Distillation is the most common unit operation in the chemical and petrochemical
industries for separation and purification of components. Controlling distillation
columns is the most challenging job for control engineers due to their highly
nonlinear dynamic characteristics and complexity. The energy requirements for
the distillation column might be reduced significantly by controlling the column
operation at optimum conditions. Basically, there are five variables required
to be controlled to achieve efficient operation, namely, composition of distillate
stream, composition of bottom stream, liquid level of reflux drum, liquid level
of base column and column pressure (De Canete et al.,
2008). In practice, on-line analyzer for composition is rarely used due
to large measurement delay, the need for frequent maintenance as well as high
capital and operating costs. In order to adapt to changing economic and market
scenarios while maximizing profit, the demand for accurate inferential estimators
(soft sensors) for controlling the product quality variable becomes paramount
Soft-sensor is a mathematical model that utilizes the measured values of some
secondary variables of a process in order to estimate the value of an immeasurable
primary variable (quality parameter) of particular importance (Zamprogna
et al., 2005). Soft sensors have been widely reported to supplement
online instrument measurements for process monitoring and control. Both First
Principle Model (FPM)-based and data-driven soft sensors have been developed
(Lin et al., 2007). If a FPM describes the process
sufficiently accurately, a FPM-based soft sensor can be derived. However, a
soft sensor based on detailed FPM is computationally intensive for real-time
applications (Zamprogna et al., 2005). Modern
measurement techniques enable a large amount of operating data to be collected,
stored and analyzed, thereby rendering data-driven soft sensor development a
Two main techniques are adopted in the development of data-driven soft sensors,
Multiple Linear Regressions (MLR) such as Partial Least Squares (PLS) and Multiple
Nonlinear Regressions (MNR). The main drawback of MLR techniques is their linear
nature which hinders them from accurately describing processes with nonlinear
nature like distillation. On the other hand, MNR techniques like Artificial
Neural Network (ANN) and Neuro-Fuzzy can easily capture and accurately represent
the nonlinear characteristics of processes and they become increasingly adopted
(Hoskins et al., 1988). In this study, an attempt
has been made to develop a neural network-based soft sensor for a pilot-scale
binary distillation column.
Artificial neural networks: Over the years, the application of ANN in
process industries has been growing in acceptance. ANN is attractive due to
its information processing characteristics such as nonlinearity, high parallelism,
fault tolerance as well as capability to generalize and handle imprecise information
(Hoskins et al., 1988). Such characteristics
have made ANN suitable for solving a variety of problems. This has been proven
in various fields such as pattern recognition, system identification, prediction,
signal processing, fault detection, soft sensors and others. In general, the
development of a good ANN model depends on several factors. The first factor
is related to the data being used. The model quality is strongly influenced
by the quality of data used. The second factor is network architecture or model
structure. Different network architecture results in different estimation performances.
The third factor is the model size and complexity. A parsimonious model i.e.,
a model with a fewer number of parameters is required for effective on-line
applications. A small network may not able to represent the real situation due
to its limited capability, but a large network may over fit noise in the training
data and fail to provide good generalization ability. Finally, the quality of
a process model also depends strongly on network training (Picton,
EQUIPMENT AND EXPERIMENTATION
The equipment used in this study is a pilot-scale binary distillation column shown in Fig. 1. The column is 5.5 m high with 0.156 m inner diameter, consisting of 15 bubble-cap trays and works under atmospheric pressure. The feed enters the column at tray number 7. The column is used to separate acetone as top product from isopropyl alcohol (IPA). Table 1 and 2 show the design specifications and the nominal operating conditions of the column.
The column was operated at different feed flow rates (0.5-0.9 L min-1) and different feed compositions (0.01-0.1 mole fraction of acetone). Series of step changes in the reflux flow rate (0.2-0.9 L min-1) and reboiler steam flow rate (0.017-0.5 kg min-1) are introduced as excitation signals to produce a wide range of temperature profiles and top product concentrations.
Samples were collected from the top product stream after the reflux drum regularly at an interval of 6 minutes and the data on other variables such as flow rates, temperatures were acquired through the data acquisition system and stored at a sampling interval of 2 sec.
||Process flow diagram of pilot-scale binary distillation column
|| Design specifications of the pilot-scale distillation column
|| Nominal operating conditions of the distillation column
|| Description of process variables
It may be noted that during the experiments, the column pressure was controlled by manipulating the cooling water flow rate, the reflux drum level by the top product flow rate and the column bottom level by bottom product flow rate. Gas Chromatographic analysis was done at a later time to find the mole fraction (XA) of acetone in the top product from the collected samples. In total, 270 samples were collected with their corresponding operating conditions. The operating variables collected consist of reflux flow rate, reboiler steam flow rate, top pressure and temperatures of all trays in the column. Table 3 lists all the operating parameters collected as input variables along with their description and units of measurement.
