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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2007; 2: 536–543
Published online 29 October 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI:10.1002/apj.098
Research Article
Dual-mode control with neural network based inverse
model for a steel pickling process
P. Thitiyasook,1 P. Kittisupakorn1 * and M. A. Hussain2
1
2
Department of Chemical Engineering, Chulalongkorn University, Bangkok, Thailand
Chemical Engineering Department, University of Malaya, Kuala Lumpur, Malaysia
Received 9 April 2007; Revised 25 July 2007; Accepted 13 August 2007
ABSTRACT: This article describes a novel implementation of the dual-mode (DM) control utilizing a neural network
inverse model on a multivariable process (a steel pickling process). This process is highly nonlinear with variableinteraction, and is multivariable in nature, hence an accurately nonlinear model is required to provide acceptable control.
The requirement of a true analytical inverse can be avoided when neural network models are used; they have the ability
to approximate both the forward and the inverse system dynamics. Various changes in the open-loop dynamics are
performed before implementation of the inverse neural network modeling technique. DM control based on neural
network inverse model strategy is used to design the controllers to control concentration and pH of the process, which
is guaranteed to remove steady-state offset in the controlled variables to obtain the maximum reaction rate and to
comply with limits imposed by legislation. The robustness of the proposed DM control is investigated with respect to
changes in disturbances and model mismatch. Comparisons are also made with the conventional inverse neural network
controller (NNDIC) and other conventional controller proportional-integral (PI). Simulation results show the superiority
of the DM controller in the cases involving disturbance and model mismatch, while the conventional controller gives
better results in the nominal case.  2007 Curtin University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: steel pickling process; neural network inverse modeling; dual-mode control strategy
INTRODUCTION
Since the main reason for obtaining large uncertainties
in a system is due to poor modeling, one possible
method to solve this problem is by using neural
networks to model the system. A neural network (NN),
which is a black-box modeling tool, has found wide
application in the fields of process identification and
process control due to its superb ability in representing
arbitrary nonlinear relationships.[1 – 3] A NN has been
shown to model dynamic models (forward modeling
techniques) well if time-delayed data are used as
inputs to it in many cases.[3,4] The ability of NNs
to model dynamic nonlinear mappings/functions makes
them attractive for use in nonlinear system control
strategies. The use of a NN for modeling the inverse of
input–output relationship is also highly promising.[4 – 6]
In this approach, the NN is trained with observed inputoutput data from the system to represent its inverse
dynamics. In other words, given the current state of
the dynamic system and the target state (e.g., set-point)
*Correspondence to: P. Kittisupakorn, Department of Chemical
Engineering, Chulalongkorn University, Bangkok, Thailand.
E-mail: paisan.k@chula.ac.th
 2007 Curtin University of Technology and John Wiley & Sons, Ltd.
for the next sampling instant, the network is trained to
produce the control action that drives the system to this
target state. The resulting inverse model NN can then be
used as a controller, typically in a feed-forward fashion.
However, it is also widely recognized that the modeling
accuracy of a network depends on the quality of the data
presented to it during the training phase. Insufficient as
well as noisy data can affect the accuracy of the network
in the modeling of the inverse function. This may cause
offset in the control trajectory. This limitation can be
overcome by using dual-mode (DM) control[7] which
incorporates both, inverse NN control mode, and the
proportional-integral (PI) control mode.
To this effect, the application of a DM controller
based on the inverse NN model for a steel pickling
plant, a fundamental industry in Thailand, is investigated in this work. The structure of the article is as
follows. It starts with process description of the steel
pickling process. Then, the general idea of inverse NN
is reviewed, and further proceeds with the inverse modeling design of the system. The designed DM approach
is implemented for process control. For comparison purposes, the conventional inverse NN and the PI controller
that is used in many industries these days are also implemented, as discussed in the final section.
Asia-Pacific Journal of Chemical Engineering
NEURAL INVERSE MODEL IN STEEL PICKLING PROCESS
• The deterioration of pickling efficiency resulting from
iron concentration is considered negligible.
