow patterns and the classification efficiency of
the system is tabulated in Table 7. There is some difficulty in
identifying few images due to certain changes in conditions while
capturing the images.
5. Feature extraction
Feature extraction involves simplifying the amount of resources
required to describe a large set of data accurately. In this paper, 120
frames of images for the six different types of flow patterns are
considered. Seventeen textural features and seven shape features
have been extracted from the preprocessed images. Hence, totally
24 different features have been extracted and the average of each
feature value over the 120 images are computed.
5.1. Textural feature extraction
The texture of an image is determined by the way the gray
levels are distributed in the region. It contains important in-
formation about structural arrangement of surfaces and their re-
lationship with surrounding environment. Although it is easy for
human observers to recognize and describe in empirical terms,
texture has been extremely refractory to precise definition and to
analysis by digital computers. Since the textural properties of
images appear to carry useful information for discrimination
purpose, it is important to develop features for textures. In this
paper, textural feature with first order statistics was considered.
These features depend only on individual pixel values and not on
the interaction or co-occurrence of neighboring pixel values. The
first order statistics involves histogram features and statistical gray
level features.
Seventeen textural features such as average gray level, max-
imum gray level, minimum gray level, standard deviation, var-
iance, etc. are extracted from the gray scale images of different
flow patterns. The average value of the extracted textural features
is listed in Table 5.
5.2. Shape feature extraction
Efficient shape features must possess certain essential proper-
ties. They should be identifiable because shapes which are found
perceptually similar by human have the same feature different
from others. The rotation, location and scaling changing of shape
must not affect the extracted features. Seven different shape fea-
tures are extracted from the images of the different flow patterns.
The shape features such as circularity, maximum bubble size, area
of the bubbles, etc. are extracted and average value for 120 images
are listed in Table 6.
6. Pattern classification using SVM
Support Vector Machine (SVM) is a supervised learning algo-
rithm suitable for classification. SVMs give good performance in
many real time applications. Sequential Minimum Optimization
(SMO) is the SVM training algorithm [22] used in this paper. SMO
solves the Lagrange multipliers analytically.
The output of SVM is computed from Lagrange multipliers.
∑ α= ( ̅ ̅)–
=
y k x xu d,
j
N
j j j
1
,
Table 4
Fuzzy based decision making for different flow patterns.
S.No. Flow pattern Decision
1. Bubbly flow W2 is Small or Medium or Large or Very Large and W1 is
Very Small or Small
2. Plug flow W2 is Medium or Large or Very Large and W1 is Small
3. Slug flow W2 is Medium or Large or Very Large and W1 is Very
Large
4. Churn flow W2 is Medium or Large or Very Large and W1 is Large
5. Annular flow W2 is Very Small or Small and W1 is Large or Very Large
6. Stratified flow W2 is Medium or Large or Very Large and W2 is
Medium
Fig. 5. Membership functions for different types of flow patterns.
Table 5
Average value of textural features extracted for the recorded video.
