Accepted Manuscript
Title: Data-driven Soft Sensors in the Process Industry
Authors: Petr Kadlec, Bogdan Gabrys, Sibylle Strandt
PII: S0098-1354(09)00007-6
DOI: doi:10.1016/j.compchemeng.2008.12.012
Reference: CACE 3763
To appear in: Computers and Chemical Engineering
Received date: 17-3-2008
Revised date: 27-11-2008
Accepted date: 30-12-2008
Please cite this article as: Kadlec, P., Gabrys, B., & Strandt, S., Data-driven Soft
Sensors in the Process Industry, Computers and Chemical Engineering (2008),
doi:10.1016/j.compchemeng.2008.12.012
This is a PDF file of an unedited manuscript that has been accepted for publication.
As a service to our customers we are providing this early version of the manuscript.
The manuscript will undergo copyediting, typesetting, and review of the resulting proof
before it is published in its final form. Please note that during the production process
errors may be discovered which could affect the content, and all legal disclaimers that
apply to the journal pertain.

Data-driven Soft Sensors in the Process
Industry
Petr Kadlec a, Bogdan Gabrys a, Sibylle Strandt b
aSmart Technology Research Centre, Computational Intelligence Research Group,
Bournemouth University, Poole BH12 5BB, United Kingdom
bEvonik Degussa AG, 45128 Essen, Germany
Abstract
In the last two decades Soft Sensors established themselves as a valuable alternative
to the traditional means for the acquisition of critical process variables, process mon-
itoring and other tasks which are related to process control. This paper discusses
characteristics of the process industry data which are critical for the development
of data-driven Soft Sensors. These characteristics are common to a large number of
process industry fields, like the chemical industry, bioprocess industry, steel indus-
try, etc. The focus of this work is put on the data-driven Soft Sensors because of
their growing popularity, already demonstrated usefulness and huge, though yet not
completely realised, potential. A comprehensive selection of case studies covering
the three most important Soft Sensor application fields, a general introduction to
the most popular Soft Sensor modelling techniques as well as a discussion of some
open issues in the Soft Sensor development and maintenance and their possible
solutions are the main contributions of this work.
Key words: Soft Sensors; Process industry; Data-driven models; PCA; ANN;
Preprint submitted to Elsevier 27 November 2008
Revised Manuscript

1 Introduction
Industrial processing plants are usually heavily instrumented with a large number
of sensors. The primary purpose of the sensors is to deliver data for process moni-
toring and control. But approximately two decades ago researchers started to make
use of the large amounts of data being measured and stored in the process industry
by building predictive models based on this data. In the context of process indus-
try, these predictive models are called Soft Sensors. This term is a combination
of the words ”software”, because the models are usually computer programs, and
”sensors”, because the models are delivering similar information as their hardware
counterparts. Other common terms for predictive sensors in the process industry
are inferential sensors (see e.g. Jordaan et al., 2004; Qin et al., 1997), virtual on-
line analyser as they are called in the Six-Sigma context (Han and Lee, 2002) and
observer-based sensors (Goodwin, 2000).
At a very general level one can distinguish two different classes of Soft Sensors,
namely model-driven and data-driven. The model-driven family of Soft Sensors is
most commonly based on First Principle Models (FPM) but model-driven Soft
Sensors based on extended Kalman Filter (Welch and Bishop, 2001) or adaptive
observer (Bastin and Dochain, 1990) have also been published (e.g. Chruy, 1997;
Jos de Assis and Maciel Filho, 2000). First Principle Models describe the physical
and chemical background of the process. These models are developed primarily for
the planning and design of the processing plants, and therefore usually focus on
the description of the ideal steady-states of the processes which is only one of their
drawbacks which makes it difficult to base Soft Sensors on them. As a solution
the data-driven Soft Sensors gained increasing popularity in the process industry.
2

Because data-driven models are based on the data measured within the processing
plants, and thus describe the real process conditions, they are, compared to the
model-driven Soft Sensors, more reality related and describe the true conditions of
the process in a better way. Nevertheless there is a lot of different issues which have
to be dealt with while developing data-driven Soft Sensors. These issues will be
discussed later on in this paper. The most popular modelling techniques applied to
data-driven Soft Sensors are the Principle Component Analysis (Jolliffe, 2002) in
a combination with a regression model, Partial Least Squares (Wold et al., 2001),
Artificial Neural Networks (Bishop, 1995; Principe et al., 2000; Hastie et al., 2001),
Neuro-Fuzzy Systems (Jang et al., 1997; Lin and Lee, 1996) and Support Vector
Machines (Vapnik, 1998).
The range of tasks fulfilled by Soft Sensors is broad. The original and still most
dominant application area of Soft Sensors is the prediction of process variables which
can be determined either at low sampling rates or through off-line analysis only.
Because these variables are often related to the process output quality, they are very
important for the process control and management. For these reasons it is of great
interest to deliver additional information about these variables at higher sampling
rate and/or at lower financial burden, which is exactly the role of the Soft Sensors.
The modelling methods applied to this kind of applications are either statistical or
soft computing supervised learning approaches. This Soft Sensor application field
is further on referred to as on-line prediction. Other important application fields
of Soft Sensors are those of process monitoring and process fault detection. These
tasks refer to detection of the state of the process and in the case of a deviation
from the normal conditions to identification of the deviation source. Traditionally,
the process state is monitored by process operators in the control rooms of the
3

processing plants. The observation and interpretation of the process state is often
based on univariate statistics and it is up to the experience of the process operator
to put the particular variables into relations and to make decisions about the process
state. The role of process monitoring Soft Sensors is, based on the historical data,
to build multivariate features which are relevant for the description of the process
state. By presenting the predicted process state or the multivariate features the Soft
Sensor can support the process operators and allow them to make faster, better and
more objective decisions. Process monitoring Soft Sensors are usually based on the
Principle Component Analysis and Self Organizing Maps (Kohonen, 1997). It was
already mentioned that processing plants embody large number of various sensors,
therefore there is a certain probability that a sensor can occasionally fail. Detection
of this failure is the next application area of Soft Sensors. In more general terms
this application field can be described as sensor fault detection and reconstruction.
Once a faulty sensor is detected and identified, it can be either reconstructed or
the hardware sensor can be replaced by another Soft Sensor, which is trained to act
as a back-up Soft Sensor of the hardware measuring device. If the back-up sensor
proves to be an adequate replacement of the physical sensor, this idea can be driven
even further and the Soft Sensor can replace the measuring device also in normal
working conditions. The software tool can be easier maintained and is not subject
to mechanical failures and therefore such a substitution can provide a financial
advantage for the process owner.
Despite all the previously listed Soft Sensor application fields and the high number
of publications dealing with Soft Sensor applications, there are still some unad-
dressed issues of the Soft Sensor development and maintenance. A lot of the origins
of these issues are in the process data which is used for the Soft Sensor building.
4

Common effects present in the data are measurement noise, missing values, data
outliers, co-linear features and varying sampling rates. To solve these problems,
there is typically a large amount of manual work needed. Another problem is that
the processing plants are rather dynamic environments. Often they develop gradu-
ally during the operation time but there can be also sudden abrupt changes of the
process, for example, if the quality of the process input changes. It is very difficult
for the Soft Sensors to react to these changes which usually results in prediction
accuracy deterioration. At present time, these issues are solved in a rather ad-hoc
manner, which leads to unnecessary high costs of the Soft Sensor development and
maintenance. Further on in this work, all the aspects, which have been briefly out-
lined in this section, are going to be reviewed in a more comprehensive way. The
rest of the paper is organized as follows. Section 2 gives an overview of different
process types and deals with their aspects from the Soft Sensor modelling point of
view. Section 3 focuses on data-driven Soft Sensors, namely on their development
methodology, on the methods which are commonly applied to soft sensing and on
open issues of the Soft Sensor modelling. A review of publications dealing with Soft
Sensor application to diverse processes is also given in Section 3. Section 4 pro-
vides a brief description of most popular data-driven pre-processing and modelling
techniques to soft sensing. Section 5 contains a discussion of the most important
open issues of Soft Sensor development and maintenance as well as an outline of the
future research directions in the Soft Sensors field. Finally, the work is concluded
in Section 6.
5

2 Industrial Processes
This section deals with the process industry environment. First, the two different
types of industrial processes and their distinguishing characteristics are discussed
in Section 2.1. This is followed by a detailed discussions of the data produced in
the process industry in Section 2.2.
2.1 Industrial process types
2.1.1 Continuous Processes
Continuous processing plants are, as their name suggests, running in uninterrupted,
continuous way. After the start-up phase of the plant they are operated in more or
less constant and hopefully optimal state. As the process should stay most of the
time in this optimal state, the Soft Sensors applied to continuous processes focus
usually on the description of this steady-state and are not able to deal with any
transient states like the process start-up and shut-down phase. Nonetheless, even
the steady state is progressively changing with time, which has a negative effect on
the prediction quality of the Soft Sensor. The most common causes of the process
operating point changes are the changes of the process product demand, the change
of the catalyst activity, clogging of heat exchangers, etc.
As continuous processes generate the majority of revenue for most of the most
process industry companies this review is biased towards this type of processes.
Majority of the application examples listed in Section 3.3 deal with continuous
processes and therefore Section 4 presents the most popular techniques for Soft
Sensor development mainly from the continuous process modelling point of view.
6

