=Paper=
{{Paper
|id=Vol-2917/paper15
|storemode=property
|title=The Development of a Genetic Method to Optimize the Flue Gas Desulfurization Process
|pdfUrl=https://ceur-ws.org/Vol-2917/paper15.pdf
|volume=Vol-2917
|authors=Ievgen Fedorchenko,Аndrii Oliinyk,Tetiana Fedoronchak,Tetiana Zaiko,Anastasiia Kharchenko
|dblpUrl=https://dblp.org/rec/conf/momlet/FedorchenkoOFZK21
}}
==The Development of a Genetic Method to Optimize the Flue Gas Desulfurization Process==
https://ceur-ws.org/Vol-2917/paper15.pdf
The Development of a Genetic Method to Optimize the Flue Gas
Desulfurization Process
Ievgen Fedorchenko, Andrii Oliinyk, Tetiana Fedoronchak, Tetiana Zaiko, Anastasiia
Kharchenko
Department of Software Tools, National University “Zaporizhzhia Polytechnic”, 64 Zhukovskoho str.,
Zaporizhzhia, Ukraine, 69063
Abstract
Sulfur dioxide is one of the most commonly found gases, which contaminates the air, damages
human health and the environment. To decrease the damage, it is important to control the
emissions on power stations, as the major part of sulfur dioxide in atmosphere is produced
during electric energy generation on power plants. The present work describes flue gas
desulfurization process optimizing strategy using data mining. The optimisation modified
genetic method of flue gas desulfurization process based on artificial neural network was
developed. It affords to represent the time series characteristics and factual efficiency influence
on desulfurization and increase its precision of prediction. The vital difference between this
developed genetic method and other similar methods is in using adaptive mutation, that uses
the level of population development in working process. It means that less important genes
will mutate in chromosome more probable than high suitability genes. It increases accuracy
and their role in searching. The comparison exercise of developed method and other methods
was done with the result that new method gives the smallest predictive error (in the amount of
released SO2) and helps to decrease the time in prediction of efficiency of flue gas
desulfurization. The results afford to use this method to increase efficiency in flue gas
desulfurization process and to decrease SO2 emissions into the atmosphere.
Keywords 1
flue gas desulfurization, sulfur dioxide, artificial neural network, genetic algorithm
1. Introduction
According to the Nature Geoscience data, NASA satellites detected 500 new sources of air
contamination, about 40 of them produce dangerous sulfur dioxide [1]. This substance is considered to
be one of the most threatening gases for the Earth atmosphere. The main sources of dioxide sulfur
releases are power plants (which work on solid and liquid fuels) and other metallurgical plants. So, the
control of SO2 amount in flue gas after coal burning is the effective method of decreasing releases into
the atmosphere [2].
The SO2 emissions can be reduced by setting equipment for desulfurization on new-built and old
coal blocks and also by following corresponding requirements about desulfurization. To increase
efficiency of desulfurization and decrease SO2 emissions, it is important to optimize the desulfurization
control system according to the industry needs [2].
The accurate estimation of relationship between process variables and factual sulfurization
efficiency is the basis for optimization of desulfurization control system. At the present time, a lot of
local equipment for analysis and monitoring flue gases can directly control SO2 concentration in flue
gases it the inlet and the outlet of desulfurization equipment and calculate its efficiency. However, this
method is just a simple connection between desulfurization process results and doesn’t show monitoring
MoMLeT+DS 2021: 3rd International Workshop on Modern Machine Learning Technologies and Data Science, June 5, 2021, Lviv-Shatsk,
Ukraine
EMAIL: evg.fedorchenko@gmail.com (I. Fedorchenko); olejnikaa@gmail.com (A. Oliinyk); t.fedoronchak@gmail.com (Т. Fedoronchak);
nika270202@gmail.com (T. Zaiko); kharchenko.13.08@gmail.com (A. Kharchenko)
ORCID: 0000-0003-1605-8066 (I. Fedorchenko); 0000-0002-6740-6078(A. Oliinyk); 0000-0001-6238-1177 (Т. Fedoronchak); 0000-0003-
1800-8388 (T. Zaiko); 0000-0002-4313-555X (A. Kharchenko)
© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
results. Simultaneously, monitoring equipment are affected with external factors and failures which are
consequently occurred can lead to inaccurate measurement results. So, the desulfurization efficiency is
affected with different factors like suspension pH value, flue gas outlet temperature, density of
absorption tower suspension and mass concentration of SO2 in the inlet of flue gases [2].
