1. Online flooding monitoring in packed towers using EDPCA method
WANG Wenwen, CAO Zewen, GAO Zengliang, LIU Yi*
Engineering Research Center of Process Equipment and Remanufacturing, Ministry of Education,
Institute of Process Equipment and Control Engineering, Zhejiang University of Technology, Hangzhou, 310014, PR China
E-mail: yliuzju@zjut.edu.cn
Abstract: Traditional flooding monitoring methods have been found insufficient to monitor various types of industrial packed
towers. In this work, an enhanced data-driven monitoring method, i.e., enhanced dynamic principal component analysis
(EDPCA), is proposed for online flooding monitoring in packed towers. The operation data samples are first clustered into
several classes using the fuzzy c-means clustering approach. Then, several single DPCA models are trained with each subset.
Furthermore, the Bayesian inference is adopted to integrate these single DPCA models. The obtained results for online flooding
monitoring of an air-water packed tower demonstrate that EDPCA can obtain better and more reliable performance, compared
with the DPCA method.
Key Words: Flooding monitoring, packed towers, Bayesian inference, dynamic principal component analysis
1 Introduction
Energy is the largest controllable cost in process operation,
such as distillation and absorption. Its efficient production
and use are keys to plant profitability. For industrial packed
towers, the closer the columns are operating to the maximum
possible capacity, the less the energy consumption will be.
However, flooding occurs when the vapor flow disrupts the
condensation flow, causing axial mixing that reduces
differentiation and decreases efficiency. When unchecked,
flooding can also cause a runaway condition that disrupts the
entire process, resulting in product losses and system
downtime [1]. Therefore, there is a constant need for online
monitoring of flooding, particularly those adaptable to a
range of different distillation systems and processes.
Previously, the efforts for flooding detection mainly
focused on three aspects: visual detection, liquid holdup
measurement and pressure monitoring. For transparent
towers, observing the buildup of liquid on packing surface is
the most direct way of flooding monitoring [2]. However, the
delay in reaction and hysteresis effects [3, 4] make it
unsuitable for practical processes. Flooding can also be
identified by an increase in liquid holdup. In order to measure
liquid holdup, both gas and liquid flows should be stopped,
while the liquid is remained in the column. Consequently, it is
difficult to be used for online monitoring. These demands
greatly hinder its application in practical production
processes [2, 5]. The other phenomenon along with flooding
is a dramatic increase in pressure. Parthasarathy [6] designed
a flooding indicator based on the differential pressure and
neural network. Regardless of its ability to predict flooding
several minutes in advance, the use of a predictive model
suggests that online pressure measurements do not detect a
change early enough to prevent flooding [5]. Additionally,
Hansuld [5] provided a new orientation for flooding
monitoring by analyzing the acoustic signals. However, the
*
This work is supported by the National Natural Science Foundation of
China under Grant 61004136 and Jiangsu Key Laboratory of Process
Enhancement & New Energy Equipment Technology (Nanjing University
of Technology). Corresponding author: Dr. Yi Liu.
signal is highly vulnerable by the impact of the surrounding
environment. Recently, the pressure monitoring method is
verified by Pihlaja [7] through a distillation column with a
specified pressure sensor of 3051S.
Different from previous methods, this paper aims to
develop a data-driven method for flooding monitoring mainly
because of the heavy applications of various distributed
control systems which can provide a large amount of
operational data to be analyzed and utilized. Among these
data driven monitoring methods, principal component
analysis (PCA) usually serves as the most fundamental one
[8]. It has been widely used in chemical processes for fault
detection and diagnosis [9-12]. Unfortunately, the application
of PCA-based monitoring methods to the packed towers has
rarely been reported. For better capturing the dynamic feature
in packed tower operations, dynamic principal component
analysis (DPCA) [13] is applied for flooding monitoring.
Additionally, in order to improve the robustness of DPCA
flooding monitoring, an enhanced method is further proposed
based on DPCA and a soft clustering method. First, the fuzzy
c-means (FCM) [14] is used to cluster the history data into
several groups. Second, several DPCA models are built for
each subset. Then, the new test sample is evaluated using
each monitoring model. Finally, the monitoring result is
analyzed and obtained by Bayesian inference. This new
flooding monitoring method is simply denoted as
enhanced-DPCA (EDPCA).