SOFT SENSOR DEVELOPMENT
Typically the development of a soft sensor can take the following steps:
||Collection of the data that will be used in the construction
and validation of the soft sensor
||Pre-processing of the data, which includes outlier removal
||Soft sensor construction and validation
Data pre-processing: Sufficient data were collected from the operation of the distillation column as explained earlier. Before the collected data can be used for the development of a soft sensor, they must be pre-processed in three steps:
||Outliers detection and removal
||Data segmentation into training and testing sets
Outliers can be defined as observations with abnormally extreme values (Eriksson
et al., 2001). Outlier detection is very critical for the soft sensor
development because outliers have negative effect on the performance of the
soft sensor model. Different reasons might be the source of outlier such as
sensor failure, transmission problems or unusual operating conditions (Fortuna
et al., 2007). Outlier can be detected easily in the score plot of
a PCA of the data (Eriksson et al., 2001). Figure
2 shows the score plot of the first two principal components (t, t)
for all 270 observations collected. From this Fig. 2, observations
38 through 42 can be identified as clear outliers and hence they have been removed
from the bulk of data.
There is a significant difference in the numerical magnitude of the different
data variables due to the difference in their units of measurement. Variables
with larger magnitude will have an unjustified stronger influence in the development
of the model (Fortuna et al., 2007). Therefore,
data normalization (or scaling) is required to assure an equal influence of
the different variables in the model. Two types of normalization can be used,
the first is the (min-max normalization) which is given by:
where, x is the measured variable, x' is the normalized variable, xmin is the minimum value of the variables, xmax is the maximum of the variables.
The second type is (z-score normalization). This normalization will make all the data to have a zero mean and unity variance and is given by:
and σ are the mean and the standard deviation of the input variable, respectively.
The z-score normalization was used in this study because it is less sensitive
to the existence of outliers in the data (Fortuna et al.,
|| Score plot of the first two principal components of a PCA
study for 270 observations
After the removal of outliers and data normalization, the remaining 265 observations data are segmented into two subsets: a 215 observations training set and a 50 observations test set.
SOFT SENSOR CONSTRUCTION
The construction of a neural network (NN) based soft sensor can take the following steps:
||Selection of important process variables and their corresponding
||Selection of the NN model type and structure
Important variables selection: Usually data collected from industrial
units suffer from co-linearity which makes many of them poorly informative in
the prediction of the quality parameter (Wang et al.,
1996). Using redundant variables increases the complexity of the model and
has bad effects on the performance of the soft sensor. One way to solve this
problem is to select only part of the input variables that have the least co-linearity
and the most correlation with the quality parameter.
Due to the process dynamic behavior, different time lags are expected to exist between different variables and their corresponding effect in the primary output. Typically the choice of the important variables and their corresponding lags is done simultaneously. First a large set of variables and their different lags are considered as input candidates for the model. Number of methods can be used identify a subset of variables as the relevant model inputs.
In this study, a PLS method is used to determine the importance of the input
variables and their most correlated lags with the primary output. The Variable
Influence Plot (VIP) represents a Weighted Sum of Squares of the Weights (WSSW)
assigned to the variables in the PLS model, which summarizes the influence and
hence the importance of each variable in the prediction of the primary output
(Fortuna et al., 2006). For each of the input
variables a sequence of 5 lags (k-1, k-2,
, k-5) were obtained with one
sample delay between each other, then the variables and their lags are used
in the PLS model. Figure 3 shows the VIP of the variables
and their lags. Two lags of each variable with the highest VIP value are shaded.
These two lags for each variable are the ones that will be used later as input
candidates for the soft sensor.
NN structure: Two neural networks are trained for the prediction of
XA, a Feed Forward (FF) network and a nonlinear autoregressive with
exogenous input (NARX) network. Both networks are of three layers with an input
layer, a hidden layer and an output layer. Levenberg-Marquardt backpropagation
with momentum technique (Hagan et al., 1996) is
used as training algorithm for both types. The relationship between the inputs
and the output of these networks can be given by the general equation:
where, í is the predicted output, xj is the jth input from
the input set x, wLij is the weight of the ith input to
the jth neuron of the Lth layer, wLoj is the bias of the
jth neuron of the Lth layer, nh is the number of neurons in the hidden
layer and ni is the number of inputs to the network, F1
is the activation function of the hidden layer, F2 is the activation
function of the output layer.
|| VIP of the input variables and their lags
The input set x for the FF network is defined as:
where, u is an input variable, k is the sample number, di and df are two successive lags of the input variables.
While the input set x for the NARX is defined as:
where, y is the actual output, dy is the maximum lag (degree) of the recurrent output.