2.1.2 Batch Processes
Batch, semi-batch or discontinuous processes (further on referred to as batch pro-
cesses only) are processes with a definite duration. Very often these processes are
started on demand for the production of required product amount. Many processes
in food and biochemistry industry, like fermentation processes, are of this type.
Another field where batch processes are very common is the speciality chemistry.
Here, the special chemicals have to be produced infrequently and often in very small
amounts and thus it would not be economical to run the plants in continuous mode.
Bonne and Jorgensen (2004) commented that: Batch processes are experiencing a
renaissance as products-on-demand and first-to-market strategies impel the need for
flexible and specialised production methods. This statement is clearly demonstrating
the increased demand for modelling tools based on batch process data.
In terms of data-driven modelling there is a difference between continuous and batch
processes. Batch process modelling has to deal with an additional discrete dimen-
sion of the data, namely the batch-to-batch variation (Nomikos and MacGregor,
1995b). While modelling these processes, one has to take into account the finite
and varying duration of the processes, the time variance of the particular batches
described by the batch trajectory, the often high batch-to-batch variance and the
starting conditions of the batches (Champagne et al., 2002). The techniques applied
for modelling and monitoring of batch processes are most commonly multivariate
statistical techniques. In the case of batch process monitoring, the most common
applied method is the principle component analysis. There are several batch pro-
cesses monitoring applications reviewed in Section 3.3.2 and a discussion of batch
process modelling tools is given in Section 4.6.
7

2.2 Characteristics of process industry data
This section presents the most critical characteristics of the process industry data
as they are identified from the Soft Sensor development and maintenance point
of view. Another general view on process data was published in Pearson (2001),
where the focus is put on the discussion of the process data distribution and the
information which can be extracted from it.
2.2.1 Missing values
Missing data are single samples or consequent sets of samples, where one or more
variables (i.e. measurements) have a value which does not reflect the real state of
the physical measured quantity. The affected variables usually have values like ±∞,
0 or any other constant value.
Missing values in the context of process industry have various causes. The most
common causes are the failure of a hardware sensor, its maintenance or removal. As
it was already mentioned, processing plants are heavily instrumented for the pur-
pose of control of the processes, therefore also the recorded process data consists
of large number of diverse variables. In such a scenario, there is a certain proba-
bility that some of the sensors will occasionally fail. One should keep in mind that
some of the sensor types are mechanical devices (e.g. flow rate sensors) and thus
suffer from abrasion effects. Another possible causes of missing data are related to
the transmission of the data between the sensors and the database, errors in the
database, problems in accessing the database, etc.
Since most of the techniques applied to data-driven soft sensing cannot deal with
8

can be critical for the PCA (Walczak and Massart, 1995; Stanimirova et al., 2007;
Serneels and Verdonck, 2008). Another problem of outlier detection is that even
when applying automatic outlier handling pre-processing steps, usually the results
have to be validated manually by the model developer. The goal of the manual
inspection is to detect any possible outlier maskings (i.e. false negative detections-
not detected outliers) and outlier swamping (i.e. false positive detections - correct
values labelled as outliers).
Typical approaches to outlier detection are based on the statistics of the historical
data. The most simple approach is the 3σ outlier detection algorithm (e.g. Lin
et al., 2007; Pearson, 2002), which is based on univariate observations of the variable
distributions. This method labels all data samples out of the range µ(x) ± 3σ(x),
where µ(x) is the mean value and σ(x) the standard deviation of the variable x,
as outliers. More robust version of this approach is the Hampel identifier (Davies
and Gather, 1993) which is in contrast to the 3σ method uses more outlier resistant
median and median absolute deviation from median (MAD) values (Pearson, 2001,
2002) to calculate the limits.
In Pearson (2001), the author discusses the outliers problem. He focuses on the
influence of outliers on the identification of linear and non-linear models. For the
handled models the Hampel identifier, which is based on a robust estimation of the
variables’ statistics, is found to be an effective approach for dealing with outliers. In
Menold et al. (1999) a moving window filter is combined with the Hampel identifier
to obtain an outlier detection and removal system. In contrast to the univariate
approaches the multivariate methods use combinations of more features to detect
the outliers. An example from this group based on the PCA is the Jolliffe parameter
(Jolliffe, 2002; Warne et al., 2004a). Gonzalez et al. (2003) is using a two-stage
11

outlier detection approach. The first stage is the application of the PCA, after this
the T 2 measure can be used to detect outlier candidates which are located outside
of the 99% confidance ellipse. These candidates are then further analysed in the
second step, where Scheffe´’s test (Gomez et al., 1996) is applied to these points.
Another, rather general review of the outlier detection problem and several outlier
detection algorithms is presented in Hodge and Austin (2004).
2.2.3 Drifting data
There are two types of drifting data and dependent on the cause of the drifts
one can distinguish between process and sensor drifts. The causes of the process
drift are the changes of the process or of some external process conditions. The
processing plants consist of a large number of mechanical elements which undergo
steady abrasion during the operation of the plant. This may have an effect on the
process itself, e.g. the flow between two parts of the process can decrease due to
the abrasion of mechanical pumps. Another cause of the drifting data can also be
external influences like changing environmental conditions (e.g. weather influence),
the purity of the input materials, catalyst deactivation, etc. These factors have not
only an influence on the data but affect the process state as well. Therefore the
drifts should be recognised, reported and appropriate actions have to be taken to
remove their cause. This is different in the case of sensor drifts which are caused by
changes in the measuring devices and not by the process itself. The critical point is
that this type of drifts, while still observed in the measured data, does not reflect
any changes in the process. Therefore in the case of sensor drifts, the action to be
taken should be the re-calibration of the measurement devices or the adaptation of
the Soft Sensor without performing any corrective actions to the process.
12

In terms of the effects on the process data, one can observe changes in the means
and variances of the single variables as well as changes of the correlation structure
of the data Li et al. (2000).
Distinguishing between the two discussed different drift causes is challenging and
once again a lot of expert knowledge is needed in order to take appropriate action.
Another challenging aspect of dealing with drifting data is the fact that the changes
may progress very slowly and may influence each other, and thus have non-linear
form, which makes them difficult to detect and compensate.
The most common approach to deal with dynamics in the data is to apply the
moving window techniques. In this case the model is updated on periodical basis
using only a defined number of the most recent samples. Some examples of the
application of this technique in the context of Soft Sensor modelling are: Wang
et al. (2005); Zhao and Chai (2004); Qin (1998); Dayal and MacGregor (1997).
Further approaches for Soft sensor adaptation are discussed in Section 3.2.5.
The problems with drifting data are not unique to the process industry data and
they can be found in several other fields dealing with changing environments. In
the machine learning terminology these problems are summarised under the term
concept drift. For detailed treatment and some solutions see Widmer and Kubat
(1996); Gama et al. (2004).
2.2.4 Data co-linearity
Another challenging issue for soft sensing, apart from those stated above, is related
to the structure of the data. Typically, the data measured in the process indus-
try are strongly co-linear. This results from the partial redundancy in the sensor
13

processes can have different run times. To be able to apply data-driven methods
to batch process historical data the data must have the same length (i.e. the same
number of samples) and thus also require synchronisation. Detailed discussion of
various synchronisation approaches is given in Section 4.6.
3 Soft Sensors in the process industry
This section deals with Soft Sensors in a detailed way. After distinguishing two types
of them in Section 3.1 a discussion of a state-of-the-art Soft Sensor development
methodology is given in Section 3.2. Section 3.3 provides a comprehensive overview
of published Soft Sensor application case studies.
3.1 Model-driven and data-driven Soft Sensors
At a very general level one can distinguish two types of Soft Sensors, namely Model-
Driven and Data-Driven Soft Sensors. Model-driven models are also called white-
box models because they have full phenomenological knowledge about the process
background. In contrast to this purely, data-driven models are called black-box
techniques because the model itself has no knowledge about the process and is
based on empirical observations of the process. In between the two extremes there
are many combinations of these two major types of models possible. A typical
example of such a combination is a model-driven Soft Sensor making use of data-
driven method for the modelling of fractions which can not be modelled easily
in terms of phenomenological models. These models are sometimes called hybrid
models but in order to avoid any confusion with the hybrid combinations of two or
16

more computational learning methods (e.g. neuro-fuzzy systems) we refer to them
as grey-box models in the remaining of this paper.
Model-driven Models (MDM), or more specifically First Principles Models (FPM),
are primarily developed for the purpose of planning and development of the process
plants. These models are based on equations describing the chemical and physi-
cal principles underlying the process. A typical example is using mass-preservation
principles, exothermal equation, energy balances, reaction kinetics in the form of
reaction rate equations for this purpose. The drawback of this type of models is that
their development requires a lot of process expert knowledge. This knowledge is not
always available. For example, for biochemical process there is often not enough
phenomenological knowledge for accurate description of the processes at hand. An-
other problem is that the models often describe a simplified theoretical background
of the process rather than the real-life conditions of the process which is influenced
by many factors out of the scope of the MDM. Additionally, the model-driven
models usually focus on the description of the optimal steady-state of the process
and are thus not suitable for the description of any transient states. Nonetheless,
model-driven Soft Sensors are popular as a support for inferential control. Examples
of inferential control applications of first principle Soft Sensor are (De Wolf et al.,
1996) and (Doyle, 1998) where the first example is based on Kalman filter and the
latter one on non-linear observer method. Another example of model-driven Soft
Sensor is (Prasad et al., 2002) where a multi-rate Kalman filter is applied to the
control of a polymerisation process.
The focus of this review and of soft sensing in general is therefore put on the Data-
Driven Models (DDM) which have emerged as very attractive modelling approaches
enhancing the toolbox of diagnostic, prognostic and decision support methods avail-
17

able for plant operators and embedded in automated control systems. These models
are based on the real-life measurements which are recorded, stored and provided
as historical data by the Process Information Management Systems (PIMS). The
models themselves are empirical predictive methods like Principle Component Re-
gression (PCR), Multi-layer Perceptron (MLP), etc.
3.2 Soft Sensor development methodology
This section describes the typical steps and issues of the common practice of Soft
Sensor development. The presented procedure is rather general and can thus be
applied for both continuous and batch processes as well as to any of the application
areas discussed in Section 3.3. An overview of the methodology is presented in
Figure 1.
First data inspection
Selection of historical data
Identification of stationary
states
Data pre-processing
Model selection, training and
validation
Soft Sensor Maintenance
Fig. 1. Methodology for Soft Sensor development
18