The remainder of this paper is structured as follows. After a
brief introduction of DPCA and FCM, a detailed description
of EDPCA modeling and monitoring method for online
flooding monitoring of packed towers are provided in Section
2. Section 3 mainly gives the experimental equipment used
for testing the monitoring methods. In Section 4, various
experiments are designed to validate and demonstrate the
advantage of the proposed method. A comparison with the
conventional DPCA method is also investigated. Finally, the
conclusion is made in Section 5.
Proceedings of the 34th Chinese Control Conference
July 28-30, 2015, Hangzhou, China
8258

2. 2 Enhanced-Dynamic Principal Component
Analysis Monitoring Method
2.1 Dynamic Principal Component Analysis
The application of PCA involves the construction of a
reduced set of score variables, called loading vectors, which
can describe the significant variation of a process. The values
of these variables can be obtained as follows:
xPt (1)
where a
t is a vector storing the values of the scores
variables; am
P is a transformation matrix; m
x is a
vector in which the values of the process variables are stored;
and m , a are the number of process variables and retained
score variables, respectively.
The classic PCA-based process monitoring involves three
main steps: (i) collect process data, (ii) compress the data
using the decomposition algorithm, and (iii) choose the
testing statistics to monitor the process behavior. A more
detailed analysis of PCA can be found in [15].
Conventional PCA implicitly assumes that the
observations at one time are statistically independent of
observations at any past time. However, the dynamics of a
typical chemical or biological process cause the
measurements to be time dependent, which means that the
data may have both cross-correlation and auto-correlation.
The PCA method can be extended to the monitoring of
dynamic systems by augmenting each observation vector with
the previous h observations and stacking the data matrix in
the following manner.
T
nt
T
nht
T
nht
T
ht
T
t
T
t
T
ht
T
t
T
t
h
xxx
xxx
xxx
X
1
121
1
)(
(2)
where T
tx is the observation sample at time t ; and h is the
time lags.
By performing PCA on the data matrix in (2), a DPCA
model is extracted. For flooding monitoring, the monitoring
statistics are the squared prediction error (SPE) and
Hotelling’s T2
[15]. The control limit is usually chosen as
95% or 99%.
Before online monitoring, there are two parameters to be
determined, i.e., the number of principal components (PCs)
and the time lags h . In this study, the method of cumulative
percent variance (CPV) is adopted to determine the number
of PCs [16]. For flooding monitoring, a 95% value of CPV
can capture enough information of the process. Experience
indicates that a value of 1h or 2 is usually appropriate
when DPCA is used for process monitoring [15].
2.2 Fuzzy C-Means Clustering
Based on a defined similarity measure, FCM organizes the
sample set into several clusters such that the samples within
the same subset can have a higher degree of similarity,
whereas samples belong to different clusters have a higher
degree of dissimilarity [14]. It is an iterative method to divide
the original set into k subsets by minimizing the following
objective function J .
k
i
n
j
2
ij
m
ij duJ
1 1
),( cU (3)
nju
k
i
ij ,3,2,1,1
1
(4)
where U is the membership matrix; c is the sample mean;
k is the number of clusters; n is the number of data points;
m is the weighting parameter, usually chosen as 2; ijd
represents the distance between jx and the center of the ith
cluster.
Through the Lagrange principle, the update formulas can
be gotten as (5) and (6).
n
j
m
ij
n
j
j
m
ij
i
u
u
1
1
x
c (5)
k
l
m
lj
ij
ij
d
d
u
1
1/2
1
(6)
A solution of the objective function J can be obtained via
the following iterative process [14]:
Step 1: Initialize the membership matrix U , which should
satisfy (3).
Step 2: Calculate the k cluster centers by (5).
Step 3: Calculate the objective function J . If the difference
of two neighbors is less than the threshold , stop;
otherwise, go to step 4.
Step 4: Update the membership iju using (6). And then
repeat Step 2 to Step 4 until the algorithm is
converged.