THE STEEL PICKLING PROCESS
The steel pickling process consists of two major steps:
pickling and rinsing.[8] The purpose of the pickling step
is to remove surface oxides (scales) and other contaminants from the metals by immersion of the metals
into an aqueous acid solution. Metals are immersed in
pickling baths containing 5, 10 and 15% by weight
of hydrochloric acid (HCl), respectively, in order to
remove scales from the metals. The metals move
counter-current to the acid stream as can be seen in
Fig. 1. The reaction occurring in the pickling baths is
as follows:
FeO + 2HCl −−→ FeCl2 + H2 O
(1)
Drag in-out pickling solution is removed from the metal
surface using rinsing water in the rinsing step, which
consist of three pure water baths. The metals move
opposite to the rinse water flow as shown in Fig. 2.
Here, the amount of drag-out solution of each bath is
assumed to be equal to the amount of drag-in solution.
The following assumptions are made for the purpose
of this study.
• The system is supposed to be perfectly mixed and
isothermal.
• All state variables are measurable directly.
• Density of the liquid is assumed to be constant.
Figure 1. Flow diagram of pickling baths control system.
Based on the above assumptions, the mathematical
model of the continuous steel pickling process as
shown in Figs 1 and 2 for the change in volume and
concentration can be derived for both, the pickling and
rinsing steps, as follows:
Pickling step (occurring in the 5, 10 and 15% HCl baths)
dh1
dt
dh2
A
dt
dh3
A
dt
dC1
V1
dt
dC2
V2
dt
dC3
V3
dt
A
= F2 − F1 − q
(2)
= F3 − F2 − F11
(3)
= F4 + F5 − F3 − F10
(4)
= F2 C2 − C1 (F1 + q) − V1 r1
(5)
= qC1 + F3 C3 − C2 (F2 + F11 + q) − V2 r2 (6)
= qC2 + F5 C20 + F4 C4 − C3 (F3
+ F10 + q) − V3 r3
Rinsing step (occurring in three pure water baths)
dh4
dt
dh5
A
dt
dh6
A
dt
dC4
V4
dt
dC5
V5
dt
dC6
V6
dt
A
= F6 − F4 − F9
(8)
= F7 − F6
(9)
= F8 − F7
(10)
= qC3 + F6 C5 − C4 (F4 + F9 + q) (11)
= qC4 + F7 C6 − C5 (F6 + q)
(12)
= qC5 + F8 Cw − C6 (F7 + q)
(13)
The meanings of all these variables are specified in the
nomenclature.
To complete the mathematical modeling of this continuous process, the expression of the reaction rate,
Eqn (1), in the pickling baths needs to be imposed. The
reaction is assumed to be first order neglecting liquid
diffusion and the deterioration of pickling acid resulting from the accumulation of oxide in the pickling bath.
Therefore, the equation of the reaction rate studied here
solely depends upon acid concentration as shown below:
r = kC
Figure 2. Flow diagram of rinsing baths control system.
 2007 Curtin University of Technology and John Wiley & Sons, Ltd.
(7)
(14)
The objective of this work is to control the concentration of HCl in all the pickling baths (C1 , C2 and C3 ) and
Asia-Pac. J. Chem. Eng. 2007; 2: 536–543
DOI: 10.1002/apj
537
538
P. THITIYASOOK, P. KITTISUPAKORN AND M. A. HUSSAIN
the pH (or H+ concentration (C4 )) in the first rinsing
bath to a desired set-point by manipulating inlet flows
F2 , F3 , F5 and F6 , respectively, as shown in Figs 1 and
2. Since the DM incorporating an inverse NN-based
model is used for the control, we will first describe
the procedure for inverse NN modeling and its use in
control in the next section.
Asia-Pacific Journal of Chemical Engineering
F(k)
C(k+1)
PLANT
+
−
Z−1
TRAINING
SIGNAL
^
F(k)
Z−k
NEURAL
NETWORK
Z−1
NEURAL NETWORK
The use of a NN in process engineering has increased
considerably in the last decade. For a given set of
inputs, NNs are able to produce a corresponding set
of outputs according to some mapping relationship.
