Soft Sensor Development for Hydrocracker Product Quality
Prediction
Paula Barbosa, Carla Pinheiro, Dora Nogueira
The main goal of this work is to maximize the productive capacity, and the revenue from each oil
barrel, GalpEnergia Sines Refinery has invested in an hydrocracking unit. Given that all fuels are subject
to strict regulation, it is necessary to have tight control over their quality. Therefore, in order to implement
future advanced control on the unit, we proceeded to a first approach of the prediction of a quality variable
of the diesel produced by making use of a soft- sensor. To develop the soft sensor for quality prediction,
variables of interest and their historical data were collected and analyzed. Step-tests were performed in
the real industrial plant in order to better understand the dynamic behaviour of the fractionator.
Subsequently, four soft sensors were developed using Principal Components Analysis followed by a
Partial Least Squares regression to obtain linear models able of quality prediction. The soft-sensors
developed were also good detectors of process faults because they included the faulty variables for
prediction.
Keywords: PCA, PLS, Multivariate Analysis, Hydrocracking, Quality prediction, Soft-Sensor.
1.
Introduction
[1,2]
better
way
,
providing
real-time
necessary for effective quality control
Chemical
plants
are
usually
[3]
information
.
highly
instrumented and have a large number of sensors
The span of tasks performed by Soft-Sensors
that collect measured data for process control and
is quite broad but the most common use is the
monitoring. About two decades ago researchers
prediction of process variables that can only be
began using the large amount of data to build
known either at low sampling rates or through off-line
predictive models, and these models are called Soft-
analysis
Sensors. The term soft sensor is a combination of
important for process control because they are
the words ‘software’ (mainly because models are
usually related to the process output quality and it is
developed in computer programs) and ‘sensors’,
naturally
because
additional information about these variables at higher
these
models
are
providing
similar
[1,4]
.
These
important
variables
and
are
usually
necessary
to
[1,5]
very
deliver
information as hardware sensors. These soft-sensors
sampling rate or lower financial burden
are often divided into two categories: model-driven
field of application of soft-sensors is of process
and data-driven
[1,2]
. Another
. Model-driven sensors (also
monitoring and process fault detection by finding the
called white-box models) are most commonly based
state of the process and identification of the deviation
on First Principle Models that describe the physical
source.
and chemical properties of the process[9,10], are
developed primarily for the planning of the plants and
usually only describe ideal process steady-states and
not real process dynamics, describing a simplified
theoretical background rather than real-life process
conditions
measured
[1]
. Data-driven models are based on data
within
the
processing
plants,
thus
describing the true conditions of the process in a
Measuring
variables
that
define
product
quality is a major problem in process industries.
These variables are called primary or quality
variables and quantify the productivity or the
specifications upon which the product is sold, like
purity or physical or chemical properties, and these
are the most difficult to measure online . The online
variables that are easy to access and measure are
often called secondary variables and can be
temperature, pressure and flow rate and can be used
pure PCA is that it can only effectively handle linear
to infer primary variables. Because of the nature of
relationships of the data and cannot deal with data
chemical and processing engineering systems, the
non-linearity. Another disadvantage is the selection
dynamics and state of the secondary variables
of the optimal number of principal components (that
reflects the dynamics and state of the primary
can
variables, meaning that changes in secondary
techniques). Another problem is that the principal
variables are indicative of changes in product quality.
components describe very well the input space but
The technique of using secondary variables to
do not explain the relations between the input and
generate estimates of product quality is usually
output data, that is usually what has to modelled .
be
addressed
by
using
cross-validation
[5]
called ‘soft-sensing’ and these inferential estimators
2.2 Partial Least Squares Regression
are usually in place of direct on-line measurement of
controlled variables if direct measurements are
(PLS)
The regression problem, that is, the modelling
[5]
expensive, unreliable or add large lag .
of primary variables, by means of a set of predictor
2. Data-driven methods for soft-sensing
variables, the secondary variables, is one of the most
The product quality in Hydrocracking units is
common problems in data-analysis in science and
significantly influenced by operating conditions and
technology, and one example of such problems may
the cracking yield is reduced with time by catalyst
include
deactivation. Therefore, the continuous monitoring of
manufactured products to the conditions of the
product quality is very important especially to avoid
manufacturing process .PLS can be seen as an
off-spec petroleum fractions, that usually cause
extension of PCA. The algorithm pays attention to
[2]
relating
the
quality
and
quantity
of
[8]
covariance matrix that brings together the input and
problems downstream at the blending stage .