2.3 EDPCA for Online Monitoring Implements
For a specific packing, different products are produced
under different spray densities. The samples in different
operation conditions exhibit different characteristics. And
with the requirements of product diversification, the packed
tower may be operated from one condition to another
resulting in the history data containing various distribution
features. In such a situation, a single global model is
insufficient to capture enough process characteristics. To
overcome this problem, a method using the probabilistic
inference is presented to integrate the monitoring results of
sub-models. First, FCM is employed to cluster the history
data into several subsets. Then, several single DPCA models
are built using each sub-class of samples. Finally, the
monitoring result is ensemble based on Bayesian inference.
The monitoring steps of the enhanced method are as
follows:
Normal operating condition (NOC) model development
(1) Obtain the normal operating data and normalize the data
using the mean and standard deviation of each variable.
(2) Cluster the training data X into several subsets 1S , 2S ,
, kS by FCM.
8259

3. (3) Build DPCA models 1DPCAM , 2DPCAM , , kMDPCA on
each subset. And the control limits of each model can be
set as kspespe lim1lim ,, and ktsts lim1lim ,, .
Online monitoring
(1) Obtain the new observation data sample and scale it with
the mean and variance in the aforementioned modeling
procedure.
(2) For the new sample newx , calculate the posterior
probability for each sample subset ip , ki ,,2,1 .
And the formula is
k
i
iinew
iinew
newi
pp
pp
p
1
)]()|([
)()|(
)|(
SSx
SSx
xS
(7)
where )( ip S and )|( inewp Sx , ki ,,2,1 are the
prior probability and the conditional probability,
respectively. Without any process or expert knowledge,
the prior probability can be calculated by the following
equation
n
n
p i
i )(S (8)
Generally, the conditional probability )|( inewp Sx is
defined on an inverse relationship of inew
D Sx , , i.e., the
distance of sample newx from the center of iS .
2
,
1
)|(
inew
D
p inew
Sx
Sx (9)
where )()(, inew
T
inewinew
D SxSxSx , and iS is the
center of the ith sub-cluster, noted as the vector
ki
n
in
i
i
i
i ,,2,1,
1
1
xS (10)
In such a situation, formula (7) becomes
k
i
i
i
newi
inewinew
DnD
n
p
1
2
,
2
, /
)|(
SxSx
xS
(11)
(3) Calculate the monitoring statistics (T2
and SPE) of the
test data based on model 1DPCAM , 2DPCAM , ,
kMDPCA .
(4) The monitoring results are integrated based on the
posterior probability 1p , 2p , , kp . Here, the final
control limits (i.e., limspe and limts ) are used to
illustrate how the monitoring results of each sub-model
are integrated, as shown in (12) and (13), respectively.
Both the two statistics and their control limits are
calculated in the same way, the weighted sum of the
control limit is still correspond to a false alarm rate of
)1( .
k
i
ii pspespe
1
limlim
(12)
k
i
ii ptsts
1
limlim
(13)
(5) Monitor whether T2
or SPE exceeds its control limit.
3 Apparatus and Procedure
The packed tower for the flooding experiment and
validation the proposed EDPCA monitoring method can be
shown in Fig. 1. The apparatus consists of a clear, acrylic
column with a diameter of 0.22 m and a height of 2.20 m.
Both the upper and the lower packing layers are 0.46 m. The
air is supplied from the bottom, while water is supplied to the
top of the column by a pump. The structured packing CY1700
is tested with a spray density range from 7~24 m3
/(m2
·h).
Using a data reading system, as shown in Fig. 2, the real-time
process variables can be recorded. All the measured variables
are listed in Table 1.
Fig. 1: A 2.20 m height structured packed tower for the flooding
experiment and validation the monitoring methods
Fig. 2: The interface of the data recording software
Table 1: Variables collected through experiment
Variables physical units
Flows
gas flow
liquid flow
m3
/h
Velocities
gas velocity
liquid velocity
m/s
Temperatures
gas temperature
liquid temperature
tower temperature
°C
Other
Variables
F factor
spray density
the opening of valve 15
differential pressure
m/s·(kg/m3
)½
m3
/(m2
·h)
scalar
Pa
The experimental procedure for data collection contains
the following three steps:
a) Pre-flooding: Manipulate the corresponding valves to
obtain a large spray density. And keep this process state more
than 30 minutes. This step aims to ensure all the packings wet.
b) Collect the process data: Manipulate the valves to obtain
a user-defined spray density, e.g., 14 m3
/(m2
·h). Then,
increase the gas velocity gradually until the packed tower is
flooding, which can be detected through the transparent tower
8260

4. wall. The change of gas velocity is manipulated by adjusting
the frequency of the fan. The variation of the frequency can
be set larger between two neighbors, if they are far away from
flooding. On the other hand, when it is close to flooding, the
change must be smaller. In this step, click the button to record
the real-time process data of the running tower.
c) Change the spray density and repeat step b) to obtain
another batch of data samples in different operating
conditions.
