Artificial Intelligence Modelling Methodologies Applied

to a Polymerization Process

Silvia Curteanu

, Elena-Niculina Dragoi

, Florin Leon

and Cristina Butnariu

“Gheorghe Asachi” Technical University of Iasi, Faculty of Chemical Engineering and Environmental Protection, 73,

Prof. dr. doc. D. Mangeron Blvd., 700050, Iasi, Romania

Faculty of Automatic Control and Computer Engineering, Bucharest, Romania

Keywords: Neural Networks, Support Vector Machines, Differential Evolution, Clonal Selection, Polymerization.

Abstract: A series of modelling methodologies based on artificial intelligence tools are applied to solve a complex

real-world problem. Neural networks and support vector machines are used as models and differential

evolution and clonal selection algorithms as optimizers for structural and parametric optimization of the

models. The goal is to make a comparative analysis of these methods for the case study of the free radical

polymerization of styrene, a complex, difficult to model process, where the monomer conversion and

molecular masses are predicted as a function of reaction conditions, i.e. temperature, amount of initiator and

time. Four modelling methodologies are developed and evaluated in terms of accuracy.

1 INTRODUCTION

Artificial neural networks (ANNs) are recommended

tools for modelling complex nonlinear processes

because they require only input-output data, with no

need for in-depth knowledge of the rules governing

the system. They often lead to accurate results and

can be integrated into optimal control procedures.

Beside ANNs, support vector machines (SVMs)

are gaining popularity over other learning methods,

mainly due to their good generalization capability

(Burges, 1998). Another important advantage is that

SVMs perform well on high dimensional problems,

and there is ongoing research on improving their

scalability (Wang et al, 2011; Zhang et al., 2012).

Developing optimal ANN or SVM models with

the adequate parameters is not an easy task. In the

trial-and-error method (frequently applied by the

majority of researchers, especially from engineering

domains), the architecture is repeatedly modified by

hand and evaluated with the goal of lowering the

error. These repeated actions increase the

computational overhead and the search is usually

based on gradient descent, whose result is prone to

being trapped in local minima (Cartwright and

Curteanu, 2013). In the polymerization field, the use

of ANN and SVM is increasing. Different types of

processes are modelled with these techniques, as

proven by the different review works (Noor et al.,

2010; Cartwright and Curteanu, 2013).

Evolutionary algorithms (EAs) are promising

methods for optimizing both the architecture and the

internal ANN parameters (Almeida and Ludermir,

2008a; Almeida and Ludermir, 2008b). Among all

EAs, differential evolution (DE) is an especially

powerful approach. Its efficiency lies in a simple,

compact structure that uses stochastic direct search

(Subudhi and Jena, 2009). A series of applications

recommend it as an efficient tool, particularly for

highly non-linear objective functions. For instance,

Lahiri and Ganta (2009) developed a method which

incorporates a hybrid ANN and DE technique for the

ANN parameter tuning. The algorithm was applied

for the prediction of the hold up of the solid liquid

slurry flow. The oxygen mass transfer in the

presence of oxygen vectors was modelled using a

feed forward multilayer perceptron neural network

with parameters optimized using two DE-based

versions: classical and self-adaptive (Dragoi et al.,

2011). In combination with neural networks, a

modified DE version, including two initialization

strategies (normal distribution and normal

distribution combined with the opposition-based

principle) and a modified mutation, was applied for

modelling the oxygen transfer when n-dodecane is

added in aerobic fermentation systems of bacteria

(Dragoi et al., 2013a). The pharmaceutical freeze

drying process was studied from multiple points of

Curteanu S., Dragoi E., Leon F. and Butnariu C..

Artiﬁcial Intelligence Modelling Methodologies Applied to a Polymerization Process.

DOI: 10.5220/0005029800430049

In Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2014),

pages 43-49

ISBN: 978-989-758-038-3

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

view (modelling and system identification) using a

hybrid combination of DE with ANNs and back-

propagation as a local search procedure (Dragoi et

al., 2012a; Dragoi et al., 2013b). The classification

of some organic compounds based on their liquid

crystalline property was performed using ANNs

optimized with two different self-adaptive versions

of the DE algorithm (Dragoi et al., 2012b).