In recent years, a lot of methods were suggested, including experimental studies, mathematical
models and machine learning methods for prediction the desulfurization efficiency. Among all methods,
mathematical models and machine learning models sparked great scientific interest. However, the
prediction of desulfurization efficiency is hard to model mathematically. Some researches simplify this
system using assumptions, which introduce errors in predictions. Moreover, calculations, which are
used in these mathematical models need great computing resources. In this context, machine learning
models are useful tools for predictions [3].
One of the most perspective ways of solving this problem is based on using artificial neural networks
and genetic algorithms, as the most progressive in relation to problem of prediction the flue gases
desulfurization efficiency. Genetic algorithms relate to the class of searching methods, which iteratively
improve the quality of solution options by recombination procedures and selections for surviving.
Genetic algorithms are widely used in solving difficult multidimensional optimization problems due to
general computation scheme, opportunities of parallel realisation and noise tolerance [4].
In the work, the modified genetic method of optimization of flue gas desulfurization process which
is based on artificial neural network is suggested. It affords to represent the time series characteristics
and factual efficiency influence on desulfurization and increase its precision of prediction.
2. Analysis of published data and problem definition
In the article [5] they propose a prediction model of the flue gas desulfurization efficiency, which is
based on long short-term memory (LSTM) neural network. Authors examined 100MW power plan in
China, considering main factors, which affect wet flue gas desulfurization of limestone and gypsum.
The LSTM neural network is used for building a prediction model of desulfurization efficiency.
The main structure of prediction model based on LSTM consists of five functional modules: an input
level, a hidden level, an output level, a network training module and a network prediction module. The
output level is in charge of processing the time series output to match the input requirement. The hidden
level uses LSTM cells to build one-layer cycle neural network. The output level gives the prediction
results. During the LSTM neural network learning the backpropagation through time algorithm is used,
which is an analogue to simple backpropagation algorithm.
The advantage of developed model (in comparison with other models) is that the model can represent
the influence of time series characteristic on factual efficiency of desulfurization and increase its
precision of prediction.
The disadvantage of developed model is that during the learning it is hard to interpret the results. It
imposes limitations on the possible improvement of the model. Also, it is impossible to predict when
the desulfurization dynamic will change (and if dynamic changes, the model will stop working).
In the work [6] they propose the prediction model of wet flue gas desulfurization of limestone and
gypsum which is based on support vector machine method (SVM). The authors consider relation
substance-gas, velocity of flue gas, volume of dioxide air, temperature, flue gas dust, concertation of
sulfur dioxide outlet, suspension pH value of an absorption tower, relation between calcium and sulfur
as independent variables and desulfurization efficiency as dependent variable. The idea of the given
method is to build a hyperplane, which is considered as an area of solutions and to separate positive and
negative examples from the initial set at most. The support vector machine is an approximative
realisation of structural risk minimization method, which is based on the idea that the level of learning
machine mistakes on the test set is represented as a sum of learning mistake and the other sum which is
depends of a measured Vapnik-Chervonenkis index.
The advantage of the given method is that to solve the classification problem (in contrast to other
methods) we can have a small amount of data.
The disadvantage of the given method is that we use not the all data for the classification but only a
small part from the borders.
In the work [7] they propose an investigation on data mining and operating optimization for wet flue
gas desulfurization systems. The authors suggest a complex criterion with using minimum expenditures
as a main function for getting optimal work conditions for wet flue gas desulfurization systems. To
increase an accuracy of data mining analysis of the main data they suggest an improved method of fuzzy
clustering. This algorithm uses the results of k-means clustering method as a primary conditions and
fuzzy clustering method as an analytic method. The procedure of the method has two steps: using k-
means clustering method to get the initial number of clusters and their centers and to use fuzzy
clustering to calculate the final results.