output data space. This method decomposes the
It is usually difficult to get precise and reliable
product composition measurements without time
delay because most composition analysers have
significant time lags and their reliability is usually
input and output simultaneously while keeping the
orthogonality constraint, having the model focussed
on the relation between the input and output
[1]
variables .
quite low. Due to the strong correlation between
secondary variables, Principal Components Analysis
(PCA) or Partial Least Squares (PLS) methods will
be applied
[6].
The objective of this method is to fit a linear
relationship between
the dependent secondary
variables and independent primary variables. PLS is
a simple and powerful approach for data-analysis for
2.1 Principal Components Analysis (PCA)
Noise can be found in almost all variables of
the majority of datasets. Latent variable models like
PCA and PLS estimate the relevant part and the
noise of each variable and therefore are used in the
[7]
complex problems because of its flexibility and ability
to deal with incomplete and noisy data with multiple
variables and observations (measurements). The
disadvantage of PLS is that like PCA, it can only
model linear relations between the data
[1]
.
present work . Principal Component Analysis (PCA)
was used for analysing the data so that only the
secondary variables important to the determination of
[5]
3.
Implementation of Step Tests
Performing step tests in the unit was of great
product quality were selected . Using PCA, the data
importance because the unit is new and had never
can be described using far fewer variables than the
been submitted to step tests. Therefore these tests
original
of
were planned and performed, in order to better
information, and also, PCA often produces linear
understand its response and behaviour. By better
combinations of variables that are useful predictors
understanding the process performance, and by
variables
with
[4]
no
significant
loss
of particular processes . One of the limitations of
submitting the unit to step tests, we hoped to use
these data to develop a soft-sensor that could
of 3%, 5%, 7%, 10%, 13% and 15% on each of the
explain and predict the behaviour of the quality
chosen secondary variables.
variable even in the case of the unit operating out of
3.3 Step Tests Results
the specified operating temperature, pressure and
The scheduling and the sequence of the
flow values.
variables testing was organized to accommodate the
3.1 Historical Data Analysis and Variable
Selection
Refinery conveniences, in order to minimize the
impact into the production profile and quality. For
Since step tests had never been performed in
each particular test a sample was taken and the time
this unit the first approach was to select the variables
stamp of the sample was annotated. Samples were
that could be tested. This first step included the study
only collected after the calculations using the
of the fractionator together with the insight and
preliminary model, indicated that the quality variable
experience of the Refinery Team and the Thesis
Y had stabilized after a given step test. As expected,
Supervisors, and after some exchange of ideas and
the step tests planned had a clear effect on the
suggestions it was agreed that the secondary
quality variable (Fig.1). Having the quality variable
variables X3, X8, X9, X10, X12, X13 and X22 were to
covering a wide range of values allows the dynamic
be tested. The next step was to build a preliminary
data to accommodate the influence of a wider range
model using the historical data available using PCA
of process conditions on the quality variable. Most of
followed by PLS (obtained in a similar fashion as
the variables tested end up appearing in the models
described in chapter 4). This model was to be used
developed in the next chapter. Variables X3, X10,
only for assessing if a given step test would indeed
X13, X8 and X22 appear in Model B, variables X3
be expected to influence the quality variable Y, and if
and X13 appear in Model C, and variable X13
it did, how long would it take the quality variable to
appears in Model A.
stabilize. Then we looked into the historical data and
4.
checked if there were disturbances in the secondary
variables
selected
previously
that
could
In this section the quality variable Y is
be
considered as ‘step-test’ (like a sudden decline or
increase of rate or temperature). Using those ‘steptest’ values, we calculated the Y results, and
evaluated and estimated the quality variable settling
time for each step test. The sequence for the
variables testing was agreed with the Refinery Team
in order to reduce the overall impact in the operating
conditions.