Another optimization tool used in this work is

the clonal selection (CS) algorithm, which belongs

to the artificial immune system (AIS) class. AIS is a

group of computational methods represented by

highly abstract models of biological immune

systems (Castro and Timmis, 2003). The main

motivation of using immune systems as a source of

inspiration for computational systems resides in their

capabilities related to self-evolution, self-

organization and self-sustainability (Ahmad and

Narayanan 2011). In addition, unlike other

biological systems such as the nervous system, the

immune system is not centrally controlled and

therefore detection and response can be locally

executed (Dasgupta and Nino, 2009). Related to the

combination of AISs with ANNs for chemical

engineering processes, to the authors’ knowledge,

only a few studies can be found (Tao et al., 2012).

For instance, different variations CS-ANN were

applied by our group for the removal of heavy

metals from residual water (Dragoi et al., 2012) and

for the optimization of CO

absorption in pneumatic

contractors (Cozma et al., 2013).

In this paper, ANNs and SVMs are employed as

acceptable alternatives to the phenomenological

models, which are difficult to develop and solve

with satisfactory accuracy for a complex

polymerization process. The goal is to perform a

comparative analysis of different approaches and to

identify the best method that generates simple but

highly efficient models. The modelling

methodologies include ANNs and SVMs, optimized

with techniques such as DE, CS or grid search. One

must emphasize the benefits of the hybrid modelling

techniques in terms of accuracy and in connection

with the particularities of the process. The novelty of

this approach lies in several aspects: the application

of different modelling techniques for a complex

chemical process, new elements introduced in the

DE optimizer and a novel combination DE-SVM.

2 DATABASE

The case study of our research work is the free

radical polymerization of styrene performed through

batch suspension technique. A complete

mathematical model previously elaborated and

solved (Curteanu, 2003) is used here as a simulator

for producing the working database. The model

contains the balance equations for the monomer

conversion, initiator concentration, distribution

moments of radicals and dead polymer and also,

equations that take into account diffusion constraints

(gel and glass effects). This last part is difficult to

model with satisfactory accuracy; therefore, input-

output data models are recommended alternatives to

be applied.

Data quality and quantity are essential for

modelling with machine learning techniques. In this

case, the collected data was chosen to cover the

whole domain of interest for the studied process and

to be uniformly distributed within this domain. Thus,

for the initiator concentration and temperature, the

ranges specific to the suspension polymerization of

styrene were 10-55 mol/l (variation step 5) and 60-

90 °C (variation step 10), respectively. Regarding

the reaction time, the interval was 0 to 2000 minutes,

because for lower concentrations of initiator and

lower temperature, the reaction time is longer

(Curteanu et al., 2010).

After the data was generated, an internal step of

data pre-processing was applied. This included

normalization, randomization and splitting the data

into training and testing subsets. The normalization

was achieved using the 0-1 method:

minmax

min

norm





(1)

Concerning data randomization, it was applied in

such a manner that all points from a single initiator-

temperature combination belong to either the

training or the testing set. In this way a separation

between experiments is maintained and the testing of

the model is not based on individual points but on an

entire experiment. The amount of training data is

80%, with the remaining 20% used for testing.

For the styrene polymerization process

considered here, the model input variables were

chosen as: initiator concentration, I

, temperature, T

and reaction time, t. The other two variables,

monomer conversion, x, and numerical average

molecular weight, Mn, represent the outputs of the

models. The modelling techniques aim to provide

predictions about the main properties (molecular

mass) and reaction characteristics (conversion) as a

function of the working conditions.

SIMULTECH2014-4thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand

Applications

3 MODELLING METHODOLOGY

Two modelling approaches, ANN and SVM, were

applied to solve this real-world chemical

engineering problem. Since both ANN and SVM

have some parameters that need to be tuned in order

to obtain optimal results, two bio-inspired

algorithms, DE and CS, were applied and compared

for model optimization.

3.1 Optimizing Neural Networks

with Differential Evolution

DE, an algorithm based on the evolutionary

paradigm, is used to simultaneously perform

parametric and structural optimization of the neural

network model for the styrene polymerization. The

variant used in this work, called SADE-NN-2

(Dragoi et al., 2012a) is a combination of a self-

adaptive DE with ANNs and back-propagation (BP).

DE has the role of performing a global search, while

BP locally improves the best solution found in each

generation. This intertwinement of the two

algorithms is possible because all DE individuals are

in fact ANNs.