In each operation, the gas velocity changes every ten
minutes. During the transition from one state to another, only
the data samples of the last five minutes are selected into the
dataset. Through the recording software, eleven process
variables listed in Table 1 can be obtained. Based on the prior
knowledge, some have correlations with each other, such as
the gas velocity and the gas flow. In view of this, eight
variables are retained for monitoring except two flows and
the opening of the valve 15. Removing the unnecessary
variables is the first step of data pre-processing before
process monitoring. Then, the samples can be simply
preprocessing using a smoothing step to improve the quality.
Because of the deficiency of visual flooding detection, a
simple method based on the column differential pressure (DP)
is adopted to determine the operation state of the packed
tower. It finds that the variance of pressure drop is very small,
even close to zero, when the column is under normal
condition. Once flooding, the value of variance will increase
to hundreds, as shown in Fig. 3. After analyzing the data of all
available spray densities, the value of 35pa2
can be used as
the limit value to determine whether the packed tower is
flooding. This simple method can divide the data samples
into two parts, i.e., normal and flooding.
0 20 40 60 80 100 120 140 160 180 200 220 240 260
0
35
200
400
600
Sample
VarianceofDP
Normal
Flooding
Fig. 3: The variance of DP under one spray density
4 Results and Discussion
The performance of EDPCA is evaluated by monitoring
the operation condition of the packed tower described in
section 3. There are two cases to evaluate the validity of the
EDPCA method. The first one aims to exhibit the better
performance of EDPCA in contrast with DPCA. The second
is designed to verify the sensitivity and robustness of EDPCA
for different operation conditions.
4.1 Cross Validation for DPCA-based Methods
Through the implementation of experimental steps in
section 3, about 4,000 samples are obtained with the spray
density ranging from 7 to 23 m3
/(m2
·h). And the number of
samples under normal condition is 2,525.
For flooding monitoring, one spray density data set is
chosen for testing, whereas the normal sets under the other
spray densities are used as the training set. Just like the cross
validation, all the spray density sets are devoted to verify
DPCA-based methods. During flooding monitoring, different
values are used and it finds that 2h is the optimal one. As
an illustrated example, the monitoring results of DPCA and
EDPCA for spray density 17 are selected for analysis, as
shown in Figs. 4 and 5, respectively. The red sold line in each
figure represents the boundary between the normal condition
and flooding condition.
41 60 80 100 120 140 160 180 200 220 240
0
5
10
15
Sample
SPE
90% Control Limit
95% Control Limit
SPE
Fig. 4: The DPCA monitoring result under spray density 17
41 60 80 100 120 140 160 180 200 220 238
0
20
40
60
80
SampleSPE
99% Control Limit
95% Control Limit
SPE
41 60 80 100 120 140 160 180 200 220 238
0
50
100
150
Sample
T2
99% Control Limit
95% Contol Limit
T2
(b)
(a)
Fig. 5: The EDPCA monitoring results under spray density 17
During the experiments, if the gas velocity is pretty low,
the packed tower is far away from flooding. There is no need
to monitor these samples. For this reason, only the monitoring
results with larger gas velocities are shown in these figures.
The control limits of DPCA are chosen as 95% and 90%.
Since the statistic T2
has little monitoring effect, only the
chart of SPE is given. As shown in Fig. 4, DPCA can monitor
the abnormal condition in advance. This makes it very
suitable for flooding monitoring, because the operators can
take an earlier action. Additionally, near the 60th sample,
there are two SPE values beyond the control limits. The
sample number equals to the value of time lags. With the
change of gas velocity, the values of process variables also
increase. This results in the increase of statistic with
considering the correlations among variables. Thus, these two
samples are not the false alarms. For some spray densities, the
monitoring results are relatively poor, as shown in Fig. 6. SPE
is failed to monitor the flooding point at sample 118. Due to
the length of this paper, the other examples are not shown
here.