Two different activation functions of the hidden layer (F1) are investigated for each network. In one case a purelin activation function is used, which simply means to use the weighted sum of variables directly as the activation signal from the hidden layer to the output layer, or:
In the second case, a tan-sigmoid is used for F1, which is given by:
Accordingly, there were four neural networks investigated for their prediction ability of the quality parameter, a FF network with a purelin hidden layer activation function (ff-lin), a FF network with a tan-sigmoid hidden layer activation function (ff-tsig), a NARX network with a purelin hidden layer activation function (narx-lin), a NARX network with a tan-sigmoid hidden layer activation function (narx-tsig). For all of the investigated networks a purelin function is used as the activation function for the output layer F2.
The next step of the soft sensor construction is to choose the input variables from the input candidates that will give the best network performance. The Root Mean Square Error (RMSE) between the predicted and the actual output in the test set of observations is used as a performance index for the neural network. RMSE can be described by:
where, N is the number of observations in the test data set.
|| Input Variables for Investigated Neural Networks
The algorithm used to select the set of input variables x for each network,
is to add the variables one by one (as a set of two lags of each) to the particular
model in order of decreasing VIP values, the network is trained using the training
set of observations, simulated for the test set and the performance is tested
by calculating RMSE for the test set. The variable that improves the network
performance (decreases RMSE) is kept and the one that increases RMSE is discarded
and then the next input variable is tested and so on. The different networks
investigated had different input structures that give the best performance as
shown in Table 4. For the NARX networks different maximum
lags (degrees) of the recurrent output variable y(k-dy) (which is
represented here by (XA(k-dy)) are investigated and it
was found that only a first degree lag (y(k-1)) improves the network performance
while the other lags increases the RMSE, thats why only XA(k-1)
is included in the NARX networks model.
Different number of neurons in the hidden layer can significantly affect the
network performance (Hagan et al., 1996), hence
the number of neurons in the hidden layer has to be optimized. To find the optimum
number of neurons in the hidden layer, the four neural networks with input structures
as described in Table 4 are trained with different number
of neurons in the hidden layer. The performance of the networks with different
number of neurons in the hidden layer is shown in Fig. 4.
For networks with purelin hidden layer activation function the network performance
was independent of the number of neurons in the hidden layer. Accordingly a
hidden layer with only one neuron is used in the structure of ff-lin and narx-lin
networks because of the decreased computation effort compared to a multi-neuron
layer. On the other hand the performance of networks with tan-sigmoid function
fluctuates with minimum RMSE value and hence best performance at 2 neurons for
ff-tsig network and 5 neurons for.
Model validation: Table 5 summarizes the performance
of the optimum structure of each type of the investigated neural network. It
can be seen from this table that all of the networks had a very good performance
with an RMSE less than 0.04, or an average error less than 7% of the total range
of top product composition measured (0.023-0.64).
||Performance of Neural Networks as Function of Number of Neurons
in the Hidden Layer: ff-lin network, ff-tsig network, narx-lin network,
||Performance of the optimum structure for the investigated
For further validation of the prediction accuracy of the optimum NN structure
based soft sensor, plots of the predicted and actual top product composition
(XA) are shown in Fig. 5 and 6.
It is clear from these figures and Table 5 that networks with
tan-sigmoid hidden activation functions have outperformed those with purelin
functions of the same type. This indicates a high level of nonlinearity for
the investigated system. In general, NARX networks of both types have outperformed
FF networks and have given an excellent prediction performance as can be seen
in Fig. 5 and 6.
Inferential control scheme: The soft sensor can be used in an inferential
control scheme as shown in Fig. 7. Here, Loop (II) is updated
each few seconds and the secondary outputs (network input variables) are used
to predict the value of the quality parameter (top product composition) which
is used by the controller to control the process.
|| Inferential control scheme
Loop (I) is updated every 30 to 40 min when the actual values of the top product
composition are available and this value is used to update the soft sensor model
by calculating the error between the actual and the predicted values which is
then added to the model as a bias.
Two types on neural networks each with two different hidden layer activation function studied have shown a good prediction ability for the top product composition of the pilot distillation column. NARX networks had a better prediction performance with both types of hidden layer activation function than FF network. Using tan-sigmoid as hidden layer activation function had a better performance than purelin activation function. Input variables and number of neurons in the hidden layer are found to depend significantly on the type of the network and its activation function. The constructed soft sensor with its optimized input variables set and neural network can be used in an inferential closed loop control scheme for the pilot-scale distillation column.
Authors gratefully acknowledge the financial support under the Science Project 03-02-02-SF0003 by the Ministry of Science, Technology and Innovation, Malaysia and Universiti Teknologi PETRONAS.