As in the case of all evolutionary algorithms, the

evolution of the population occurs by applying

mutation, recombination and selection steps until a

stopping criterion is met. Initially, a set of potential

solutions are generated using a random approach. In

this work, a Gaussian distribution is used. After that,

mutation has the role to add diversity and the

population of mutants is combined in the crossover

step with the current one to create a trial population.

In the DE case, two types of crossover can be

encountered: binomial (each characteristic of the

trial individual is randomly copied from one of the

two parents) or exponential (blocks of characteristics

are inherited alternatively from the parents). In

SADE-NN-2, the binomial version is used, as it was

observed that efficiency is increased only for a small

number of case studies when the exponential version

is employed.

Concerning the selection step, where the trial

individual competes with the current individual for

the right to participate in the next generation, a

tournament version with a “one-to-one” survival

criterion is used.

The characteristic feature of DE when compared

with other EAs is the mutation step in which a trial

vector is generated by adding to a base individual a

scaled differential term (Price et al., 2005). In

SADE-NN-2, this mutation principle is modified,

such that the individuals participating to the

differential terms are sorted based on their fitness.

Since it was observed that in various situations the

DE version called DE/Best/2/Bin (where the base

vector is represented by the best individual in the

population, 2 differential terms are employed and

the crossover type is binomial) obtains acceptable

results, this version was considered as a base for the

current study.

As the SADE-NN-2 is a self-adaptive method (in

which the F and Cr control parameters are included

into the optimization procedure, i.e. they evolve

simultaneously with the individuals) a separate

procedure for parameter optimization was not

required.

A direct encoding with real values was chosen

for the ANNs, because it is the least expensive

computationally. For each position in the population,

at each generation, at least one decoding procedure

is required. The ANN parameters chosen for

encoding are the number of hidden layers, the

number of neurons in each hidden layer, the weights,

the biases and the activation functions. Unlike the

majority of applications where the variation of the

activation functions is performed at the layer level,

in the SADE-NN-2, the variation is applied at the

neuron level.

3.2 Optimizing Neural Networks with

Clonal Selection

The second algorithm employed for neural network

optimization is clonal selection. It describes the

basic characteristics of the immune response when

an antigenic stimulus is applied to a vertebrate

(Abdul Hamid and Abdul Rahman, 2010).

The main immunological principles used are: a

specific memory set, selection and cloning of the

best antibodies, removal of the worst antibodies,

affinity maturation of the best immune cells and the

generation of a diverse set of antibodies (Dasgupta

and Nino, 2009). The main steps of the algorithm are

initialization, selection, cloning, affinity maturation

(the process of variation and selection achieved

through hyper-mutation) and receptor editing. The

last four steps are repeated until a stopping criterion

is met.

As in the DE case, the initialization is based on

the Gaussian distribution. In the selection step, the

best 30% of the population is cloned 10 times. After

that, each clone is hyper-mutated and its affinity

(computed using an affinity function similar to the

fitness function used in EAs) is determined. The

mutated clones with the highest affinity are selected

for introduction into the population. In the last step,

ArtificialIntelligenceModellingMethodologiesAppliedtoaPolymerizationProcess

5% of the population with the worst affinity is

replaced with newly generated individuals.

The CS-NN algorithm (Dragoi et al., 2012c) uses

the same type of ANN (feed-forward multilayer

perceptron) and the same encoding procedure as in

SADE-NN-2. In this manner, the differences

obtained between the two approaches are driven

only by the optimization procedures (DE or CS) and

their effectiveness can be assessed in a meaningful

way.

The characteristics of CS-NN which

distinguishes it among other CS variants (except its

combination with neural networks) are: the

introduction of the opposition-based principle in the

initialization phase and the introduction of a hyper-

mutation combining 3 types of hyper-mutation

(Gaussian, non-uniform and pair-wise interchange),

based on a random procedure.

3.3 Modelling with Support Vector

Machines

One of the main advantage of the SVM is the small

number of parameters that the user has to choose:

the type of kernel with its parameters and a cost

parameter which defines the balance between

tolerance for training errors and generalization

capability. For our case study, two support vector

regression (SVR) models were designed, for each

parameters of interest: x and Mn.

The experiments were performed using the

implementation provided by the LIBSVM library

(Chang and Lin, 2011), using the ε-SVR or the

µ-SVR variants. In ε-SVR, ε is a parameter of the

loss function with values in the [0, ∞) domain. Also,

the radial basis function (RBF) kernel was selected.