This relationship is encoded into the network structure
during a period of training (also called learning), and is
dependant upon the parameters of the network, that is,
weights and biases. Once the network has been trained
(on the basis of known sets of input/output data), the
input/output mapping is produced in a period of time
that is faster than the time taken when using rigorous
deterministic modeling.[9,10]
Neural network inverse models
Inverse models provide the NN structure, which represents the inverse of the system dynamics in the region
of the training/identification. There are several ways
to carry out this identification process. The technique
used here is known as the generalized inverse learning method.[11,12] Here, the network is fed with the
required future or reference output together with the
past inputs and the past outputs to predict the current
input or control action. The trained network represents
the inverse model of the system. The assignment of the
input nodes consists of the past and present values of
the known flows and concentrations associated with the
individual tanks and the desired value of the plant output, C (k + 1), corresponding to the required set-point
or reference signal. The output node of the NN inverse
model consists of the manipulated variable for the tank,
i.e. flow entering the associated tank. Although various
prediction horizons can be used for these inverse models, this study concentrates on a simple one-step-ahead
horizon, which assumes that there is no additional time
delay between the control action and the output.
Procedure for obtaining neural network
inverse models
Inverse modeling refers to training the network models
to predict the control actions, which are used as the
controllers.[13,14] During training, each member of the
 2007 Curtin University of Technology and John Wiley & Sons, Ltd.
Z−k
Figure 3. The method for the training of neural network
inverse models.
training set is presented to the network individually, and
upon each input presentation, the weights are adjusted.
The procedure is repeated until a certain performance
index is achieved. In this case, the network is said
to have converged to its targeted value. Initially, the
adaptable weights and bias are set to small randomized
values, and the network normally does not respond well
mainly due to the random weights used. As the weights
are adapted during training, the performance index will
also improve. The training is stopped when the error
rate is small or reaches its defined value. The method
for training the NN inverse models is shown in Fig. 3.
In this work, the single hidden layer feed-forward
networks are used, which are trained using the Levenberg–Marquardt method. Mathematically, these four
inverse models are expressed as functions of inputs to
the model as below:
Pickling Baths
5%HCl Bath F2 (k ) = f −1 (F2 (k − 1), C2 (k − 1),
C2 (k ), C1 (k ), C1 (k + 1))
10%HCl Bath F3 (k ) = f
(15)
−1
(F2 (k − 1), F2 (k ),
F3 (k − 1), C1 (k − 1), C1 (k ), C3 (k − 1),
C3 (k ), C2 (k ), C2 (k + 1))
(16)
15%HCl Bath F5 (k ) = f −1 (F3 (k − 1), F3 (k ),
F5 (k − 1), C2 (k − 1), C2 (k ), C3 (k ), C3 (k + 1))
(17)
Rinsing Baths
1# Rinsing Bath F6 (k ) = f −1 (F6 (k − 1), C3 (k − 1),
C3 (k ), C5 (k − 1), C5 (k ), C4 (k ), C4 (k + 1))
(18)
The stopping criteria for the training are set to either
1000 epochs or when the overall errors on the outputs
are lower than 10−4 (where the errors are evaluated as
the mean-squared error (MSE) function). The MSE is
expressed mathematically below where n is the number
Asia-Pac. J. Chem. Eng. 2007; 2: 536–543
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
NEURAL INVERSE MODEL IN STEEL PICKLING PROCESS
of data, Ftg is the target/desired flow value and FN is
the NN output.
MSE =
n
1
(Ftg (k ) − FN (k ))2
n
(19)
k =1
All the inputs and outputs are scaled between 0.05
and 0.95 to ensure that all the values computed in the
network training are of the same order of magnitude.
The inputs and outputs are scaled using the following
equations:
(valueAC − min value)(0.95 − 0.05)
valueSD =
(max value − min value)
+ 0.05
(20)
The actual value is given by
(valueSD − 0.05)(max value − min value)
valueAC =
0.95 − 0.05
+ min value
(21)
where valueSD is the scaled down value and valueAC is
the actual value.
The training is switched between the two sets of data
until the MSE has been satisfied in both cases. They are
switched between each other during training to improve
the NN system identification capability. In obtaining the
inverse model using a NN, the number of hidden nodes
plays a very important role in the network performance.