3.2.1 First data inspection
During this initial step, the first inspection of the data is performed. The aim of this
step is to gain an overview of the data structure and identify any obvious problems
which may be handled at this initial stage (e.g. locked variables having constant
value, etc.). The next aim of this stage is to assess the requirements for the model
complexity. An experienced Soft Sensor developer can, already at this stage, make
a reasonable decision whether, in the case of an on-line prediction Soft Sensor, to
use a simple regression model, a rather more complex and powerful PCA regression
model or a non-linear neural network to build the Soft Sensor. In some cases, the
model family decision at this stage may not be correct, therefore the models and
their performance should be always evaluated and compared to alternative models
at the later development stages.
A particular attention is paid to the assessment of the target variable. It has to
be checked, if there is enough variation in the output variable and if this can be
modelled at all.
3.2.2 Selection of historical data and identification of stationary states
Here, data to be used for the training and evaluation of the model are selected.
Next, the stationary parts of the data have to be identified and selected. In vast
majority of the cases further modelling will only deal with the stationary states of
the process. The identification of the stationary process states is usually performed
by manual annotation of the data.
In Jiang et al. (2003) the steady state detection of continuous processes is discussed
and a wavelet transform based approach is applied to perform this task.
19

3.2.4 Model selection, training and validation
This phase is critical for the final Soft Sensor. As the model is the engine of the Soft
Sensor, selection of the optimal type is crucial for the Soft Sensors performance. So
far, there is no unified theoretical approach for this task and thus the model type and
its parameters are often selected in an ad-hoc manner for each Soft Sensor. Model
selection is also often subject to developer’s past experience and personal preference
which can be of disadvantage for the final Soft Sensor. This can be observed in the
domain of published Soft Sensor applications where many of the authors strongly
focus on one model type (e.g. PLS) which is in their field of expertise.
Nevertheless, despite the lack of a common theoretically superior approach to model
selection there are few techniques which can be adopted to this task. A possible
approach is to start with a simple model type or structure (e.g. linear regression
model) and gradually increase model complexity as long as significant improvement
in the model’s performance can be observed (using e.g. the Student’s t-test (Gosset,
1908)). While performing this task it is important to asses the performance of the
model on independent data (Weiss and Kulikowski, 1991; Hastie et al., 2001). The
same approach can also be applied to the parameters selection of the pre-processing
methods like for instance variable selection.
Additionally, for some industrial processes it can be difficult to obtain sufficient
amount of historical data for the model development. In such cases it is of advan-
tage to resort to statistical error-estimation techniques like K-fold cross-validation
(Kohavi, 1995). This method makes an optimal uses of the available data by parti-
tioning it in such a way that all of the samples are used for the model performance
validation. Another alternative in these circumstances is to apply statistical re-
21

3.3.1 On-line prediction
The most common application of Soft Sensors is the prediction of values which can-
not be measured on-line using automated measurements. This may be for techno-
logical reasons (e.g. there is no equipment available for the required measurement),
economical reasons (e.g. the necessary equipment is too expensive), etc. This often
applies to critical values which are related to the final product quality. Soft Sensors
can in such scenarios provide useful information about the values of interest and in
the case when the Soft Sensor prediction fulfils given standards, it can be also in-
corporated into the automated control loops of the process. Soft Sensors have been
widely used in fermentation, polymerisation and refinery processes. The common
denominator of these processes is their dynamics which can not be easily described
in terms of rigorous models and that there is often no way of collecting the nec-
essary information on-line. From the computational learning point of view these
problems are equivalent to supervised regression. The data-driven models are based
on historical data of the process. This data consists of the past plant measurements
which form the input data space of the Soft Sensor. The target values are the lab
measurements, infrequent observations, etc., of the values of interest.
Linear regression models are the most straightforward way of modelling the target
values. In this case, the modelled variable is a linear combination of the input
variables.
A Soft Sensor for the modelling of the particle size in a grinding plant was published
in Casali et al. (1998). The developed Soft Sensor is an ARMAX-type stepwise re-
gression model. The input for the model are systematically selected based on the
correlation between the analysed input feature and the output including delayed
26

The performance of two ANN variants, namely the Multi-Layer Perceptron (MLP)
and the Radial Basis Function Network (RBFN), are compared to a Support Vector
Regression (SVR) model in Desai et al. (2006). The data sets for the comparison are
two simulated batch bioprocesses. It is clearly shown, that the performance of the
SVR Soft Sensor is superior in comparison to the other two methods. The authors
also provide a theoretical explanation of the performance benefits. The ability to
locate global minima of the presented problems and the interpretability of the learnt
knowledge in terms of the training data (support vectors) are stated as advantages
of the proposed SVR Soft Sensor.
Another performance comparison between an MLP and an RBFN was published
in James et al. (2002). In this work, these two models are also compared to a
grey-box model based on a first principle model and either an MLP or an RBFN.
The performance was tested in terms of a biomass concentration prediction in a
biochemical batch process. They describe the hybrid model as the best performing
one. However, the performance gain comes at the cost of a-priori knowledge which
have to be input into the model.
In Wang et al. (2006) an RBFN-based Soft Sensor for the modelling of a membrane
separation process was developed. The Multiple Input Multiple Output (MIMO)
Soft Sensor predicts some critical process performance values (like gas concentra-
tions). The aim of the Soft Sensor is to deliver additional on-line information for
the process control.
An ensemble approach for Soft Sensor development based on Multi-Layer Percep-
trons was published in Kadlec and Gabrys (2008b). In this work the problem of
optimal network complexity selection was approached in the context of ensemble
30

methods. The optimal MLP topology was established by training several models
with different complexities and assessing their relative performance. In such a way
performance distributions across the different parameter values were calculated. The
final ensemble is built by weighting the contributions of ensemble members by their
estimated generalisation performance. This Soft Sensor was applied to an industrial
drier process.
Su et al. (1998) published an application of Recurrent Neural Network (RNN) to
the modelling of the degree-of-cure, which is an important quality indicator in an
epoxy/graphite fiber composites production process. The Soft Sensor is a grey-box
model, making partial use of a-priori information about the process. The Soft Sensor
was parametrised, trained and evaluated using simulated process data and after
some minor tuning tested using real process data and target values obtained from
off-line laboratory measurements. The authors were satisfied with the performance
of the Soft Sensor and deployed it in the real-life process environment.
Also an RNN was applied to the prediction of biomass concentration in Chen et al.
(2004a). RNN was applied in this work due to its theoretical ability to capture
dynamic effects underlying the data. Although the RNN model performance is not
compared to any other model type, the authors conclude that recurrent artificial
neural networks are capable of achieving a satisfactory prediction performance.
Another RNN application to the prediction of the melt-flow-length for filling of
molds in injection molding process was presented in Chen et al. (2004b). The au-
thors decided to use the recursive version of ANN because of its capability to store
temporal patterns which is of advantage in the modelled process. The developed
Soft Sensor provides accurate results of the melt-flow-length prediction.
31

Yang and Chai (1997) focus on soft sensing in a dynamic environment. The authors
discuss the application of a multi-step predictor and decide to use an RNN for
its implementation. They are using an Inner Recurrent Neural Network, where
only the hidden layer has recursive connections. The usefulness of the algorithm is
demonstrated based on three dynamic simulated processes.
The authors of Fellner et al. (2003) propose a grey-box technique for the implemen-
tation of a-priori knowledge in a data-driven model. They focus on ANN, which pro-
vides the possibility to deploy nodes (neurons) which represent the process knowl-
edge, e.g. single differential equations, etc. The nodes are abstract signal processing
units transforming the input information to their output using arbitrary, but dif-
ferentiable, equations. The authors apply the proposed ANN to the estimation of
diacetyl in a biochemical process.
Another method commonly applied to soft sensing is the PCA/PLS-based regression
(see Section 4.1).
A self-validating Soft Sensor is presented in Qin et al. (1997). The input data
is validated using a PCA-based approach for fault detection published in Dunia
et al. (1996). In the case of a detected failure, the sensor can be reconstructed
using the correlation structure of the affected input measurement to the other input
space variables, which is one of the valuable capabilities of the PCA. After this
pre-processing step, which on one hand removes the co-linearity of the input data
and on the other hand provides the ability for the reconstruction of sensor faults,
a Soft Sensor using traditional modelling techniques is built. This Soft Sensor is
successfully evaluated on a real-life problem dealing with air emission monitoring
process data.
32