3.4 Support Vector Machines and

Differential Evolution

The fourth approach for modelling the styrene

polymerization process is a novel algorithm

combining DE with SVM (DE-SVM). DE acts as an

optimizer, while the SVM models the process.

Distinctively from the SADE-NN-2, in DE-SVM,

DE only performs parameter optimization. The

training procedure is the classic one used for SVMs.

The same self-adaptive DE version used in

SADE-NN-2 was also employed in DE-SVM. Thus,

the performance differences obtained are solely

determined by the performance of the model and not

by the ability of the optimizer to determine the best

solution. If the population was formed of neural

models in the case of SADE-NN-2, in the case of

DE-SVM, the individuals forming the population are

lists of SVM parameters such as: SVM type

(µ-SVR, ε-SVR), kernel type (linear, polynomial,

RBF and sigmoid), degree (applicable only for

polynomial kernel type), γ (a coefficient of

polynomial and sigmoid kernels) and C, the cost

parameter.

4 RESULTS AND DISCUSSION

After gathering the data describing the process, a

series of simulations with the four considered

algorithms were performed. In the case of the

modelling approaches based on ANNs (SADE-NN-2

and CS-NN), some limitations to the structure of the

network were imposed, in order to reduce the

complexity of the encoded individuals and,

therefore, to reduce the computational effort.

Consequently, for the hidden layers, it was

considered that a network with one hidden layer can

efficiently model the polymerization process. This

restriction is based on the authors’ experience: in the

majority of our studies a network with one hidden

layer provided satisfactory results. Also, it was

considered that 30 neurons in the hidden layer are

sufficient. A lower limit was imposed as well: the

algorithms can generate networks with no hidden

layers or with one hidden layer, with a number of

neurons between 4 and 30.

Initially, with both SADE-NN-2 and CS-NN, a

set of models with two outputs corresponding to the

parameters of the process, x and Mn, were generated.

Although the mean squared error (MSE) computed

on the normalized data had acceptable values: 0.081

and 0.125 in the training phase for SADE-NN-2 and

CS-NN, respectively, and 0.122 and 0.158 in the

testing phase, the average relative errors (AREs)

were not acceptable, exceeding 40% for some of the

outputs. Therefore, for each output a separate neural

model was created. A set of five best results are

listed in Table 1 for SADE-NN-2 and in Table 2 for

CS-NN.

As it can be observed from Tables 1 and 2, for

the x and Mn parameters, the best error in the testing

phase is obtained with CS-NN (CN1 model and CN6

respectively). These observations are also in trend

with the average values.

Concerning the SVM models, Table 3 presents

the best results obtained with

ε-SVR. A grid-search

approach was used to find the best values for the

model parameters. It is recommended to use

exponentially growing sequences of C and γ in order

to identify good parameters (Hsu et a1., 2010). The

SIMULTECH2014-4thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand

Applications

Table 1: Best results obtained with SADE-NN-2 for each

process parameter.

Output

variable

Topo-

logy

MSE

training

MSE

testing

Model

3:19:01 0.0128 0.0094 DN1

3:19:01 0.0105 0.0104 DN2

3:11:01 0.0147 0.0132 DN3

3:04:01 0.0136 0.014 DN4

3:19:01 0.0109 0.077 DN5

Avera

e 0.0125 0.0248

3:19:01 0.0039 0.0036 DN6

3:11:01 0.0058 0.0048 DN7

3:11:01 0.0045 0.0051 DN8

3:14:01 0.0047 0.0073 DN9

3:11:01 0.0118 0.0125 DN10

Avera

e 0.0047 0.0045

Table 2: Best results obtained with CS-NN for each

process parameter.

Output

variable

Topo-

logy

MSE

training

MSE

testing

Model

3:20:01 0.0069 0.0083 CN1

3:19:01 0.0094 0.0103 CN2

3:17:01 0.0091 0.0115 CN3

3:11:01 0.0127 0.0128 CN4

3:16:01 0.0099 0.0159 CN5

Avera

e 0.0096 0.0117

3:08:01 0.0009 0.0016 CN6

3:10:01 0.0012 0.0017 CN7

3:12:01 0.0327 0.0031 CN8

3:16:01 0.003 0.0041 CN9

3:20:01 0.0051 0.0064 CN10

Avera

e 0.0085 0.0033

chosen values for the experiments are (2

-3

, 2

) for

C, and (2

-3

, 2

) for γ, with step 0.5. Low values for

MSE show the good performance obtained with

RBF kernel for both output variables, while the

polynomial kernel performance is not suited for

modelling the Mn variable.