Soft Sensor Development
predicted using 25 online secondary variables
available in the database. These variables include
flowmeters, temperature and pressure sensors and
all are online measured variables. The selection of
which variables should be included in the soft-sensor
is a complex task and the strategy consists in finding
a good variable subset capable of making accurate
predictions. In this study two methods are used to
obtain the soft-sensors to predict the quality variable:
3.2 Sensitivity Analysis
Partial Least Squares (PLS) as a linear modelling
To evaluate the impact that the tests could
tool, and Principal Component Analysis (PCA) as a
have on the quality variable Y, the fractionator was
tool to select a good model variable set and to strip
modelled using the simulator Petro-SIM™ version
down the models from outliers and noise. Datasets
4.1. After modelling the unit in Petro-SIM™, the
were collected directly from the Digital Control
amplitudes of the step tests were tested to access
System (DCS) and the Real Time Database (RTDB)
their influence in Y. Based on previous tests
of the Refinery and were used to build four models.
performed in other units of the Refinery, it was
The soft-sensors obtained from these data were
decided to test the impact of the following steps of -
labelled as Model A, B, C and D, and the datasets
3%, -5%, -7%, -10%, -13% and -15%, and if changes
are:
Pre-tests
samples
X3
1,035
1,03
1,025
X10
Y
1,02
1,015
X12
1,01
X9
1,005
X13
1
X8
0,995
0,99
X22
0
5
10
15
20
25
Sample number
30
35
40
45
Figure 1: Step-tests results.
Model A: The soft-sensor is obtained from
could be collected and if the results could be
training data collected during the week of the step
compared to the other dataset’s results and if we
tests, in 2013 from October 27
th
st
to October 31 ,
using the same data to calibrate the model.
could extract a better soft-sensor from it. The
purpose of developing Model D was to access the
importance of step tests in the modelling of the
Model B: The soft-sensor is obtained from
training data collected in 2013 between the August
1
st
st
and the October 31 , using the same data to
calibrate the model.
quality variable, therefore this model was developed
st
using only the historical data from 1 of February to
st
October the 26 of 2013. These soft-sensors were all
st
validated with data collected between the 1 and 27
Model C: The soft-sensor is obtained using
st
training data collected in 2013, from 1 of February
of November. The software used in PCA and PLS
modelling was PLS Toolbox advanced chemometrics
to October the 31 , using the same data to calibrate
software
the model.
environment.
st
Model D: The soft-sensor is obtained using
st
training data collected in 2013, from 1 of February
st
to October the 26 , using the same data to calibrate
the model.
th
used
within
MATLAB®
computational
As there isn’t a universally accepted method
to obtain the best models for each set of data, each
one of the models presented here was obtained by
firstly using PCA to select outliers, excluding them
from the dataset and immediately using the PLS to
The justification for this procedure is based in
build the soft-sensor and compare the Variance
the fact that we wanted to understand thoroughly the
Accounted For (VAF) obtained with the VAF of
information the step tests could provide (and of
preliminary soft-sensors. After that step, some
course extracting the maximum of knowledge of such
outliers were selected by fine-tuning the model: if the
testing, using it in Model A), and we wanted to
model revealed decreased quality, then these data
understand what kind of information we could extract
samples were not considered as outliers; if not, those
from all the data collected in the DCS since the
data samples were excluded from the dataset.
beginning of operation (Model C). Furthermore, we
were aware of the substantial difference of size
4.1 Principal Components Analysis
between these two datasets, so it was decided to
Choosing the number of principal components
build another dataset with an intermediate size
has no universal rules or procedures , but a
(Model B) to understand what kind of information
principal component with an eigenvalue equal or
[9]
Figure 2: Correlations map for Model A,B.C and D
greater than one is believed to be of statistical
[10]
first eight PC’s have eigenvalues greater than one
. After selecting the number of PC’s, the
having the first two PC’s captured 44.19% of
next step was to detect the presence of outliers. The
variance and eight PC’s captured 82% of variance,
relevance
2
Hotelling’s T statistic measures the distance of a
therefore a PCA model was constructed with that
given score sample from the origin and the Q
number of principal components. In the case of
residuals statistic is the squared projection error and
Model A no sample was taken off of the original data,
measures the error from a given sample to the
the data had no ouliers. For the development of
principal component model. So for instance, if after
Model B, the sampling interval was increased.