Rong (Wang and Rong, 1997). The presented NFS is trained using a two-step ap-
proach consisting of a clustering and a back-propagation algorithm. One of its ad-
vantages is that the connectionist structure is determined automatically. The pro-
posed approach is applied to the modelling of a distillation column, more specifically,
to the propylene purity modelling at the output of the column.
An example of this type of Soft Sensor is an ANFIS-based Soft Sensor applied to
rubber viscosity prediction in Merikoski et al. (2001). Because there is no auto-
mated way to measure rubber viscosity, which is an important quality indicator, a
Soft Sensor is necessary to deliver the data. In the publication, it is claimed that
the accuracy of the Soft Sensor meets the requirements for implementation in the
process control loop.
Another ANFIS-based Soft Sensor was presented in Warne et al. (2004b). In this
work the data is pre-processed using PCA transformation which on one hand helps
to deal with the co-linearity of the data and on the other hand limits the size of the
input space of the ANFIS model which in turn reduces the complexity of the model
significantly. The presented methodology is applied to the prediction of polymeric-
coated substrate anchorage which is an important quality measure of the process
product.
Neuro-fuzzy Soft Sensor based on rough set theory and optimized by a genetic
algorithm is discussed in Luo and Shao (2006). The rough set theory is used to
obtain a reduced set of rules which are then implemented in the form of an MLP.
The genetic algorithm is used to get an optimal discretisation of the input variables.
The performance of the algorithm is demonstrated on a refinery case study, namely
on the prediction of freezing point of the light diesel fuel in a Fluid Catalytic
35

where the NNPLS and the Non-Linear Principle Component Analysis (NLPCA) al-
gorithms were applied to the prediction of emissions of NOx gas in exhaust streams.
In this case, the input data is pre-processed by mapping it on principle components
space using the NLPCA algorithm. After this pre-processing the actual model,
an NNPLS technique, predicts the target values. The application shows that the
model outperforms a linear model and also demonstrates an immunity with regards
to missing values.
A hybrid system consisting of Particle Swarm Optimisation which is used for the
training of an MLP was presented in Li et al. (2005). In this work the PSO algorithm
is combined with the Alopex algorithm (see Tzanakou et al. (1979)) to avoid local
minima to which the PSO is prone. The proposed algorithm is applied to an ethylene
distillation column data set.
Another hybrid approach to Soft Sensor modelling has been developed by Kordon et
al. (Kordon et al., 2002; Kordon, 2004, 2005; Kordon et al., 2005). In this case, the
hybridisation is done on a lower level. The involved methods perform pre-processing
of the data for the succeeding modelling steps. The methodology for the inferential
sensor building consists of three different steps. The first step is the analysis of the
data by an analytical neural network (Kordon, 2004). The aim of this step is to
perform feature selection on the input data and to deal with time delays between
the selected features. In the next step the data is processed using SVM. During this
step the outlier detection is done. In the third step the actual Soft Sensor is built.
This is performed by applying the Genetic Programming (GP) algorithm. The GP
algorithm selects a function from a pool of available functions and trains it to model
the output variable using the pre-processed input data. The Soft Sensor is a set of
analytical functions which maps the input space to the target variable space. The
37

proposed approach was applied to several real-life problems, e.g. the interface level
estimation in an organic process in Kalos et al. (2003).
The work of Chen et al. (Chen et al., 2000) was already briefly mentioned. The
Soft Sensor presented in this work is a grey-box model of a model-driven first
principle model and a data-driven artificial neural network. The ANN, which is
Radial Basis Function Network (RBFN), is used to model the non-linear reaction
rates. This model is then incorporated into the mass-balance model of a stirred-tank
bioreactor. The performance of the proposed hybrid Soft Sensor is illustrated on an
experimental case-study dealing with single microbial population.
A non-traditional approach to soft sensing is presented in Rao et al. (1993). There
is an ”Intelligent Soft Sensor” presented in this publication. It is a large system
consisting of a symbolic rule-based part, numerical part and a graphical part. This
allows to integrate quantitative as well as qualitative knowledge into the model.
The three parts are merged by a meta-system. The system is developed for a batch
digester quality control support of a sulphite pulping system.
Gonzalez et al. are discussing the performance of an ARMAX stepwise regression,
Takagi and Sugeno, fuzzy combinational, PLS, wavelet-based and MLP models in
Gonzalez et al. (2003). All these models are applied to a rougher flotation bank
modelling. The model input are both the process measurements and the combined
features. The combined features are built using a-priori process knowledge and
represent meaningful process descriptors. Apart from this contribution a novel 2-
level approach for outlier detection combining PCA capabilities and Scheffe´’s test
is provided. After the application to the modelling of copper concentration grade
the authors conclude that the dynamic PLS as well as the MLP and wavelet-based
38

Li et al. (2000) is dealing with the application aspects of the PCA and related
methods to the process industry problems. The focus is put on the development of
a Recursive PCA (RPCA) approach targeting adaptive process monitoring. Within
this framework it has also been shown that the method can deal with outliers,
missing values and delayed measurements. The authors presented an effective ap-
proach for the update of the correlation matrices as well as two algorithms for the
incremental update of the PCA base using the old PCA structure. Additionally a
review of the most common techniques for the selection of the number of princi-
ple components, which is an important question while developing PCA models, is
also presented. Based on the review a new technique for recursive selection of the
number of principle components is shown. For the purpose of the adaptive process
monitoring, it is necessary to update the confidence limits of the model with the
new incoming data, therefore the authors define also a monitoring scheme, which
detects and handles data outliers, missing values and process faults before updating
the model. Finally, the proposed monitoring scheme is applied to a rapid thermal
annealing process monitoring.
Rotem et al. (2000) applied the model-based PCA (MBPCA) method to the fault
detection of an ethylene compressor. The detection system is based on the first
principle model of the process, which makes the method applicable only to this
specific process.
A process monitoring Soft Sensor using an adaptive version of the PCA (Fast Mov-
ing Window PCA - FMWPCA) was published in Wang et al. (2005). The adaptivity
of the model is achieved by updating the data structures necessary for the PCA
calculation using a novel moving window technique. This technique updates the
PCA base (i.e. removes the oldest data sample and adds the new, current, one)
40

in a single step which makes this technique computationally efficient. Addition-
ally, an N-step-ahead process monitoring approach is presented which increases the
immunity towards the faulty data. The effectiveness of the described algorithm is
demonstrated using a simulated Fluid Catalytic Cracking unit process.
In Amazouz and Pantea (2006) an application of PCA and PLS to batch process
monitoring is presented. The proposed procedure is split into two steps, the first
is applying the PCA to manually explore the data space and to identify reference
or ”good” batches which are in the second stage used to develop the PLS model.
Having a PLS model of this reference batch one can compare the new incoming
process data (test data) to this model. If there is a deviation between the new data
and the reference model data an analysis of the PLS scores provides information
about the variable(s) causing the deviation. The authors are also planing to develop
a database of typical process faults and to use an expert system for automatic
process fault identification.
The applicability of the PLS, namely the Multi-way PLS algorithm to modelling
of batch process quality variables as well as process monitoring and control was
presented in Zhang and Lennox (2004). The studied process is a simulated penicillin
production fermentation batch process. The quality variable prediction is done using
standard PLS regression model. The process monitoring is carried out using the SPE
and T 2-statistics of the model.
He et al. (2005) are discussing an alternative approach to process monitoring and
process fault detection. The presented method is a three-step approach to process
monitoring. The first step is called ”Pre-analysis” and at this stage a number of
clusters in the process data is manually estimated using 2D and 3D PCA-scores
41

plots. Using the estimated number of clusters, the data is partitioned by the k-
means algorithm. In the second step, the data are visualised after transforming
them using the Fisher Discriminant Analysis (FDA). The authors tend to use the
FDA instead of the PCA due to the discrimination abilities of the FDA. Within this
step the normal and faulty process states are annotated. The final step is then the
calculation of the fault directions for the separate fault classes using the pairwise
FDA. The calculated fault direction provides information about the source of the
particular process fault. The algorithm is applied to a simulated as well as to an
industrial process.
Marjanovic et al. (2006) deals with the identification of batch process end points
which can improve the process effectiveness. The applied technique is the Multi-way
PLS (MPLS). The devised technique proves to be very effective and can thus be
implemented for the real-time batch process monitoring.
A set of practical applications of process monitoring and quality prediction using Self
Organizing Map (SOM) was published in Alhoniemi (1999). In this work SOMs have
been found useful for the monitoring of a continuous pulp digester. Before feeding
the data into the SOM model they have been manually pre-processed using a-priori
knowledge of the process. Another application presented in the work is the quality
prediction of steel production based on the concentration of the input elements and
some process parameters. The last application of SOMs presented in the work is
the analysis of the data from paper and pulp industry.
A complex Soft Sensor for process fault detection and identification has been pre-
sented in Yang et al. (2000). The Soft Sensor is based on an MLP and is applied to
the detection of three typical faults in a Fluid Catalytic Cracking (FCC) reactor.
42

The MLP is fed with input from different sources. One source of input is a model-
driven Soft Sensor. This sensor predicts the catalyst circulation rate based on the
energy balance equation within the FCC reactor. The output of the Soft Sensor is
then mapped to trends of the catalyst circulation rate, e.g. stable, increasing, etc.
The trends are then provided to the MLP. The other inputs to the MLP are trends
of directly measurable process variable like the reactor temperature, reactor feed
flow rate, etc, which are determined using the wavelet transformation. The devel-
oped approach works well for the given process but because of the involvement of
the process specific FPM, it is not applicable to any other processes.
In a recent publication (Kampjarvi et al., 2008) a complex Soft Sensor for the
detection and isolation of process faults is devised which is based on PCA, RBFN
and SOM. The Soft Sensor is developed in the framework of an ethylene cracking
process. The authors demonstrate improved accuracy of the system after including
calculated variables, which are built using process knowledge. The final Soft Sensor
achieves high performance and is included into the model predictive control of the
process.
3.3.3 Sensor fault detection and reconstruction
The vast majority of modelling techniques applied within the process industry as
Soft Sensors are not able to handle data from faulty sensors as a matter of their
normal operation, therefore there is a need to identify and replace sensor and process
faults before the actual model building and application.
Process and sensor faults are detected and handled using the PCA in Dunia and
Qin (1998a) and Dunia and Qin (1998b). The faults are detected in the PCA resid-
43

multivariate Principle Component Analysis (Section 4.1), Partial Least Squares
(Section 4.2), Artificial Neural Networks (Section 4.3), Neuro-Fuzzy Systems (Sec-
tion 4.4 ) and Support Vector Machines (Section 4.5). Finally, the last part of the
section deals with the modelling of batch processes (Section 4.6).
4.1 Principle Component Analysis
The PCA algorithm reduces the number of variables by building linear combinations
of them. This is done in such a way that these combinations cover the highest
possible variance in the input space and are additionally orthogonal to each other.
In the context of the process industry data this is a very useful feature because the
data there are often co-linear (see Section 2.2). In this way the co-linearity can be
handled and the dimensionality of the input space can be decreased at the same
time. The PCA is usually applied as pre-processing step followed by the actual
computational learning method.
An extensive and general derivation, interpretation and application aspects of the
PCA is provided in Jolliffe (2002). Application possibilities of the PCA in the pro-
cess industry are reviewed in Warne et al. (2004a) and Gonzalez (1999).
There are several extensions of the original PCA algorithm which target some of
their published drawbacks. Among them are the Model-Based PCA Rotem et al.
(2000) and the Non-Linear PCA (Dong and McAvoy, 1996). Another extensions
of the PCA focused on the derivation of an adaptive version of this transforma-
tion. Such extensions are the Recursive PCA in (Li et al., 2000), the Moving Win-
dow PCA (Wang et al., 2005) and the Time-Lagged PCA in Lee et al. (2004). An
overview of different PCA versions is provided in Figure 3.
48