The advantages of the given method are a simple realisation, the lack of need of an initial layout and
low requirements for computing resources.
The disadvantage the given method is its low resistance to outliers, which can create the average.
We can use modified k-median clustering as an option to solve this problem. Also, another disadvantage
is that the result of the work depends on the primary selection of centroids and, in a general case, this
method doesn’t give optimal results and can find only suboptimal solutions.
In the work [8] they propose an artificial intelligence-based emission reduction strategy for
limestone forced oxidation flue gas desulfurization system. The authors created a neural network based
on a multilayer perceptron (MLP) to study relations between controlled input variables and output
variables. The given model demonstrated the ability to learn difficult kinetic of reaction between
reagents. The input parameters of the model are: suspension pH value, inlet mass of SO2, temperature,
outlet NOx temperature, percentage composition of oxygen, volume of air for oxidation, density of
absorber suspension, oxygen volume, dust mass as a part of volume of flue gas expenditure. The output
parameters of the model are: SO2 mass, Hg, NOx and outlet dust mass. The model consists of one hidden
layer that have 27 neurons. The learning is based on backpropagation method. The learning is performed
till it reaches the stop criterion. In other words, when it reaches the change of repeatability mistake on
0,0000001 or during the learning the maximum number of epochs will be achieved (a minor decreasing
of mistake happens abroad the epochs).
The advantage of the given method is that it has a high rate of continuity which is realised with the
synapse connections help. Also, during the learning of the given neural network (thanks to its inner
composition) it sets the regularity between input and output data and generalizes obtained selection-
based experience.
The disadvantage of the given method is that it uses a backpropagation method and, as a result, the
learning process takes long time. The overgrowth of neural network can lead to its paralysis, when the
synaptic weight stops changing not even reaching the end of the learning. The size of a step needs to be
always controlled and it is necessary to keep network learning as it steadily forgets previous learning
selections.
In the work [9] they propose a solution to optimization problem of wet flue gas desulfurization
system. They developed a modified model of wet flue gas desulfurization to predict SO2 emission. It
combines a mathematical model and an artificial neural network. They suggested modified particle
swarm optimization (PSO) with penalty method algorithm to increase the saving of desulfurization
process, which is directed to minimize operational costs. The PSO method is based on calculation every
iteration of centroid coordinates and their velocity. In other words, they solve the optimization problem
of fitness function minimizations: the less the value of fitness function is on every iteration, the closer
the result is to the optimal centroid of a swarm. Fitness function is defined as an average value of
Euclidean distance between particle vector and a vector that define a centroid coordinate.
As a result, the operating parameters were optimized, including lime mortar pH, temperature, lime
mortar density and a number of working circulator pumps. The results show that PSO with penalty
function provide satisfying productivity of repeatability to decrease the operational costs with some
limits.
The disadvantage of the given method is that it easily occurs in local search in multidimensional
space and requires great amount of time to find the solution.
In the work [10] they propose prediction and optimization of a desulphurization system using a
neural network and a genetic algorithm. The authors consider desulfurization coefficient and economic
value as two objectives. They created a model with 10 inputs and 2 outputs. A modified genetic
algorithm for building a model and optimizing the cost of desulfurization was created. The genetic
algorithm has two steps. In the first step, the genetic algorithm finds suboptimal architecture of artificial
neural network (ANN). In the second step, the genetic algorithm defines suboptimal values of weight
coefficient and ANN bias. The first step can be considered as a preparation stage before learning. This
step helps to simplify a future task of defining weight and bias. The authors used the following
approach: a chromosome was built with a number of neurons from a hidden layer, impulse, velocity of
learning, type of activation function and ANN learning algorithm and a couple of other parameters. In
connection with various variables it is impossible to use inversion operator in general case. A vector
(which characterizes the input of a variable in a learning array) was included in the number of additional
genes. Zeros and ones spread among loci randomly with a notation, that the number of zeros can’t
exceed the half of the number of output variables. The insertion of this type of genes in a chromosome
was to identify a suboptimal set of variables. After identifying the ANN architecture, the neural learning
starts. After that, the ANN forms the row of weight vectors and biases (which are set to n×1 size) and
vector of mean squared error of learning. An initial population is created from a row of vectors
(chromosomes), which sooner will evolve with using genetic algorithm.