Currently, there are no specified methods in obtaining
the correct number of nodes. In this work, the hidden
nodes are chosen by the MSE minimization technique.
In this technique, the hidden nodes are varied in various
quantities and the MSE error is then monitored. The
network with the corresponding hidden nodes that gives
the minimum MSE value is selected as the final network
configuration. As an example, Table 1 shows the MSE
values obtained from the inverse NN model for the
15% HCl bath using different numbers of hidden nodes.
Based on these minimizing MSE error values, it is found
that 4, 8, 12 and 16 hidden nodes in the inverse NNs
appear to be the best to be applied respectively, as
Table 1. MSE value for different number of hidden
nodes in the inverse neural network model for 15%
HCl bath.
Numbers of
hidden nodes
4
8
12
16
20
Mean Squared Error
(MSE) after validation
2.088 × 10−5
3.211 × 10−5
1.268 × 10−5 (least value)
2.214 × 10−5
1.082 × 10−4
 2007 Curtin University of Technology and John Wiley & Sons, Ltd.
Figure 4. Procedure for obtaining inverse neural network
models.
controllers for the 5, 10, 15% HCl and #1 rinsing bath
in the control strategy. The NN inverse model-based
control has constraints inherent in it since the constraint
is set by the range of the training data.
Detailed procedures to obtain reliable inverse NN
models are summarized in Fig. 4.
DUAL-MODE CONTROL BASED ON NEURAL
NETWORK INVERSE MODEL STRATEGY
Normally, the implementation of the inverse NN model
to control the process gives some errors between
set-point and control variable (offset) since an exact
inverse model is difficult to obtain, as has been proved
theoretically.[15] In order to remove this offset and
improve the process response, PI controller is also
implemented in this proposed DM control strategy
which makes use of both, the inverse NN and PI
controller. The basic concept of the DM algorithm can
be divided into two modes of operation. That is, in
the first mode, the inverse NN controller is applied
whenever an error between the state (control variables)
and set-point lies outside the limit values, E (Eqn (22)),
while in the second mode, the PI controller is employed
inside the limit error region to bring the state to the
desired set-point. In this work, the limited value is
set to ±3% of the set point in each bath, where E is
defined as:
(22)
|Csp − C (k )| = E
Asia-Pac. J. Chem. Eng. 2007; 2: 536–543
DOI: 10.1002/apj
539
540
P. THITIYASOOK, P. KITTISUPAKORN AND M. A. HUSSAIN
The main benefit of the DM controller is that, under
nominal operating conditions, when the state is located
far away from set-point, the inverse NN controller can
bring the state to the desired set-point without a drastic
change of the manipulated variable and oscillation.
However, when the state is located within a limited
region (E ), the PI controller starts to gain control
and brings the state to the desired set-point without
offset, which normally occurs when controlling using
the inverse NN controller only. In addition, the control
action given by the PI controller in DM gradually
changes and is less drastic when compared to using
the conventional controller PI alone. Due to such
advantages, the DM control offers an attractive control
methodology for process control application.
RESULTS AND DISCUSSION
The objective of the simulation studies is to control
the concentration of HCl in the 5, 10, 15% HCl and
#1 rinsing bath to nominal values of 1.40, 2.87, 4.41
and 1 × 10−3 mol/l (pH 3) by adjusting the manipulated
variables F2 , F3 , F5 and F6 , respectively. They are
divided into three cases of control studies, which are
the nominal case, disturbance case and model mismatch
case, respectively.