Features Flow pattern
Bubbly flow Plug flow Slug flow Churn flow Annular flow Stratified flow
1. Average gray level of the image 252.66 204.21 253.88 204.09 173.66 253.91
2. Maximum gray level 243.11 230.43 250.02 235.01 245.31 253.20
3. Minimum gray level 12.70 50.66 13.52 48.92 48.08 30.04
4. Variance 260.84 257.06 250.00 252.73 255.01 258.08
5. Standard deviation 16.12 16.03 15.81 15.87 15.97 16.06
6. Skewness 0.0002 0.0016 0.0015 0.0012 0.0020 0.0011
7. Kurtosis 0.0071 0.0097 0.0021 0.0105 0.0074 0.0213
8. Modified standard deviation 24.54 24.13 23.79 24.07 24.22 24.59
9. Modified skew 0.0012 0.0014 0.0001 0.0014 0.0014 0.0014
10. Entropy 6.71 6.59 7.20 7.30 6.48 7.55
11. Standard deviation of histogram features 74.13 50.78 105.92 96.16 52.71 129.42
12. Range 175.06 122.02 231.09 193.02 126.51 251.72
13. Smoothness 0.998 0.9996 0.9998 0.999 0.9997 1.000
14. Average histogram 115.08 89.5 118.02 93.00 98.00 124.5
15. Uniformity 40.29 19.27 44.09 21.62 25.29 15.77
16. Local entropy 6.02 5.94 6.08 5.91 5.93 5.82
17. Third moment 5.14 5.00 5.36 5.09 5.02 5.56
C. Shanthi, N. Pappa / ISA Transactions 68 (2017) 425–432428

5. where k is a Kernel function that measures the similarity of
̅ ̅x and xj. The Lagrange multipliers are computed through a quad-
ratic program. The dual objective function ψ is given by
( )∑ ∑ ∑ψ α α α α α( ̅) = ̅ ̅ − ≤ ≤ ∀
= = =
y y k x x C
1
2
0 ,
i
N
j
N
i j i j i j
i
N
i i i
1 1
,
1
∑ α =
( )=
y 0
1i
N
i i
1
where N - Number of training samples. C is the trade-off between
training error and generalization factor. The Karush- Kuhn- Tucker
(KKT) conditions for Eq. (1),
α α α= ⇔ ≥ < < ⇔ = = ⇔ ≤y u C y u C y u0 1,0 1 and 1i i i i i i i i i
where ui is the output of the SVM for ith
training.
The SMO algorithm first computes second Lagrange multiplier
α2. If the target y1 ♯ y2, then
α α α α= ( − ) = ( + − )CL max 0, , H min C,2 1 2 1
If y1 ¼Target y2, then
α α α= ( + − = ( + )H KL max 0, C, min C,2 1 2 1
The second derivative of the objective function can be written
as
η= ( ̅ ̅ ) + ( ̅ ̅ )– (( ̅ ̅ )K x x K x x x x2K1, 1 2, 2 1, 2
Under normal conditions, the objective function will be positive
and η will be greater than zero. Now, SMO computes the minimum
along the direction of the constraint.
α α
η
= +
( − )y E ENew
2 2
2 1 2
Where Ei ¼ui –yi is the ith sample training error.
⎧
⎨
⎪⎪
⎩
⎪
⎪
α
α
α α
α
=
≥
< <
≤
H if H
if L H
L if L
New Clipped
New
New New
New
2
,
2
2 2
2
Consider S¼ αy y and1 2 1 is computed from αNew clipped
2
,
( )α α α α= + −sNew New clipped
1 1 2 2
,
SMO algorithm will be suitable even when η is negative, in such
case ψ should be evaluated at the end of each line segment.
( ) α α= + − ( ̅ ̅ ) − ( ̅ ̅ )f y E b K x x s K x x1 1 1 1 1, 1 2 1, 2
( ) α α= + − ( ̅ ̅ ) − ( ̅ ̅ )f y E b s K x x K x x2 2 2 1 1 , 2 2 2 , 2
α α= + ( − )L s L1 1 2
α α= + ( − )H s H1 1 2
ψ = + + ( ̅ ̅ ) + ( ̅ ̅ ) + (( ̅ ̅ )L f Lf L K x x L K x x K x x
1
2
1
2
SLLL 1 1 2 1
2
1, 1
2
2, 2 1 1, 2
ψ = + + ( ̅ ̅ ) + ( ̅ ̅ ) + ( ̅ ̅ )H f Hf H K x x H K x x S K x x
1
2
HHH 1 1 2 1
2
1, 1
2
2, 2 1 1, 2
The threshold ‘d’ is computed after every step, so that the KKT
conditions are satisfied.
SVM classification is attempted with the features such as
standard deviation and entropy. A data set is formed by taking 20
frames for each type of flow pattern. Hence 120 Â 2 matrix is
taken as the data set. Here the rows represent the number of
frames and the columns represent the features. Fig. 6(a)–(f) re-
presents the output for each type of flow pattern using SVM
without PCA. It can be seen from the figures that the results are
appreciable in the case of slug, stratified and churn flow patterns.