The advantage of the given method is increased accuracy of classification using genetic algorithm-
based approach. The genetic algorithm allows to select the best combination of the basic ANN features
by practical consideration. This combination can vary not only in different tasks but also because of
changing the static data variables. In this way, this approach allows to optimize desulfurization process.
The disadvantage of the given method is the need in great computing resources. So, the given genetic
algorithm can be used only with the access to calculating resources.
The analysis of the works [5-10] affords to claim that the pursuance of the research about
optimization and prediction of desulfurization flue gases from nitrous oxide is a live issue. Also, during
the work it was figured out that the most efficient method of solving the problem is to use neural
networks. This is because they have such advantages as an ability to adaptation in case of changes (that
helps them to work even in a critical situation), self-learning, the speed of work (the compilation of
prediction and planning can be faster than using exact algorithms), also a great resistance to data noise
with an opportunity to use limitless number of independent variables. In the same time, regardless to
obvious advantages, the main disadvantage is the difficulty in choosing an efficient learning method
and creating the primal amount of data. Also, there is a difficulty in the right distribution the matrix
weight on an initial step in the contexts of indeterminacy. We can use genetic method to solve this
problem. The benefits of this method are the increased accuracy and decreased amount of time, which
is spent on learning. It is efficient to learn some neural networks like multilayer perceptron, ANN with
general regression, Kohonen networks and etc [11]. The usage of the evolution genetic algorithm while
learning helps to decrease the number of learning cycles by using the parameters which have bigger
weight.
So, to solve the problems, which occur in researched methods, it was decided to develop a modified
genetic method for setting the weight coefficients of ANN to increase the efficiency of flue gas
desulfurization process and to decrease the SO2 emissions into the atmosphere.
3. The purpose and objectives of the study
The object of the study – desulfurization systems on coal power plants.
The subject of the study – the prediction methods of flue gas desulfurization efficiency
The purpose of the work – to develop a modified genetic method based on a neural network to solve
the optimization problem of flue gas desulfurization
The research method – tradition models (decision tree, nearest neighbour algorithm, ant colony
optimization algorithm), neural networks, combined methods (neural networks and genetic algorithms,
neural networks and multi-agent systems)
4. The development of a genetic method to optimize flue gas desulfurization
process
Nowadays, the most famous evolutionary method is a genetic algorithm of finding a global
extremum of a multi-extrema function. The idea is in parallel processing of set with alternative
solutions, meanwhile the algorithm searches the most perspective of them. It says about the opportunity
to use genetic algorithms in resolving optimization problems and making decisions. That’s why it has
been selected to set up the synaptic weight of the neural network [12-13].
In the beginning, an initial population is created in the given method by chromosomes. These
chromosomes contain the information about values of network weigh coefficients from the created
structure. Chromosome contains G genes, which store the information about weight values and biases
of all neurons from the created network. In the developed method a valid coding is used. It is used to
represent values of weight coefficients as chromosomes. The best way to code the weight (taking into
account the topology we have) is a matrix coding. The matrix size is equivalent to ANN matrix
topology. The elements of the matrix are weight coefficients of corresponding connection. The length
of chromosome is calculated by the formula (1):
L
λ Q1 (T + 1) + ∑ Ql (Ql −1 + 1) ,
= (1)
l =1
where Ql – the number of the neurons from the first layer; T – the number of elements in the learning
sample; L – the number of neural network layers [14]
After forming, the rating of the initial population chromosomes starts. To do this, firstly we need to
decode every chromosome from the population into the set of neural network weight coefficients. Then,
the calculation of fitness-function value starts. This function rates the quality of the selected architecture
by the value of neural network learning mistake using these formulae (2) and (3):
Fopt = min ( F ) , (2)
1 Ct
= ∑ ( Oi − Ri ) ,
2
F (3)
2Ct i =1
where Ci –the power of learning pairs; Oi – the resulting value, which was received by output neuron in
the network on an ith step while learning; Ri – the required value of output neuron on an ith step while
learning [15].