A general description of the PLS technique is provided in Geladi and Esbensen
(1991) and Abdi (2003). As PLS is a very popular technique in chemical engineering
and in chemometrics, there are several publications dealing with the application
aspects of PLS to this domains (Frank and Friedman, 1993; Kourti, 2002).
The original PLS algorithm suffers from similar problems as its PCA counterpart. It
is also modelling only linear relations between the data. Therefore there have been
also some advanced versions of the PLS proposed. Making the PLS applicable to
non-linear problem is the target of the Multi-way PLS (MPLS) (Bro, 1996) and of
the Neural Network PLS (NNPLS) (Qin and McAvoy, 1992). An adaptive version of
the PLS called Recursive PLS (RPLS) is proposed in Qin (1998). Another adaptive
version of the PLS based on the moving window technique is the Exponentially
Weighted PLS (EWPLS) (Dayal and MacGregor, 1997). The different versions of
the PLS algorithm are reviewed in Figure 4.
Neural Network
PLS
Multi-way
PLS
Partial
Least
Squares
Recursive
PLS
Exp. Weighted
PLS
Non-linear
Adaptive
Fig. 4. PLS and its derivations
4.3 Artificial Neural Networks
The original intention of Artificial Neural Networks (ANN) was to build computa-
tional models motivated by the operation of biological neurons which are the basic
50

information processing units in nervous systems. The task of both the biological
and the artificial neuron is to collect information at the inputs, to process this in-
formation and to output it. There is a large variety of computational intelligence
models which are more or less biologically plausible and can be summarized under
the term Artificial Neural Network.
A general introduction to the theory of ANN is given in Bishop (1995). This book
describes a large number of different ANN variants, learning algorithms, application
areas, etc. Another theoretical considerations of ANN is presented in Hastie et al.
(2001), in this work the ANN are presented in a general statistical context. The ap-
plication aspects of large number of ANN variants, including dynamic and adaptive
ANN, are discussed in Principe et al. (2000). This book is especially recommended
for Soft Sensor modelling as there is a large number of mutual topics between the
book and the process industry applications of ANN. Detailed discussion of some
problems of process industry data and of the suitability of ANN to solve this prob-
lem is provided in Qin (1997). Apart from the discussion of the ANN issues in the
process industry the work proposes also some possible solution to them.
Among the large number of ANN variants mentioned above, the most common,
in the process industry as well as in general, are the feed-forward networks, like
the Multi-Layer Perceptron (MLP) (Bishop, 1995) and the Radial-Basis Function
Network (RBFN) (Poggio and Girosi, 1990). Both of these models are universal
function approximators (Funahashi, 1989).
The structure of Recursive Neural Networks (RNN) is similar to the one of the feed-
forward networks, the only significant difference is a feed-back connection (Mandic
and Chambers, 2001). This gives the network the capability to extract and learn
51

temporal sequences from the data which can be of advantage in the context of
process industry data as these often show re-occurring temporal patterns.
Self-Organizing Map (SOM) or Kohonen Map (Kohonen, 1997) is a type of ANN
which is able to deal with unsupervised problems and is thus applicable to process
monitoring tasks. SOMs consist of an usually high dimensional input layer and an
output layer (also called competitive layer) which is arranged in a two- or three-
dimensional grid. During the learning the grid is arranged in such a way that the
low dimensional representation of the data preserves its high dimensional topology.
This makes them also useful for the visualisation of high-dimensional data. Figure
5 shows an overview of the ANN variants which are interesting from the process
industry point of view.
Multi-layer
Perceptron
Radial Basis
Function Network
Artificial
Neural
Networks
Recursive Neural
Network
Self-Organizing
Maps
Fig. 5. ANN versions commonly used in process industry
The drawback of ANNs is that during their learning that they are prone to get stuck
in local minima, which can result in sub-optimal performance. Another problem
are the difficulties with the estimation of optimal topology of the networks. The
topology of the ANN is critical for their performance because their generalisation
power is to a large extent dependent on the complexity of the networks. There is
also an issue with the interpretability of the learnt knowledge. The learnt knowledge
is distributed in the weights between the particular neurons and is not available
52

in terms of human understandable representation. The generalisation performance
of the ANN is dependent on the model parameters. This dependency cannot be
described in clear analytical terms and is very much dependent on the underlying
data.
4.4 Neuro-Fuzzy Systems
Neuro-Fuzzy System (NFS) is a hybrid intelligent model which combines the learn-
ing and universal approximation abilities of the ANN with the human-like reasoning
of the Fuzzy Inference System (FIS) (Zadeh, 1996). It is a realisation of the fuzzy
system by a connectionist structure of an ANN. The aim of the fusion of the two
methods is to provide a learning system which provides the advantages of both of
the involved techniques while at the same time dealing with their drawbacks. An-
other appealing property for the process industry application of the NFS models is
that the technique is based on receptive fields and thus intrinsically provides means
for the building of local models. An introduction to NFS is provided in Jang et al.
(1997) and Nauck et al. (1997).
The evolving variants of NFS are very well suited to dealing with dynamic environ-
ment. These systems are called evolving because they adapt automatically together
with the changing environment represented by the data. An evolving system is
thought to be able to change its structure, to grow and shrink and to update its
parameters (Angelov and Kasabov, 2005). In this way the model is able to deploy
new local models related to new states of the input data if necessary.
An early example of such a method, which was able to adapt its structure according
to the complexity of the underlying problem, was published in Gabrys and Bargiela
53

(1999). Examples of several other evolving neuro-fuzzy methods are Angelov and
Buswell (2002); Angelov and Filev (2004); Rong et al. (2006).
4.5 Support Vector Machines
Due to their theoretical background in the statistical learning theory Support Vector
Machines (SVM) gained attention in the computational learning community. Their
derivation and theoretical justification can be found in Vapnik (1998). Application
aspects of the SVM are discussed in Yan et al. (2004); Feng et al. (2003); Li and Li
(2005).
While grounded in the theory, SVMs have been demonstrated to work very well
for a wide spectrum of applications so it is not surprising that they have also been
successfully applied as Soft Sensors. While some successes have been reported there
is still a lot of work needed especially when dealing with very large data sets for
which the computational complexity of SVM training process can be prohibitive.
4.6 Techniques for batch process modelling
When measuring K variables at J time points one batch leads to J×K data tables.
Therefore a set of N batches leads to a three-way matrix of the size N × J ×K.
To apply the so far discussed methods it is necessary to unfold the three dimensional
matrix into a two dimensional table. This task has been approached by Nomikos
and MacGregor (1994, 1995b), where the Batch-Wise-Unfolding (BWU) method for
unfolding the data has been discussed for graphical presentation of this approach.
This unfolding technique is based on the Multi-way PCA or PLS (Wold et al.,
54

1987; Nomikos and MacGregor, 1995a) and nowadays widely used in batch process
industry.
Another approach to unfolding the three-way matrix was developed by Wold et al.
(1998). This method is called Observation-Wise-Unfolding (OWU) and it was de-
scribed in details in (Eriksson et al., 2001). While BWU mainly deals with the
batch-to-batch variation, OWU describes the dynamic behaviour of the batches
and summarizes the main trajectory of all variables. Time or maturity is regarded
as a y-variable and the progress of the batch is modelled using the PLS method.
The two discussed unfolding methods (BWU and OWU) have the conditions for se-
lecting the batch database in common. In the case of monitoring batch processes, it
is often of interest to compare the current batch to a set of well performing batches.
These batches are selected according to quality or any other performance indicator
and often referred to as the golden batch. The model is built based on the data set
which fulfils the quality requirements. The tested batch is then monitored with re-
spect to the model and therefore compared to the golden batch. However, if on-line
prediction of the output quality is of interest, it is advisable to build a model of all
batches, those with good and those with poor quality. This will introduce enough
variability into the model and lead to a better performing prediction model.
In van Sprang et al. (2002) a good comparison of both unfolding approaches is
given.
A major drawback of the BWU method is the necessity of having batches with
equal length which is not always the case due to the variability in the production
and some other influences which are out of control of the process controllers. To
overcome this problem a maturity variable (e.g. conversion) can be introduced as it
55

was presented in Nomikos and MacGregor (1995b) and in Neogi and Schlags (1998).
In the case of OWU, the varying length of the data tables is not a big issue as long
as the variation of the batch length is kept in certain limits.
Applying the PCA or PLS also requires mean centering and scaling to unit variance
of the unfolded data. In this way the mean trajectory is removed from the data
and the remaining data explains the variation of the batch around the average
batch which in turn allows an effective batch-to-batch comparison of the underlying
process. A major drawback of the discussed approach is the assumption that the
data of the whole batch is available. To solve this issue Rnnar et al. (1998) proposed
a hierarchical method, where the batch is divided into several stages and separate
models are built for each of the stages. The final model is a hierarchical combination
of the component models.
Another issue of batch process modelling lies in the fixed model. For example in
case of process monitoring, when the process shows slow changes from batch to
batch it will lead to a lot of false alarms. To overcome this Lee and Vanrolleghem
(2003) and Lee et al. (2003), suggest a moving window techniques for updating the
model after a new successful batch was finished. It has been shown that through the
continuous update of the model batch-to-batch changes can be effectively handled.
Lee and Vanrolleghem (2003) applied the technique to a sequencing batch reactor
for biological waste water treatment and Lee et al. (2003) to a simulated fed-batch
penicillin production process.
An advanced to batch process monitoring and fault detection was presented in
Kourti et al. (1995). In this work, in addition to the three-way data table, a two-
dimensional data matrix with initial conditions like, product quality measurements
56