For the combination of DE with SVM, the best

models obtained for the process parameters are

presented in Table 4.

In order to determine the efficiency of the best

models, the coefficient of determination (r

) was

also computed (Table 5).

By analyzing the results it can be observed that

in some cases, the coefficient of determination is not

closely correlated to the MSE. This fact can be

explained by the data distribution, since the system

has a different dynamic for each combination of

temperature-initiator.

In order to visualize the differences between the

predicted and expected data, for the modelling of the

Table 3: Results obtained with ε-SVR for the output

variables.

Output

variable

Method

parameters

MSE

training

MSE

testing

Model

C = 256; γ = 2;

RBF kernel;



= 0.1

0.004 0.004 S1

C=0.707; γ = 0.125;

Polynomial kernel

degree 2;



= 0.25

0.021 0.02 S2

C=0.353; γ = 0.125;

Polynomial kernel

degree 3;



= 0.25

0.022 0.02 S3

C = 512; γ = 2;

RBF kernel,



= 0.1

0.09 0.27 S4

C=2.828; γ = 0.125;

Polynomial kernel

degree 2;



= 3

7.5 2.4 S5

C=2.828; γ = 0.125;

Polynomial kernel

degree 3;



= 3

7.5 2.4 S6

Table 4: Results obtained with DE-SVM for the output

variables.

Para

meter

Method

parameters

MSE

training

MSE

testing

µ-SVM, RBF kernel

C = 0.28;γ = 3.341

0.0085 0.0075

µ-SVM, RBF kernel

C = 5.96; γ = 2.212

0.0010 0.0014

Table 5: The performance of the best models obtained

with the four methods.

Para-

meter

Model

training

testing

DN1

0.9617 0.9580

CN1

0.9768 0.9581

S1 0.96 0.9304

DE-SVM 0.9714 0.9656

DN6

0.9871 0.9800

CN6

0.9915 0.9731

S4 0.99 0.9813

DE-SVM 0.9936 0.9767

x parameter, a set of figures with testing data were

generated. Since different combinations of

temperature and initial value of the initiator were

tested, two significant examples are given below:

temperature of 368K and 10 mol/l of BPO initiator

(Figure 1) and temperature of 338K and 50 mol/l of

initiator (Figure 2).

Concerning the Mn modelling, the DE-SVM

approach is the best in terms of MSE testing. Similar

to the x parameter, a series of figures for two

temperature-initiator value combinations were

generated for it (Figures 3 and 4).

ArtificialIntelligenceModellingMethodologiesAppliedtoaPolymerizationProcess

Figure 1: Comparison between the predictions of x

obtained with the four methods and the expected data

when the process parameters are 368K (temperature) and

10 mol/l (initial value of initiator).

Figure 2: Comparison between the predictions of x

obtained with the four methods and the expected data

when the process parameters are 353K (temperature) and

50 mol/l (initial value of initiator).

Figure 3: Comparison between the predictions of Mn

obtained with the four methods and the expected data

when the process parameters are 348K (temperature) and

15mol/l (initial value of initiator).

Figure 4: Comparison between the predictions of Mn

obtained with the four methods and the expected data

when the process parameters are 383K (temperature) and

20 mol/l (initial value of initiator).

4 CONCLUSIONS

Four modelling methodologies were developed and

tested on a complex chemical process, i.e. free

radical polymerization of styrene. They include

ANN and SVM as models, structurally and

parametrically optimized with DE and CS. Although

both neural network and support vector machine

models are found suitable for the polymerization

process, selecting one of the techniques rely on the

user experience. However, it must be mentioned that

the combination SVM-DE deserves special attention

due to its accessibility and accuracy observed in the

results.

ACKNOWLEDGEMENTS

This work was supported by the “Partnership in

priority areas – PN-II” program, financed by ANCS,

CNDI - UEFISCDI, project PN-II-PT-PCCA-2011-

3.2-0732, No. 23/2012.

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ArtificialIntelligenceModellingMethodologiesAppliedtoaPolymerizationProcess