As we can see, the fitness function will rate the mistake (this mistake defines how the resulting
output differs from the needed) as the difference between the resulting output of the network and the
needed one. So, as the smaller this mistake is the higher the value of fitness is. In other words, we need
to set the matrix to the state, when the neural network learning mistake will be minimum.
According to the given results of the fitness function, a selection of individual starts. It is necessary
to generate new solutions, which based on rank selection. To do this, the current population is sorted
according to fitness function results. Every chromosome assigned with a number, which shows not its
absolute value but its place in the sorted population rank. This approach lets to control selective pressure
and to limit the number of offspring of one chromosome. The coefficients of selection pressure [16-17].
Linear ranking of all chromosome is calculated by the formula (4):
Pos − 1
Psl ( Pos ) = 2 − SP + 2 ⋅ ( SP − 1) ⋅ , (4)
С −1
where Pos – the position of chromosome in population (Chromosome with the smallest value of the
fitness function (Fmin) has Pos =1, and chromosome with the largest value of the fitness function (Fmax)
has Pos=C value); С – the number of chromosome (individuals) in population; SP – the coefficient of
selection pressure, which can be calculated by the formula (5):
Fmax
SP = , (5)
Favg
where Fmax – a chromosome with the largest value of the fitness function, Favg – an average value the
fitness function of all population [18-19].
The advantage of the ranking method is an opportunity to use it both for function maximisation and
minimization. It also doesn’t require scaling due to the problem of pre-timing repeatability, what is very
topical for the roulette wheel method.
The crossover operator from the given method produces two offspring from two parental
chromosomes. In other words, two new vectors are generated from the two vectors with valid numbers.
SBX-crossover is used as a base. This crossover imitates the work of a binary crossover operator. If P1=
(p11, p12,…,p1λ) and P2=(p12, p22,…,p2λ) are chromosomes of two parents, then the genes of offspring’s
chromosomes are calculated with formulae (6) and (7):
=
c1j
1
2
( (1 − ω) ⋅ p1j + (1 + ω) p 2j ) , (6)
=
c 2j
1
2
( (1 + ω) ⋅ p1j + (1 − ω) p 2j ) , (7)
where j=1,2, …, λ; λ – is the length of chromosome; pj1, pj2 – are the first and the second parents’ genes;
ω – the number, which is calculated by the formula (8):
1
( 2v ) , v ≤ 0,5
b+1
ω = 1
, (8)
1 b +1
, v > 0,5
2 (1 − v )
where ν – is a normally distributed random number, ν∈(0,1); b – is a value, that affects the probability
of offspring appearance far from parents b∈[2,5]. During the research, it was found that low b values
allow to generate offspring which are far located from parents, while increased b influences the
offsrping to appear closer to parents’ pairs [20-21].
The mutation operator in evolutionary algorithms shows the wide searching and capturing new areas
of searching space. To set up this algorithm, a user has to additionally decide what the value for mutation
should be used. With low mutation, the algorithm will rarely capture new areas of searching space and
will more quickly converge to local extrema. With high mutation, the algorithm will more frequently
explore different areas of searching space but it will no localize perspective areas of searching space.
Accordingly, the selection of mutation operator is directly affecting the quality of algorithm work and
results.
To solve this problem, we realized a method to calculate the possibility of mutation change. At first,
method searches the level of population development on every iteration. In other words, the average
fitness-function value of all individuals. After that, the result is compared to the fitness function value
of every individuals. If fitness function value of an individual is lower than the average fitness function
value of all individuals, then the possibility of mutation grows. The possibility of chromosome mutation
is calculated by the formula (9):
Fmax ( e ) − F ( P ( e ) )
0.5 , if F ( P ( e ) ) ≥ F ( e )
βmut =
Fmax ( e ) − F ( e ) , (9)
0.5, if F ( P ( e ) ) < F ( e )
where Fmax(e) – is a fitness function maximum value on the current population, F ͞ (e) – is an average
fitness function value of the current population [22].