Soft Sensor modelling from both fields. Apart from the traditional methods for
soft sensing like the PCA and the ANN, hybrid methods are currently becoming
popular. Another method which recently caught the attention of Soft Sensor devel-
opers is SVM based regression. The applications presented in this review outline
the advantages and drawbacks of these approaches.
This review provides also an extensive list of applications of Soft Sensors across
many fields of the process industry. The presented examples focus on the applica-
tion of Soft Sensor as: on-line predictors, process monitoring and sensor fault and
reconstruction tools.
Based on the reviewed applications we have identified a set of the most important
data-driven techniques, which are applied to Soft Sensor modelling, and provide a
discussion of these methods which focuses on a brief introduction into the method
followed by a review of publications dealing with theoretical and practical aspects
of the methods.
References
Abdi, H., 2003. Partial least squares (pls) regression. Encyclopedia of Social Sci-
ences, Research Methods. Thousand Oaks (CA): Sage (2003)Encyclopedia of So-
cial Sciences, Research Methods. Thousand Oaks (CA): Sage (2003).
Alhoniemi, E. S. A., 1999. Process monitoring and modeling using the self-
organizing map. Integrated Computer-Aided Engineering 6 (1), 3–14, 6 (1).
Amazouz, M., Pantea, R., 2006. Use of multivariate data analysis for lumber drying
process monitoring and fault detection. In: Crone, S. F., S., L., Stahlbock, R.
(Eds.), International Conference on Data Mining. pp. 329–332, pp. 329–332.
60

Davies, L., Gather, U., 1993. The identification of multiple outliers. Journal of the
American Statistical Association 88 (423), 782–792, 88 (423).
Dayal, B. S., MacGregor, J. F., 1997. Recursive exponentially weighted pls and its
applications to adaptive control and prediction. Journal of Process Control 7 (3),
169–179, 7 (3).
De Wolf, S., Cuypers, R. L. E., Zullo, L. C., Vos, B. J., Bax, B. J., 1996. Model
predictive control of a slurry polymerisation reactor. Computers and Chemical
Engineering 20, 955–961, 20.
Desai, K., Badhe, Y., Tambe, S. S., Kulkarni, B. D., 2006. Soft-sensor development
for fed-batch bioreactors using support vector regression. Biochemical Engineer-
ing Journal 27 (3), 225–239, 27 (3).
Devogelaere, D., Rijckaert, M., Leon, O. G., Lemus, G. C., 2002. Application of
feedforward neural networks for soft sensors in the sugar industry. In: Neural
Networks, 2002. SBRN 2002. Proceedings. VII Brazilian Symposium on. pp. 2–6,
pp. 2–6.
Ding, F., Chen, T., 2005. Modeling and identification for multirate systems. Acta
Automatica Sinica 31 (1), 105–122, 31 (1).
Dong, D., McAvoy, T. J., 1996. Nonlinear principal component analysis–based
on principal curves and neural networks. Computers and Chemical Engineering
20 (1), 65–78, 20 (1).
Dong, D., McAvoy, T. J., Chang, L. J., 1995. Emission monitoring using multivariate
soft sensors. In: American Control Conference, 1995. Proceedings of the. Vol. 1.
Vol. 1.
Dote, Y., Ovaska, S. J., 2001. Industrial applications of soft computing: A review.
In: Proceedings of the IEEE. Vol. 89. pp. 1243–1265, pp. 1243–1265.
Doyle, F. J., 1998. Nonlinear inferential control for process applications. J. Process
63

Funahashi, K., 1989. On the approximate realization of continuous mappings by
neural networks. Neural Networks 2 (3), 183–192, 2 (3).
Gabrielsson, J., Jonsson, H., Trygg, J., Airiau, C., Schmidt, B., Escott, R., 2006.
Combining process and spectroscopic data to improve batch modeling. AICHE
JOURNAL 52 (9), 3164, 52 (9).
Gabrys, B., 2002. Neuro-fuzzy approach to processing inputs with missing values in
pattern recognition problems. International Journal of Approximate Reasoning
30 (3), 149–179, 30 (3).
Gabrys, B., 2004. Learning hybrid neuro-fuzzy classifier models from data: To com-
bine or not to combine? Fuzzy Sets and Systems 147, 39–56, 147.
Gabrys, B., Bargiela, A., 1999. Neural networks based decision support in presence
of uncertainties. Journal of Water Resources Planning and Management 125 (5),
272–280, 125 (5).
Gabrys, B., Ruta, D., 2006. Genetic algorithms in classifier fusion. Applied Soft
Computing 6 (4), 337–347, 6 (4).
Gama, J., Medas, P., Castillo, G., Rodrigues, P., 2004. Learning with drift detection.
In: Advances in Artificial Intelligence SBIA 2004: 17th Brazilian Symposium on
Artificial Intelligence. Vol. 3171. p. 286295, p. 286295.
Geladi, P., Esbensen, K., 1991. Regression on multivariate images: principal compo-
nent regression for modeling, prediction and visual diagnostic tools. J. Chemometr
5 (97), 111, 5 (97).
Gomez, E., Unbehauen, H., Kortmann, P., Peters, S., 1996. Fault detection and
diagnosis with the help of fuzzy-logic and with application to a laboratory tur-
bogenerator. Proc. of the 13th IFAC World Congress, volume N, 175–180Proc. of
the 13th IFAC World Congress, volume N.
Gonzalez, G. D., 1999. Soft sensors for processing plants. Intelligent Processing and
65

Prentice Hall Upper Saddle River, NJ, Prentice Hall Upper Saddle River, NJ.
Jiang, T., Chen, B., He, X., Stuart, P., 2003. Application of steady-state detection
method based on wavelet transform. Computers and Chemical Engineering 27 (4),
569–578, 27 (4).
Jolliffe, I. T., 2002. Principal Component Analysis. Springer, Springer.
Jordaan, E., Kordon, A., Chiang, L., Smits, G., 2004. Robust inferential sensors
based on ensemble of predictors generated by genetic programming. In: Proceed-
ings of PPSN2004, Birmingham, UK. pp. 522–531, pp. 522–531.
Jos de Assis, A., Maciel Filho, R., 2000. Soft sensors development for on-line biore-
actor state estimation. Computers and Chemical Engineering 24 (2), 1099–1103,
24 (2).
Kadlec, P., Gabrys, B., 2008a. Adaptive local learning soft sensor for inferential
control support. In: CIMCA 2008. IEEE, Vienna, IEEE, Vienna.
Kadlec, P., Gabrys, B., 2008b. Learnt topology gating artificial neural network.
In: 2008 IEEE International Joint Conference on Neural Networks (IJCNN2008).
IEEE, Hong Kong, pp. 2605–2612, pp. 2605–2612.
Kalos, A., Kordon, A., Smits, G., Werkmeister, S., 2003. Hybrid model development
methodology for industrial soft sensors. In: 2003 American Control Conference.
pp. 5417–5422, pp. 5417–5422.
Kampjarvi, P., Sourander, M., Komulainen, T., Vatanski, N., Nikus, M., Jms-
Jounela, S. L., 2008. Fault detection and isolation of an on-line analyzer for an
ethylene cracking process. Control Engineering Practice 16 (1), 1–13, 16 (1).
Kittler, J., Hatef, M., Duin, R. P. W., Matas, J., 1998. On combining classifiers.
Pattern Analysis and Machine Intelligence, IEEE Transactions on 20 (3), 226–
239, 20 (3).
Kohavi, R., 1995. A study of cross-validation and bootstrap for accuracy estimation
67