The monitoring results of EDPCA for spray density 17
m3
/(m2
·h) are shown in Fig. 5. For flooding monitoring, the
number of clusters is selected as 3 by comparing different
values such as 2, 4, 5. The control limits are chosen as 99%
and 95%. In fact, taking misinformation into consideration,
99% is more suitable for flooding monitoring for its low false
alarm rate. Unlike DPCA, both SPE and T2
can achieve a
good performance by giving alarms in advance. For normal
data, the statistics keep below the 99% control line expect for
8261

5. boundary samples. As the reason has been discussed in
DPCA, the symbol of flooding in EDPCA is also determined
by three successive samples excess the control limit.
38 58 78 98 118 138 158 178 198 218 238 258 278
0
1
2
3
4
5
Sample
SPE
90% Control Limit
95% Control Limit
SPE
Fig. 6: The DPCA monitoring results under spray density 7
The EDPCA method can detect the abnormal situation in
advance with a low false alarm rate. And the robustness of
EDPCA is also better than DPCA. For different spray density
samples, the monitoring results of EDPCA can also obtain
good results.
4.2 Flooding Monitoring for Designed Experiments
In order to further test the sensitivity and robustness of
EDPCA, some other experiments are designed. During these
experiments, the gas velocity is firstly increased gradually
until flooding occurs. Then the packed tower recovers to the
normal condition by reducing the gas velocity. This
procedure is repeated twice within the same spray density.
During the monitoring process, the 2,525 normal data
collected before is used to train sub-models. For modeling
parameters, only a 99% control limit is used. And the others
remain the same. As illustrated examples, some main results
are shown in Figs. 7-9. The spray densities are 16, 9 and 23
m3
/(m2
·h), respectively.
As shown in Fig. 7, all the samples of spray density 16
m3
/(m2
·h) are collected under the normal operating condition,
since the operators would rather select a low gas velocity to
avoid flooding. The red solid boxes in these figures denote
the flooding areas. For designed experiments, the EDPCA
method shows the superiority to DPCA. Under the same
conditions, the monitoring results of DPCA are poor. This is
the reason why they are not displayed in this section. For
normal data shown in Fig. 7, both of SPE and T2
are kept
under the control lines. The statistics especially SPE may
exceed its control line for normal samples, the reason has
been described in previous section and the sign of flooding is
determined as more than three consecutive samples beyond
the control limit.
For monitoring results of spray density 9 m3
/(m2
·h) (Fig. 8),
the SPE points in the dashed box go beyond the control limit
before the real flooding happens. This cannot be looked as
misinformation. For process detection, the best case is to give
alarms early before the real fault happens to get enough
recovery time. During the operation, the values of variables
are not constant. They fluctuate within a certain range. In
actual production, there are more factors affecting the packed
tower. Thus, any excess of the two statistics should be paid
great attention. For EDPCA, there may be some
disadvantages in either SPE or T2
. It is suggested that the
combination of the two statistics can keep the tower avoid
flooding.
For a larger spray density monitoring results, as shown in
Fig. 9, a part of flooding samples are detected, while the other
values are under control lines. There are two reasons for this.
First, the flooding condition has various degrees. During this
experiment, the flooding is not as serious as other spray
densities. Second, Deville [17] has demonstrated that there
are more than one incipient flood points and the first one does
not represent the true hydraulic limit of a column. In such a
situation, the first flooding point may be not accurate.
Therefore, in our opinion, it is important that the monitoring
system can give alarms timely if faults happen in practical
applications.
48 67 87 107 127 147 167 187 207 227 245
0
2
4
6
8
Sample
SPE
48 67 87 107 127 147 167 187 207 227 245
0
5
10
15
Sample
T2
99% Control Limit
T2
SPE
99% Control Limit
(a)
(b)
Fig. 7: The EDPCA monitoring results under spray density 16
(There is no flooding for this case.)