calculation of the limits of these two statistics with
Instead of analysing only the week of step tests, the
significant level of 95%, a sample shows a high value
training data from August the 1
in the Q statistic, then this sample does not comply
October of 2013 (in a total of 194 samples) was fed
with the principal component model. If a sample
into the PLS Toolbox, autoscaled and cross-validated
2
st
th
to the 31
of
shows a high value in the Hotelling’s T statistic, it is
with venetian blinds, with 10 data splits. After outlier
assumed that maybe the unit is not operating at its
removal, a PCA model was to be built with 6 PC’s,
usual operating rates (with high deviations from the
explaining 68,49% of the data variance (having the
[11]
In the case of a given sample
first two PC’s explaining 36,26% of variance). Model
showing high values in both Q residuals and
C was set up using all the data available since
mean values)
2
Hotelling’s T
statistics, the principal component
st
February the 1 to October 31
st
of 2013, having a
model is not valid for this sample, and it was
grand total of 549 samples. As on the previous
considered an outlier.
model, the data were autoscaled and venetian blinds
cross-validated using 40 splits. After outlier removal,
Model A was derived based on the 42
laboratory analysis obtained in the week of the steptests performed at Sines Refinery. This dataset was
loaded to PLS Toolbox, autoscaled, leave-one-out
cross-validated and a PCA model was obtained. The
a PCA model with 6PC’s was obtained, having
80,97% of variance explained (having the first two
PC’s explained 58,41% of variance). To understand
how much the step-tests influenced model
Figure 3: Loadings plots for Model A, B, C and D.
development and their predictions, Model D was
developed based only in data from the 1
st
secondary variables. In the loadings plot, the
of
variables located farther from the origin have a large
of October of 2013,
impact in the PCA model, and variables located in
having a total of 507 samples as its dataset. The
the vicinity of the origin have negligible impact. The
data were autoscaled and venetian-blinds cross-
variables nearest to Diesel D86 show high positive
validated using 40 splits. After outlier removal a PCA
correlation with it, and the variables farther from
model with 5 PC’s was built, having 77,24% of
Diesel D86 show great negative correlation with it.
variance explained (the first two PC’s explained
Geometric interpretation of partial correlation is made
57,22% of variance).
using vectors that start at the origin of the plot (Fig.
th
February of 2013 and the 26
3) and end at each variable point. Correlation
After selecting the number of PC’s the next
step was to analyse the correlation map and the
loadings plot of each model. The correlation maps in
Fig. 2 show the pair-wise correlation coefficients
between the 25 variables and the quality variable of
each model. The intensity of the colours mirror the
amount of correlation, so, higher positive correlations
show intense shades of red and higher negative
correlations show intense shades of blue. The
loadings plots on Fig. 3 also show the relations
between the quality variable Diesel D86 and the
between all the secondary variables and Diesel D86
is obtained using the cosine of the angle between
their corresponding vectors. Angles between 0 and
90º correspond to positive correlations and angles
between 90º and 180º correspond to negative
correlations. Vectors having angles close to 90º
correspond to small correlations between their
variables and angles closer to 0º or 180º correspond
to substantial correlation.
Using both the correlations map and the
loading plots for each Model, the secondary variables
selected to build the soft sensor are in table 1.
Table
1:
Variables
selected
Model B:
0,0055 1 1,0277 3 0,0792 2 0,0060 5 0,0048 6 0,0050 7 0,3131 for
PLS
8 0,0684 10 0,0039 11 0,6706 13 0,6637 15 0,2244 17 2,0526 18 modelling for each model.
0,2754 20 12,6802 21 10,8107 22 Model
A
B
C
D
27,9043 23 22,1807 24 15,6703 25 Variables
X1, X2, X5, X7, X13, X14, X15, X17,
X21, X23, X24, X25
X1, X3, X2, X4, X6, X7, X8, X10, X11,
X13, X15, X17, X18, X20, X21, X22,
X23, X24, X25
X3, X2, X11, X13, X14, X15, X17,
X18, X19, X20, X23, X24,X25
X2, X11, X13, X14, X17, X18, X19,
X20, X23, X24, X25
196,0344
(2)
Model C:
2,2609 3 0,0029 2 0,0334 11 0,4001 13 0,3324 14 0,1006 15 0,1226 17 2,7232 18 0,2527 X19 0,1815 X20 34,2095 X23 155,7240 X24 For Model A, variables X4 and X16 were not
10,8638 X25 202,3602
used in the model because they degraded the results
(3)
Model D:
in the model calibration. For Model C, in later stages
of model development, it was found that X7 would
0,0118 2 0,0114 11 0,1203 13 deteriorate
0,2316 14 0,4581 17 2,0338 18 model
quality
and
therefore
this
secondary variable was left out of the model. As for
0,7490 19 2,2141 20 27,5397 23 Model D, X16 would deteriorate model quality and
88,0357 24 224,7459 25 69,4008
(4)
was left out of it.