Kuncheva, L. I., 2004. Combining Pattern Classifiers: Methods and Algorithms.
Wiley-IEEE, Wiley-IEEE.
Lee, C., Choi, S. W., Lee, I.-B., 2004. Sensor fault identification based on time-
lagged pca in dynamic processes. Chemometrics and Intelligent Laboratory Sys-
tems 70 (2), 165–178, 70 (2).
Lee, D. S., Vanrolleghem, P. A., 2003. Monitoring of a sequencing batch reactor
using adaptive multiblock principal component analysis. Biotechnology and Bio-
engineering 82 (4), 489–497, 82 (4).
Lee, J. H., Dorsey, A. W., 2004. Monitoring of batch processes through state-space
models. AIChE Journal 50 (6), 1198–1210, 50 (6).
Lee, J. M., Yoo, C. K., Lee, I. B., 2003. On-line batch process monitoring using a
consecutively updated multiway principal component analysis model. Computers
and Chemical Engineering 27 (12), 1903–1912, 27 (12).
Li, M. Z. Z., Li, W., 2005. Study on least squares support vector machines algorithm
and its application. Proceedings of the 17th IEEE International Conference on
Tools with Artificial Intelligence, 1082–3409Proceedings of the 17th IEEE Inter-
national Conference on Tools with Artificial Intelligence.
Li, S. J., Zhang, X. J., Qian, F., 2005. Soft sensing modeling via artificial neural net-
work based on pso-alopex. Machine Learning and Cybernetics, 2005. Proceedings
of 2005 International Conference on 7, 7.
Li, W., Yue, H. H., Valle-Cervantes, S., Qin, S. J., 2000. Recursive pca for adaptive
process monitoring. Journal of Process Control 10 (5), 471–486, 10 (5).
Lin, B., Recke, B., Knudsen, J., Jrgensen, S. B., 2007. A systematic approach for
soft sensor development. Computers and Chemical Engineering 31 (5), 419–425,
31 (5).
Lin, C., Lee, C., 1996. Neural fuzzy systems: a neuro-fuzzy synergism to intelligent
69

systems. Prentice-Hall, Inc. Upper Saddle River, NJ, USA, Prentice-Hall, Inc.
Upper Saddle River, NJ, USA.
Luo, J. X., Shao, H. H., 2006. Developing soft sensors using hybrid soft comput-
ing methodology: a neurofuzzy system based on rough set theory and genetic
algorithms. Soft Computing-A Fusion of Foundations, Methodologies and Appli-
cations 10 (1), 54–60, 10 (1).
Macias, J. J., Zhou, P. X., 2006. A method for predicting quality of the crude oil
distillation. In: Evolving Fuzzy Systems, 2006 International Symposium on. pp.
214–220, pp. 214–220.
Mandic, D. P., Chambers, J. A., 2001. Recurrent Neural Networks for Prediction:
Learning Algorithms, Architectures and Stability. Wiley, Wiley.
Marjanovic, O., Lennox, B., Sandoz, D., Smith, K., Crofts, M., 2006. Real-time
monitoring of an industrial batch process. Computers and Chemical Engineering
30 (10-12), 1476–1481, 30 (10-12).
Meleiro, L. A. C., Finho, R. M., 2000. A self-tuning adaptive control applied to an
industrial large scale ethanol production. Computers and Chemical Engineering
24 (2-7), 925–930, 24 (2-7).
Menold, P. H., Pearson, R. K., Allgower, F., 1999. Online outlier detection and
removal. Proceedings of the 7th Mediterranean on Control and Automation
(MED99), Haifa, Israel, 1110–1133Proceedings of the 7th Mediterranean on Con-
trol and Automation (MED99), Haifa, Israel.
Merikoski, S., Laurikkala, M., Koivisto, H., 2001. An adaptive neuro-fuzzy infer-
ence system as a soft sensor for viscosity in rubber mixing process. Tech. rep.,
WSEAS NNA-FSFS-EC 2001, Puerto de la Cruz, Tenerife, Spain, 11-15 February
2001, paper 446; http://www.ad.tut.fi, WSEAS NNA-FSFS-EC 2001, Puerto de
la Cruz, Tenerife, Spain, 11-15 February 2001, paper 446; http://www.ad.tut.fi.
70

12 (3), 353–372, 12 (3).
Principe, J. C., Euliano, N. R., Lefebvre, W. C., 2000. Neural and adaptive systems.
Wiley New York, Wiley New York.
Qin, S. J., 1997. Neural networks for intelligent sensors and control - practical
issues and some solutions. Neural Systems for Control, 213234Neural Systems for
Control.
Qin, S. J., 1998. Recursive pls algorithms for adaptive data modeling. Computers
and Chemical Engineering 22 (4-5), 503–514, 22 (4-5).
Qin, S. J., McAvoy, T. J., 1992. Nonlinear pls modeling using neural networks.
Computers & Chemical Engineering 16 (4), 379–391, 16 (4).
Qin, S. J., Yue, H., Dunia, R., 1997. Self-validating inferential sensors with appli-
cation to air emission monitoring. Ind. Eng. Chem. Res 36, 1675–1685, 36.
Radhakrishnan, V. R., Mohamed, A. R., 2000. Neural networks for the identification
and control of blast furnace hot metal quality. Journal of Process Control 10 (6),
509–524, 10 (6).
Rao, M., Corbin, J., Wang, Q., 1993. Soft sensors for quality prediction in batch
chemical pulping processes. In: Intelligent Control, 1993., Proceedings of the 1993
IEEE International Symposium on. pp. 150–155, pp. 150–155.
Rnnar, S., MacGregor, J. F., Wold, S., 1998. Adaptive batch monitoring using
hierarchical pca. Chemometrics and Intelligent Laboratory Systems 41 (1), 73–
81, 41 (1).
Rong, H. J., Sundararajan, N., Huang, G. B., Saratchandran, P., 2006. Sequential
adaptive fuzzy inference system (safis) for nonlinear system identification and
prediction. Fuzzy Sets and Systems 157 (9), 1260–1275, 157 (9).
Rotem, Y., Wachs, A., Lewin, D. R., 2000. Ethylene compressor monitoring using
model-based pca. AIChE Journal 46 (9), 1825–1836, 46 (9).
72

Ruta, D., Gabrys, B., 2000. An overview of classifier fusion methods. Computing
and Information Systems 7 (1), 1–10, 7 (1).
Ruta, D., Gabrys, B., 2005. Classifier selection for majority voting. Information
Fusion 6 (1), 63–81, 6 (1).
Schafer, J. L., Graham, J. W., 2002. Missing data: Our view of the state of the art.
Psychological Methods 7 (2), 147–177, 7 (2).
Scheffer, J., 2002. Dealing with missing data. Research Letters in the Information
and Mathematical Sciences 3 (1), 153–160, 3 (1).
Serneels, S., Verdonck, T., 2008. Principal component analysis for data containing
outliers and missing elements. Computational Statistics and Data Analysis 52 (3),
1712–1727, 52 (3).
Smith, H., Fingar, P., 2003. Business process management: The third waveBusiness
process management: The third wave.
Stanimirova, I., Daszykowski, M., Walczak, B., 2007. Dealing with missing values
and outliers in principal component analysis. Talanta 72 (1), 172–178, 72 (1).
Su, H. B., Fan, L. T., Schlup, J. R., 1998. Monitoring the process of curing of
epoxy/graphite fiber composites with a recurrent neural network as a soft sensor.
Engineering Applications of Artificial Intelligence 11 (2), 293–306, 11 (2).
Tzanakou, E., Michalak, R., Harth, E., 1979. The alopex process: Visual receptive
fields by response feedback. Biological Cybernetics 35 (3), 161–174, 35 (3).
Valentini, G., Masulli, F., 2002. Ensembles of learning machines. In: 13th Italian
Workshop on Neural Nets. Vol. 2486 of Series Lecture Notes in Computer Sci-
ences. Springer-Verlag, p. 322, p. 322.
van Sprang, E. N. M., Ramaker, H. J., Westerhuis, J. A., Gurden, S. P., Smilde,
A. K., 2002. Critical evaluation of approaches for on-line batch process monitor-
ing. Chemical Engineering Science 57 (18), 3979–3991, 57 (18).
73

Van sprang, E. N. M., Ramaker, H. J., Westerhuis, J. A., Smilde, A. K., Wienke,
D., 2005. Statistical batch process monitoring using gray models. AIChE Journal
51 (3), 931–945, 51 (3).
Vapnik, V. N., 1998. Statistical learning theory. Wiley New York, Wiley New York.
Venkatasubramanian, V., Rengaswamy, R., Kavuri, S. N., 2003a. A review of process
fault detection and diagnosis part ii: Qualitative models and search strategies.
Computers and Chemical Engineering 27 (3), 313–326, 27 (3).
Venkatasubramanian, V., Rengaswamy, R., Kavuri, S. N., Yin, K., 2003b. A review
of process fault detection and diagnosis part iii: Process history based methods.
Computers and Chemical Engineering 27 (3), 327–346, 27 (3).
Venkatasubramanian, V., Rengaswamy, R., Yin, K., Kavuri, S. N., 2003c. A review
of process fault detection and diagnosis part i: Quantitative model-based methods.
Computers and Chemical Engineering 27 (3), 293–311, 27 (3).
Vilalta, R., Drissi, Y., 2002. A perspective view and survey of meta-learning. Arti-
ficial Intelligence Review 18 (2), 77–95, 18 (2).
Walczak, B., Massart, D. L., 1995. Robust principal components regression as a
detection tool for outliers. Chemometrics and Intelligent Laboratory Systems
27 (1), 41–54, 27 (1).
Walczak, B., Massart, D. L., 2001a. Dealing with missing data part i. Chemometrics
and Intelligent Laboratory Systems 58 (1), 15–27, 58 (1).
Walczak, B., Massart, D. L., 2001b. Dealing with missing data: Part ii. Chemomet-
rics and Intelligent Laboratory Systems 58 (1), 29–42, 58 (1).
Wang, L., Shao, C., Wang, H., Wu, H., 2006. Radial basis function neural networks-
based modeling of the membrane separation process: Hydrogen recovery from
refinery gases. Journal of Natural Gas Chemistry 15 (3), 230–234, 15 (3).
Wang, S., Cui, J., 2005. Sensor-fault detection, diagnosis and estimation for centrifu-
74