Asia-Pacific Journal of Chemical Engineering
Nominal case
The controllers are designed to bring the concentration
of HCl in each bath to the desired value when the initial
condition is set at the steady state for 20 min from
the start. Figure 5(a), (b) and (c) show the control of
HCl concentration in 15% HCl bath using DM control,
NNDIC and PI control, respectively. The results in
these figures indicate that the DM controller can bring
the concentration to the desired set-point without any
offset and oscillation of manipulated variable, while
the NNDIC brings the concentration closely to the setpoint with minimal offset. The PI controller brings
the concentration to the set-point without offset, but
however, there is drastic change of the manipulated
variable and wide oscillation in the initial state of the
control. These control strategies are also applied for
the 5 and 10% HCl, and the #1 rinsing bath; however,
only the 15% HCl bath control result is shown because
this bath has the highest HCl concentration and is very
difficult to control, from which we can observe the
effect of the controllers. Their performances are also
evaluated using the Integral Absolute Error (IAE). The
IAE results for the nominal case of these four baths are
summarized in Table 2. They showed that relatively,
the PI controllers give slightly better results than the
DM control and NNDIC in terms of lesser IAE values
Figure 5. Concentration control in 15% HCl bath under the nominal case: (a) DM control (b) NNDIC (c) PI control. This
figure is available in colour online at www.apjChemEng.com.
 2007 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2007; 2: 536–543
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
NEURAL INVERSE MODEL IN STEEL PICKLING PROCESS
Table 2. Performance comparison between dual mode,
NNDIC and PI controls under the nominal case.
IAE values
Bath
5% HCl bath
10% HCl bath
15% HCl bath
#1 Rinsing bath
DM
NNDIC
PI
1.756
3.425
4.967
0.044
2.109
37.925
21.697
0.274
0.342
2.607
13.281
0.007
for the 5 and 10% HCl, and the #1 rinsing baths. For
the 15% HCL bath, the control action of PI controller
is very drastic causing overshoot of concentration, and
therefore, a higher IAE value is obtained as compared
to the DM controller.
Disturbance case
In this case, the disturbance, which is the change
in the concentration of C20 in the stream F5 , is
introduced by increasing and reducing 15% from its
nominal operation values. Initially, the process is left
under control until t = 200 min, at which instant,
a disturbance is introduced. During the period t =
200–300 min, the control action is halted at the last
value to allow the process to respond to the new
load condition. At t = 300 min, the DM, NNDIC and
PI control actions are reintroduced into the system.
Figure 6 shows the results of the DM, NNDIC and PI
controls for 15% HCl bath by increasing 15% of C20
from its nominal value. It can be seen from Fig. 6 that
when the disturbance is introduced (t = 200–300 min),
the process responds by the increase in concentration of
the baths due to the increase of HCl concentration (C20 )
to 15% HCl bath. After t = 300 min, the DM strategy
can bring back the concentrations to the required value
without offset and oscillation, while NNDIC strategy
bring back the concentrations close to the required value
and give offsets and the PI control strategy could not
bring the concentrations to the set-point. Relatively,
similar results are obtained for the 10% HCl bath
and the #1 rinsing bath. In the 5% HCl bath, the PI
controller can bring the concentration to its set-point
but there is rigorous adjusting of the F2 up to 4 l/min
causing overshoot in concentration. In reducing the
concentration C20 by 15%, the results show that the
DM strategy can still control the process and bring
the concentrations to their set-points, while the NNDIC
strategy brings the concentrations to their set-points
with slight offsets, but the PI controller cannot control
the process. Table 3 summarizes the IAE values of
DM, NNDIC and PI controls for the four baths. They
indicate that the DM controller is most robust and gives
Figure 6. Concentration control in 15% HCl bath under the disturbance case (15% increase of the concentration,
C20 ): (a) DM control (b) NNDIC (c) PI control. This figure is available in colour online at www.apjChemEng.com.
 2007 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2007; 2: 536–543
DOI: 10.1002/apj
541
542
P. THITIYASOOK, P. KITTISUPAKORN AND M. A. HUSSAIN
Asia-Pacific Journal of Chemical Engineering
Table 3. Performance comparison between DM, NNDIC
and PI controls under the disturbance case (15%
increasing of the concentration, C20 ).
the model mismatch is introduced. During the period
t = 200–300 min, the process control action is halted
at the latest value to allow the process to respond
to a new load condition. At t = 300 min, the DM,
NNDIC and PI control actions are reintroduced into
the system. Figure 7 shows the results of DM, NNDIC
and PI controls for 15% HCl bath by increasing 15%
of the kinetic rate constant. When the model mismatch
is introduced (t = 200–300 min), the process responds
by a decrease in concentration in baths due to the
increase of rate of reaction in the acid bath. After t =
300 min, the DM control brings back the concentrations
to their required values without the offset, while the
NNDIC strategy brings back the concentrations close
to their required values and gives offsets, but PI control
strategy cannot bring the concentrations to the set-point.