4.3 Model Calibration
4.2 Partial Lest Squares Model
The calibration consisted of using equations
After variable selection using PCA, the data
1, 2, 3 and 4 to predict each models training data,
for each model were loaded to the PLS Toolbox,
and the results of model performance are shown in
autoscaled and leave-one-out cross-validated for
Table 2.
Model A, venetian blinds cross validated using 10
splits for Model B and venetian blinds cross-validated
using 40 splits for Models C and D. For Model A and
B, 10
Table 2: Performance criteria VAF for the
modelling results.
Latent Variables (LV) were selected for
developing the soft model, for Model C, 9 LV’s were
selected and finally, for Model D, 7 LV’s were
A
selected.
B
The soft sensors obtained were:
C
Model A:
0,0012 1 0,0386 2 0,1298 5 0,0217 7 1,3417 13 3,2987 14 0,8355 15 0,7202 17 23,3623 21 5,8127 23 71,1457 24 51,0246 25 147,7861
Model
(1)
D
Dataset
th
st
27 to 31
October
st
1 August to
st
31 October
st
1 February to
st
31 October
st
1 February to
th
26 October
Calibration
VAF (%)
77,8
Validation
VAF (%)
20,4
61,3
56,3
68,1
78,9
17,2
70,9
4.4 Model Validation
samples 8 and 9). The range of Y temperatures of
The validation consisted of using an unseen
st
th
Model B calibration data was larger than Model A
dataset (from the 1 to the 27 of November 2013)
and closer to the range of the validation data Y
as input data in equations 1, 2, 3, 4 and the results
values, enabling Model B to present a better fit than
obtained can be seen in the plots of figure 4 and
Model A when comparing VAF only, since most of
table 2.
the predictions fall out of experimental laboratory
error. Also, the better fit in validation (when
4.5 Model results discussion
comparing VAF) can be explained because Model B
The performance criteria Variance Accounted
For (VAF) was used to assess the quality of the
models by comparing the model’s fit to the real data,
as shown in equation 5.
includes more secondary online variables than Model
A. However Model B shows a clear upper bias in its
predictions (Fig 4). Model C was calibrated and
validated outperforming all models in capturing the
1 ̂ ! 100
(5)
Where "# is the real Y sample laboratory
result, "̂# is the model predicted value for Y. The
range of the calibration dataset of the Y values is
[0,994; 1.031] for Model A, [0.973; 1.034] for Model
B, and [0.921; 1.133] for both Models C and D. The
range of the validation dataset of Y is [0.941; 1.083]
nonlinear data dynamics. The VAF of validation, with
a value of 78.9 is considerably higher than the
previous three models. Figure 4 show that even not
predicting the values of samples 7 to 14, the model
follows data dynamics and for all other samples the
model makes In the calibration step, Model D
provides the worst performance (with a VAF of 17.2),
a fact that could not be explained especially because
models C and D differ only by two secondary
for all models.
variables and have a difference of one week of data
Model A fit to calibration data has a VAF of
(44 samples) for their development. However, Model
77.8, showing that the model could fit the data very
D validation shows second best fitting, having a VAF
well. As to validation, the model VAF is the worst of
of 70.9. Figure 4 shows that the model describes the
all the four models (having a VAF of 20.4), because
data dynamics but some of the predictions (excluding
the range of Y values used for model development is
those from the 7 sample to the 14 ) fall out of the
narrower than the range of calibration Y data. Also,
laboratory analysis error. Model D was developed to
the size of the dataset used for model development
understand if the step tests data were important in
and calibration was only of one week of unit
the model development. The results show that
operation. The model could not fit data outside the
without considering the step tests samples in model
values (sometimes even not describing the dynamics
D derived in poorer quality predictions compared to
th
th
of the data, as seen in predictions of the 8 and 9
th
th
Model C predictions.