But in the case of bubble, plug and annular flow patterns, it can be
seen that a clear demarcation is not obtained to separate the de-
sired flow patterns from the other types. Hence principal com-
ponent analysis is performed to improve the output qualitatively
and quantitatively.
7. Pattern classification using SVM with PCA
Principal Component Analysis (PCA) is an important technique
used in data visualization and analysis. It is used to reduce the
dimension of a large set of data. In other words, it is a tool to
extract relevant information from complex data sets. Consider the
first principal component U1 with maximum variance. Suppose
that all centered observations are stacked into the columns of
matrix X,
ω=U XT
1
where ω ¼ [ ω1, ω2……….ωn]
( )( ) ω ω ω= =U X Svar var T T
1
Where S is the n  n covariance matrix of X. ( )var U1 can be
made arbitrarily large by increasing the magnitude of ω. Therefore,
choose ω to maximize ωT Sω while constraining ω to have unit
length.
ω ω ω ω=max S Subject to 1T T
To solve this optimization problem a Lagrange multiplier α1 is
introduced
ω α ω ω α ω ω( ) = − ( − ) ( )L , S 1 2T T
1
Differentiating with respect to ω gives n equations
ω α ω=S 1
Table 6
Average value of shape features extracted for the recorded video.
Features Flow pattern (pixels)
Bubbly flow Plug flow Slug flow Churn flow Annular flow Stratified flow
1. No. of bubbles in the image 15 2 1 10 0 0
2. Maximum size of the bubbles 40 38 92 74 90 60
3. No. of bubbles with size one pixel 3 0 0 1 0 0
4. Sum of areas of the bubbles 200 350 415 400 75 100
5. Radius of the circle that best fits the image 7.9 12 11.7 11.5 4.8 5.6
6. Circularity 0.99 0.77 0.97 0.96 1.04 1.01
7. Compactness 1.00 1.29 1.03 1.03 0.96 0.98
C. Shanthi, N. Pappa / ISA Transactions 68 (2017) 425–432 429

6. Fig. 6. Flow pattern using SVM without PCA.
(f) Stratified flow
Fig. 7. Flow pattern using SVM with PCA.
C. Shanthi, N. Pappa / ISA Transactions 68 (2017) 425–432430

7. Multiplying both sides by ω ,T
ω ω α ω ω α= −ST T
1 1
Var( )U1 is maximized if α1 is the largest eigenvalue of S.
α and1 ω are an eigenvalue and an eigenvector of S. Differentiating
Eq. (2) with respect to the Lagrange multiplier α1 gives the con-
straint.
ω ω = 1T
The first principal component is given by the eigenvector with
the largest associated eigenvalue of S. Similarly, all the principal
components can be determined from the dominant eigenvectors
of S.
In co-variance method the mean of the data matrix is com-
puted and the value is subtracted from each value in the matrix.
The co-variance matrix is computed and the eigenvalues and ei-
genvectors of this matrix are determined. The feature matrix is
constructed and five principal components are obtained. The five
principal components are maximum size of bubbles in the image,
sum of the areas of the bubbles, standard deviation of histogram
features, uniformity and average histogram.
The first and second principal components are taken as input to
the SVM classifier. A data set is formed using 20 frames for each
type of flow pattern. Hence totally 120 frames are considered. The
data set used in this case has a dimension of 120 Â 6. Here the
rows represent the number of frames and the columns represent
the principal components. Different values of first and second
principal components are given as input to the SVM. The values
are plotted accordingly and the different flow patterns are iden-
tified as shown in Fig. 7.(a)–(f).
8. Results and discussion
The objective of this paper is to identify six different flow patterns
such as bubble flow, slug flow, plug flow, stratified flow, annular flow
and churn flow using fuzzy logic and SVM with PCA. The fuzzy logic
based classifier, SVM classifier and PCA based SVM classifiers are
tested with 120 frames (20 frames of each flow pattern) of six flow
patterns. The classification accuracy is listed in Table 7.