gal chiller systems using principal-component analysis method. Applied Energy
82 (3), 197–213, 82 (3).
Wang, S., Xiao, F., 2004. Ahu sensor fault diagnosis using principal component
analysis method. Energy & Buildings 36 (2), 147–160, 36 (2).
Wang, X., Kruger, U., Irwin, G. W., 2005. Process monitoring approach using fast
moving window pca. Industrial & Engineering Chemistry Research 44 (15), 5691–
5702, 44 (15).
Wang, Y., Rong, G., 1997. A self-organizing neural-network-based fuzzy system.
Artificial Neural Networks, Fifth International Conference on (Conf. Publ. No.
440), 106–110Artificial Neural Networks, Fifth International Conference on (Conf.
Publ. No. 440).
Warne, K., Prasad, G., Rezvani, S., Maguire, L., 2004a. Statistical and computa-
tional intelligence techniques for inferential model development: a comparative
evaluation and a novel proposition for fusion. Engineering Applications of Artifi-
cial Intelligence 17 (8), 871–885, 17 (8).
Warne, K., Prasad, G., Siddique, N. H., Maguire, L. P., 2004b. Development of
a hybrid pca-anfis measurement system for monitoring product quality in the
coating industry. In: Systems, Man and Cybernetics, 2004 IEEE International
Conference on. Vol. 4. Vol. 4.
Weiss, S., Kulikowski, C., 1991. Computer systems that learn: classification and
prediction methods from statistics, neural nets, machine learning, and expert
systems. Morgan Kaufmann Publishers Inc. San Francisco, CA, USA, Morgan
Kaufmann Publishers Inc. San Francisco, CA, USA.
Welch, G., Bishop, G., 2001. An introduction to the kalman filter. An introduction
to the kalman filter.
Widmer, G., Kubat, M., 1996. Learning in the presence of concept drift and hidden
75

contexts. Machine Learning 23 (1), 69–101, 23 (1).
Wold, S., Geladi, P., Esbensen, K., Ohman, J., 1987. Multi-way principal compo-
nents and pls analysis. Journal of Chemometrics 1 (1), 41–56, 1 (1).
Wold, S., Kettaneh, N., Fridn, H., Holmberg, A., 1998. Modelling and diagnostics of
batch processes and analogous kinetic experiments. Chemometrics and Intelligent
Laboratory Systems 44 (1-2), 331–340, 44 (1-2).
Wold, S., Sjstrm, M., Eriksson, L., 2001. Pls-regression: a basic tool of chemometrics.
Chemometrics and Intelligent Laboratory Systems 58 (2), 109–130, 58 (2).
Wolpert, D. H., 1992. Stacked generalization. Neural Networks 5 (2), 241–259, 5 (2).
Yan, W., Shao, H., Wang, X., 2004. Soft sensing modeling based on support vector
machine and bayesian model selection. Computers and Chemical Engineering
28 (8), 1489–1498, 28 (8).
Yang, S. H., Chen, B. H., Wang, X. Z., 2000. Neural network based fault diagno-
sis using unmeasurable inputs. Engineering Applications of Artificial Intelligence
13 (3), 345–356, 13 (3).
Yang, Y., Chai, T., 1997. Soft sensing based on artificial neural network. In: Amer-
ican Control Conference, 1997. Proceedings of the 1997. Vol. 1. Vol. 1.
Zadeh, L. A., 1996. Fuzzy sets. World Scientific Series In Advances In Fuzzy Sys-
tems, 19–34World Scientific Series In Advances In Fuzzy Systems.
Zamprogna, E., Barolo, M., Seborg, D. E., 2004a. Development of a soft sensor for
a batch distillation column using linear and nonlinear pls regression techniques.
Control Engineering Practice 12, 917–929, 12.
Zamprogna, E., Barolo, M., Seborg, D. E., 2004b. Estimating product composition
profiles in batch distillation via partial least squares regression. Control Engi-
neering Practice 12 (7), 917–929, 12 (7).
Zhang, H., Lennox, B., 2004. Integrated condition monitoring and control of fed-
76

Publication Applied
method(s)
Applic.
type
Process description Process
type
Casali et al. (1998) SRM (ARMAX) OP particle size estimation in a grinding plant Cont.
Park and Han (2000) PCA/PLS+LWR OP toluene composition in a splitter column,
diesel temperature in crude oil column
Cont.
Kadlec and Gabrys
(2008a)
MLR ensemble OP industrial drier Cont.
Devogelaere et al. (2002) MLP OP sugar quality estimation Cont.
Jos de Assis and Ma-
ciel Filho (2000)
MLP, FPM, eKF OP biomass estimation in a fermentation process Batch
Qin (1997) MLP, NNPLS OP refinery Batch
Meleiro and Finho (2000) MLP OP control loop support of ethanol production
support
Batch
Park and Han (2000) MLP+Expert
System
OP silica content control in the steel production Cont.
Fortuna et al. (2005) MLP OP C4 and C5 concentration prediction in a
debutanizer refinery process
Cont.
Desai et al. (2006) MLP, RBFN,
SVR
OP two simulated biochemical processes Batch
Wang et al. (2006) RBFN OP membrane separation process modelling Cont.
Kadlec and Gabrys
(2008b)
MLPs ensemble OP industrial drier Cont.
James et al. (2002) MLP, RBFN,
Hybrid
(MLP/RBFN+FPM)
OP biomass concentration prediction Batch
Su et al. (1998) RNN+FPM OP degree-of-cure prediction in epoxy/graphite
fiber composites process
Cont.
Chen et al. (2004a) RNN OP biomass concentration prediction Batch
Chen et al. (2004b) RNN OP melt-flow-length prediction in injection
molding process
Cont.
Yang and Chai (1997) RNN OP three simple simulated processes Cont.
Fellner et al. (2003) generalised ANN OP diacetyl concentration prediction Batch
Lin et al. (2007) PCA OP product estimation in cement kiln, NOX
monitoring
Cont.
Qin et al. (1997) PCA OP, SFD air emission monitoring Cont.
Zamprogna et al. (2004b) PLS, PCA OP simulated distillation column Batch
Dayal and MacGregor
(1997)
EWPLS OP stirred reactor, flotation circuit Cont.
Qin (1998) RPLS OP research octane number prediction in a refin-
ery process
Cont.
78

Feng et al. (2003) LS-SVM OP gasoline absorbing rate in FCC Cont.
Yan et al. (2004) LS-SVM OP light diesel freezing point detection in FCC Cont.
Merikoski et al. (2001) ANFIS OP rubber viscosity estimation Cont.
Warne et al. (2004a) PCA+ANFIS OP polymeric-coated substrate anchorage Cont.
Luo and Shao (2006) NFS + GA OP light diesel freezing point detection in FCC Cont.
Arazo-Bravo et al. (2004) NFS OP penicillin production bioprocess Batch
Wang and Rong (1997) NFS OP propylene purity prediction in a distillation
column
Cont.
Macias and Zhou (2006) evolving NFS OP crude oil distillation in refinery process Cont.
Dong et al. (1995) NLPCA+NNPLS OP NOx prediction in exhaust gas Cont.
Li et al. (2005) PSO+MLP OP ethylene distillation column Cont.
Kalos et al. (2003) analytic
NN+SVM+GP
OP interface level estimation in a neutralization
unit
Cont.
Chen et al. (2000) FPM+RBFN OP microbial population in a bioreactor Batch
Rao et al. (1993) Intelligent Soft
Sensor
OP sulphite pulping system Batch
Gonzalez et al. (2003) SRM, TS, FC,
PLS, WBM, ANN
OP copper concentrate grade in a rougher flota-
tion bank process
Cont.
Li et al. (2000) RPCA PM rapid thermal annealing process Batch
Nomikos and MacGregor
(1995b)
PCA PM polymerisation process Batch
Rotem et al. (2000) MBPCA PFD ethylene compressor Batch
Wang et al. (2005) FMWPCA PM simulated FCC unit process Cont.
Amazouz and Pantea
(2006)
PCA+PLS PM Lumber drying Batch
Zhang and Lennox (2004) PLS OP, PM simulated penicillin production process Batch
He et al. (2005) FDA PM quadruple tank process; polyester film man-
ufacturing process
Cont.
Alhoniemi (1999) SOM PM, OP cont. pulp digester; steel production process;
pulp and paper industry
Cont.
Yang et al. (2000) FPM+ANN PFD FCC reactor Cont.
Kampjarvi et al. (2008) PCA, SOM,
RBFN
PM,
PFD
ethylene cracking process Cont.
79

Abbreviation Explanation
Methods:
AnaNN Analytical Neural Network
ANN Artificial Neural Networks
eKF enhanced Kalman Filter
EWPLS Exponentially Weighted Partial Least Squares
FC Fuzzy Combinational
FMWPCA Fast Moving Window Principle Component Analysis
FPM First Principle Model
GP Genetic Programming
LWR Locally Weighted Regression
MBPCA Model-Based Principle Component Analysis
MLP Multi-Layer Perceptron
MPLS Multi-way Partial Least squares
MLR Multiple linear regression
NFS Neuro-Fuzzy System
NLPCA Non-Linear Principle Component Analysis
NNPLS Neural Network Partial Least Squares
PCA Principle Component Analysis
PCR Principle Component Regression
PLS Partial Least Squares
PLSR Partial Least Squares Regression
PSO Particle Swarm Optimization
RBFN Radial Basis Function Network
RNN Recurrent Neural Network
RPCA Recursive PCA
SOM Self-Organizing Network
SRM Stepwise Regression Method
SVM Support Vector Machines
SVR Support Vector Regression
TLPCA time lagged Principle Component Analysis
TS Takagi and Sugeno model
WBM Wavelet-Based Model
Application Types:
OP On-line Prediction
PFD Process Fault Detection
PM Process Monitoring
SFD Sensor Fault Detection
Table 2
List of abbreviations
81