samples – figure 4) used for its development, but
data within that range was very well fitted as seen in
figure 4: all predictions except those ranging from the
7
th
sample to the 14
th
sample are very good since
most of them fall within the laboratory experimental
analysis error. Model B fit to calibration data has a
VAF of 61.3, a value smaller than Model A
calibration. Model B validation (with a VAF of 56.3)
was substantially better than that for Model A
validation (VAF of 20.4), especially because the
model followed the dynamics of the data as seen in
figure 4 (which Model A wouldn’t in the case of
5.
Soft-Sensor fault detection
During the step of model validation, the first
st
dataset selected spanned from the 1 of November
2013 to January 13
th
of 2014. The four models
proposed where tested with this data set and a very
clear bias emerged for a specific period (as seen in
the left hand plot of Fig. 5), from samples 53 to 135.
In this article, we will only show results in fault
detection for Model C. The fact was reported back to
the Refinery Team in search of an explanation. The
Refinery Team advised that an exploratory look
Figure 4: Validation results for all Models
should be done on the dataset because they too
comparison to the historical data. That meant that the
could not find an explanation for such evident bias in
positive contribution of the variable to de prediction
all model’s predictions. The Hydrocracker unit had
would
indeed an operational problem and the unit was shut
predicted values of the quality variable. Having
down, but they were fully operating only a few days
reported these conclusions to the Refinery Team, we
after, and so there was no explanation why the
were informed that indeed a pipe had clogged when
model’s predictions were systematically biased.
the unit was shut down and that affected the
Following the Refinery Team advice, the dataset was
measuring of X18.
substantially
decrease,
decreasing
the
thoroughly analysed and it was found that one
6.
measured variable, X18, was having values very
different
of
nominal
those
historically
operating
measured
conditions
and
substantial deviations from their previous normal
operating measurements. Variable X18 was used in
Model C. To confirm or discard the suspicion that
X18
was
effectively
influencing
the
model’s
predictions, the model’s predictions for the quality
variable were again obtained using the average of
the historical past values before the shut down for
X18, instead of the measured values. The results
obtained for the predicted quality variable are
presented in the right hand plot of figure 5, showing
that the approach was successful in proving that the
measurements of variable X18 were affected by any
equipment failure that changed their values to a
range different from the normal operating range. In
Model C, the variable’s coefficient is positive but the
measured values decreased about 20% in
The aim of this study was to develop a soft
under
reported
Conclusions
sensor capable of predicting the quality variable, Y.
Two methods were used to obtain the soft-sensors to
predict this quality variable: PLS as a linear
modelling tool and PCA as a tool to select a good
model variable set and to strip down the models from
outliers and noise. Based in both historical and step
tests
data,
four
soft-sensors
were
developed,
calibrated with plant data and validated with new
data that had not been used during the calibration
step. The different datasets used in each model
development affected their prediction results but all
the models follow the same dynamics behaviour for
the quality variable and feature good predictions, but
the use of a linear prediction tool in a clearly nonlinear unit is cause of error. Model C seems to be the
best choice to be built into the DCS system as an
inferential sensor, to provide real time information of
the Y prediction to the operators and also to be used
Figure 5: Fault detection for Model C
for control purposes. Model C was built with most of
the historical data available. Having a larger dataset
to build the model is of great advantage since it
surely covers most of the process conditions and
quality variable range. In calibration the model fits
better to the real data than Model B and D but worse
than Model A. In validation Model C has the best
behaviour of the four models, since the dataset used
for its development and calibration had a larger Y
value range than the dataset used for validation,
joining the best validation result with the advantage
of a smaller number of model variables. During the
validation step of this study, we were able to make
use of one of the advantages of soft-sensors:
process monitoring and fault detection. By using
three models to fit the validation data, we discovered
a clear bias between predicted and real values of
Diesel D86 during a certain time period. This
prompted a careful analysis of the dataset and the
detection of faulty measures on two variables
measured online in the plant. The soft sensors
developed were good detectors of process faults
because they included the faulty variables for
[3]
B.
Lin,
B.
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