In fuzzy logic based classification, it is observed that the clas-
sification accuracy is more than 80% in the case of bubble, plug and
annular flow. From Table 7 it is observed that in the case of slug,
stratified and churn flow the results obtained are not satisfactory.
It is found that performance of SVM classification is improved
when compared to the fuzzy logic classification except the strati-
fied flow. In SVM with PCA, it is observed that good results are
obtained for all the six types of flow patterns. It is finally observed
that SVM with PCA is found suitable for the classification of all six
types of flow patterns namely annular, bubble, churn, plug, slug
and stratified flow, with less computational complexity.
9. Conclusion
In this paper, an optimized gas-liquid flow pattern recognition
system using fuzzy logic and SVM with PCA is presented. The vi-
deos of various flow patterns are acquired with the help of a digital
camera. The image based analysis is carried out to calculate the
maximum and minimum object widths. The fuzzy logic system is
designed based on the extraction of image features and the system
is validated for various flow patterns. Also, flow regime identifi-
cation of gas/liquid two-phase flow has been performed using
feature extraction and SVM. In addition, a new method for feature
selection is introduced. The results are improved by applying PCA
in which five principal components are considered out of the 24
features. Hence, PCA reduces the complexity of the system. There
is some difficulty in identifying the images due to certain changes
in conditions while capturing the image. It is finally observed that
SVM with PCA gives much better results compared to the identi-
fication based on fuzzy logic and SVM. Hence, the proposed SVM
with PCA can be used to optimize the feature selection and for
efficient identification of flow patterns for industries with two-
phase flows.
Appendix
Mean ∑ ∑=
−
=
−
mn x
m
x
n1
0
1
0
1
(I(x,y)
Variance ( )∑ ∑ ( ) −( − ) =
−
=
−
I x y mean,mn x
m
x
n1
1 0
1
0
1 2
Standard deviation Variance
Skewness
( )
∑ ∑ ( ( ) − )
σ =
−
=
−
I x y Mean,
mn X
m
y
n1
0
1
0
1 3
3
Kurtosis
( )
∑ ∑ ( ( ) − )
σ− =
−
=
−
I x y Mean,
mn X
m
y
n1
0
1
0
1 4
4
Modified standard deviation
∑ ∑ ( ( ) − ) ( ( ))=
−
=
−
I x y Mean P I i j, ,X
m
y
n
0
1
0
1 2
Modified skew
( )
∑ ∑ ( ( ) − ) ( ( ))
σ =
−
=
−
I x y Mean P I i j, ,X
m
y
n1
0
1
0
1 3
3
Smoothness −
σ+
1
1
1 2
Uniformity ∑ ( )=
−
p zi
L
i0
1 2
Third moment ∑ ( − ) ( )=
−
p z m p zi
L
i i0
1 3
Entropy
Table 7
Classification Accuracy.
Flow patterns Classification Accuracy (rounded to the nearest integer)
Fuzzy Logic SVM SVM with PCA
Bubbly flow 83 85 98
Plug flow 87 90 99
Slug flow 70 77 95
Churn flow 50 52 90
Annular flow 85 89 99
Stratified flow 66 63 92
C. Shanthi, N. Pappa / ISA Transactions 68 (2017) 425–432 431

8. ∑ ( ) ( )=
−
p z zlogi
L
i i0
1
2
Average histogram ∑ ( )=
−
N iL i
L1
0
1
Circularity ΠA
p
4
2
Compactness
Π
p
A4
2
In the above equations m and n denote the number of rows and columns in the image matrix, I(x,y) denotes a particular pixel value in
the loaded image, p(Zi) is the histogram of intensity levels in a region, where I ¼ 1,2,3,….,L-1. Here L denotes the number of possible
intensity levels. ‘A’ denotes the area of the circle that best fits a cluster of bubbles.
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C. Shanthi, N. Pappa / ISA Transactions 68 (2017) 425–432432