41 72 92 112 132 152 172 192 213 233 254 274 292
0
5
10
15
20
Sample
SPE
99% Control Limit
SPE
41 72 92 112 132 152 172 192 213 233 254 274 292
0
10
20
30
40
Sample
T2
99% Control Limit
T2
(b)
(a)
Fig. 8: The EDPCA monitoring results under spray density 9
60 80 100 126 146 166 186 206 229 249 269
0
2
4
6
8
10
Sample
SPE
99% Control Limit
SPE
41 60 80 100 126 146 166 186 206 229 249 269
5
10
15
20
25
30
35
Sample
T2
99% Control Limit
T2
(b)
(a)
Fig. 9: The EDPCA monitoring results under spray density 23
8262

6. 5 Conclusion
This paper has developed the data-based online flooding
monitoring methods for packed towers. DPCA is first
adopted for online flooding monitoring in packed towers. To
improve the monitoring performance, an EDPCA process
monitoring model has been proposed. By integrating the
FCM clustering algorithm and the DPCA modeling method,
EDPCA can extract the characteristics of training data in a
relatively good manner. Compared with DPCA, EDPCA
shows better and more reliable monitoring performance.
Moreover, it can be implemented in a straightforward way.
Therefore, EDPCA can be utilized as an alternative online
flooding monitoring method for packed towers.
References
[1] J. Mackowiak, Fluid Dynamics of Packed Columns. New
York: Springer-Verlag, 2010.
[2] R.F. Strigle, Packed Tower Design and Applications:
Random and Structured Packings. Texas: Gulf Publishing
Company, 1994.
[3] G.P. Celata, M. Cumo, G.E. Farello, and T. Setaro, Hysteresis
effect in flooding, International Journal of Multiphase Flow,
17(2): 283-289, 1991.
[4] M. Shoukri, A. Abdul-Razzak, and C. Yan, Hysteresis effects
in countercurrent gas-liquid flow limitations in a vertical tube,
The Canadian Journal of Chemical Engineering, 72(4):
576-581, 1994.
[5] E. Hansuld, L. Briens, and C. Briens, Acoustic detection of
flooding in absorption columns and trickle beds, Chemical
Engineering and Processing: Process Intensification, 47(5):
871-878, 2008.
[6] S. Parthasarathy, H. Gowan, and P. Indhar, Prediction of
flooding in an absorption column using neural networks, in
Proceedings of the 1999 IEEE International Conference on
Control Applications, 1999, 2: 1056-1061.
[7] R.K. Pihlaja, Detection of distillation column flooding. U.S.:
8216429, 2012.
[8] S. Yin, X.D. Steven, X.C. Xie, and H. Luo, A review on basic
data-driven approaches for industrial process monitoring,
IEEE Transactions on Industrial Electronics, 61(11):
6418-6428, 2014.
[9] Q. Jiang, X. Yan, Just-in-time reorganized PCA integrated
with SVDD for chemical process monitoring, AIChE Journal,
60(3): 949-965, 2014.
[10] Z.K. Hu, Z.W. Chen, W.H. Gui, and B. Jiang, Adaptive PCA
based fault diagnosis scheme in imperial smelting process,
ISA Transactions, 53(5): 1447-1453, 2014.
[11] S.W. Choi, J. Morris, and I. Lee, Dynamic model-based batch
process monitoring, Chemical Engineering Science, 63(3):
622-636, 2008.
[12] J. Gertler, J. Cao, PCA-based fault diagnosis in the presence
of control and dynamics, AIChE Journal, 50(2): 388-402,
2004.
[13] W. Ku, R.H. Storer, and C. Georgakis, Disturbance detection
and isolation by dynamic principal components analysis,
Chemometrics and Intelligent Laboratory Systems, 30(1):
179-196, 1995.
[14] J.C. Bezdek, R. Ehrlich, and W. Full, FCM: The fuzzy
c-means clustering algorithm, Computers & Geosciences,
10(2-3): 191-203, 1984.
[15] L.H. Chiang, E.I. Russell, and R.D. Braatz, Fault Detection
and Diagnosis in Industrial Systems. London:
Springer-Verlag, 2001.
[16] S. Valle, W.H. Li, and S.J. Qin, Selection of the number of
principal components: The variance of the reconstruction
error criterion with a comparison to other methods, Industrial
& Engineering Chemistry Research, 38(11): 4389-4401,
1999.
[17] Y. Deville, Neural processor comprising means for
normalizing data. U.S.: 5784536, 1997.
8263