In reducing 15% of the kinetic rate constant, the results
again show that the DM control can control the process
and bring the concentrations to their set-points, while
the NNDIC strategy can control the process and bring
the concentrations close to their set-points with slight
offsets, but the PI controller cannot control the process
at all. Table 4 shows the IAE values of DM, NNDIC and
PI controls for the four baths. They again indicate that
the DM control has the most robustness and gives better
IAE values
Bath
5% HCl bath
10% HCl bath
15% HCl bath
#1 Rinsing bath
DM
NNDIC
PI
1.183
3.661
38.492
0.052
3.508
77.595
74.997
0.444
12.252
623.919
696.903
0.087
better control performance than the NNDIC and PI
controllers with very much smaller IAE error values,
when disturbances are present in the system.
Model mismatch case
In this work, the rate of reaction in the acid bath is
considered as the model mismatch in the parameter
under consideration. The model mismatch is introduced
by increasing and reducing 15% of the kinetic rate
constant from its nominal value. Initially, the process is
left under control until t = 200 min, at which instant,
Figure 7. Concentration control in 15% HCl under the model mismatch case (15% increase of reaction rate, k):
(a) DM control (b) NNDIC (c) PI control. This figure is available in colour online at www.apjChemEng.com.
 2007 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2007; 2: 536–543
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
NEURAL INVERSE MODEL IN STEEL PICKLING PROCESS
Table 4. Performance comparison between DM, NNDIC
and PI controls under the model mismatch case (15%
increase of the reaction rate, k).
IAE values
Bath
5% HCl bath
10% HCl bath
15% HCl bath
#1 Rinsing bath
DM
NNDIC
PI
3.998
8.162
11.665
0.049
11.116
101.759
73.782
0.424
136.385
220.565
289.428
0.041
control performance than NNDIC and PI controller for
the model-mismatch case as well.
CONCLUSION
In practice, most real chemical processes are nonlinear
and multivariable in nature, which make them difficult
to control by using conventional controllers. Modelbased advanced control techniques are then required
to obtain tighter control. However, in many cases it
is even impossible to obtain a suitable process model
due to the complexity of the underlying processes or
the lack of knowledge of critical parameters of the
models. A promising way to overcome these problems
is to use inverse NNs as nonlinear black-box inverse
models of the inverse dynamic behavior of the process.
Nevertheless, inverse a NN model cannot produce the
exact model and offset which normally occurs when it
is implemented in control of the process. Therefore, the
DM is an attractive control methodology for process
control application because it can get rid of the offset
and improves robustness of the controller. In this work,
DM control strategy is tested and implemented for
controlling concentrations of pickling and rinsing baths
in a steel pickling process, which is highly nonlinear
and involves multivariable interactions in nature. It
was observed that DM control strategy can bring the
control variables to their set-points without offset and
oscillations in all the cases studies, i.e. nominal case,
disturbance case and model mismatch case. Comparison
of performance with the NNDIC and the conventional
PI controller indicates that the DM control strategy
gave better results in cases involving disturbances and
model mismatches, and gave lesser IAE values than
 2007 Curtin University of Technology and John Wiley & Sons, Ltd.
the NNDIC and PI control. These results show that the
DM control strategy gives acceptable and encouraging
results for highly nonlinear and multivariable system
such as this steel pickling process and can improve the
robustness of such control systems.
NOMENCLATURE
area of operating tank (= 7.29 × 10−2 m2 )
HCl concentration (mol/l)
volumetric rate (l/min)
height of operating tank (m)
reaction rate constant (= 3.267 × 10−4 mol/(l min))
amount of acid solution that stuck with samples
(= 5 × 10−3 l/ min)
t time (min)
V volume of operating tank (m3 )
Subscripts
20 20% by weight HCl
w water
sp set-point
A
C
F
h
k
q
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DOI: 10.1002/apj
543
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