If pj gen can mutate, a new changed value pjnew can be calculated by the formula (10):
ξ
e
p new
j = p j + b ( ο j − p j ) 1 − , (10)
emax
where b – is a random number in the interval [0,1]; oj – randomly generated number from a set
{pmin, pmax}, where pmin, і pmax – is a low and high border of a possible change of pj value; e – is a number
of current generation; emax – is a maximum number of generations; ξ – is a refinement parameter, that
is depends on repeatability type of international process. After reaching steady state, when the best of
individuals hasn’t changes during all generations, the value will halve. The result is, the searching area
expands and it overcome local extrema traps [23-24].
Such adaptive mutation in genetic algorithm (evolution) realisation allows to stick to the necessary
balance between two multiscale gene changes (mutations), as during first steps we have, in the main,
multiscale changes (that provide wide searching area). Meanwhile, on the final steps (by reduced scale
of mutation) the decision becomes more accurate.
It is necessary to use adaptive mutation for every individual, but it is not enough to prevent
repeatability of population in local optimum. Let us assume, that ith individual has a potential to mutate
(the possibility is 97%). On the one hand, such a high birth mutation from ith individual means that a
chromosome can be born with random parameters. The parameters don’t have any helpful information
about previous evolution. On the other hand, ith individual stays in the population because of the high
fitness function value, displacing future generations with lower values. To avoid repeatability
completely, let initiate selection which will thin population out and sift individual with a high mutation
possibility by formula (11):
( )
if βmut P i > δ : removed P i , (11)
where βmut – is a mutation possibility of Pi chromosome; δ – is a selection border, which shows the
degree of mutating and sifts ‘life-threating’ individuals [25].
The developed method stops its work when reaches the maximum number of functional epochs.
(User has inputted this number)
The proposed genetic method can completely explore searching area, avoid local extrema on genetic
searching step and successfully use found ‘good’ decisions (in other words, it can improve results
steadily using intermediate decisions).
5. The results of the algorithm
To build a prediction model of flue gas desulfurization efficiency we used experimental data of a
coal boiler with 1000 MW power (from 07:00 24 of May 2020 to 06:00 31 of December 2020). The set
has 5 attributes and 5330 examples:
− SO2 inlet (mg/m3);
− water consumption in an absorber (m3/ hour);
− lime consumption (ton/hour);
− secondary reagent consumption (ton/hour);
− SO2 outlet (mg/мm3) [6].
To solve the problem, we selected Python-based IDE because it is easy to work with arrays and
datasets there. We used NumPy library (Python package for scientific computing). To build a neural
network model and to work with it, we chose Keras library [26] and Theano library [27].
The important requirement for data modelling is quality. If data have ‘noise’, seasonal component,
outliers, gaps, then it will negatively effect on the accuracy of prediction and the quality of the models.
Also, data (which are for learning datasets for ANN) should be normalized to decrease inaccuracy and
to increase the quality of training.
Fresh data processing before transferring to the model have 6 steps [28]:
− to clean datasets with empty or unidentified fields
− to process gaps in predictor’s data;
− to process abnormalities in predictor’s data;
− to delete seasonal components from time series;
− to convers data to types used in calculations;
− data normalization.
While data gaps processing, empty values are replaced by a median value that is calculated by the
formula (12):
∑f
+ S Me − 1
M e = X Me + i M 2 , (12)
f Me
where XMe – is a low value of median interval; iM – the median interval; SMe – the sum of observation
which accumulated before median interval; fMe – the number of observations in median interval. In this
way, we have the minimum statistical error which depends on rows values. The processing of
abnormalities in data is a cleaning from abnormally high or low values. Time series can be cleaned
from seasonal components by the decomposition method [29].
The normalized value of x is calculated by the formula (13):
x − min (x)
z(x) = . (13)
max (x) − min (x)
The created network learnt for 100 epochs. While testing, we used the method of dividing the data
sample into learning and testing samples in percentage 75/25%.
To rate the quality of prediction models we used Mean Absolute Error (MAE) and Mean Square
Error (MSE) [30-31].
Figure 1 and Figure 2 shows the results of a fully-connected perceptron with one hidden layer.
Figure 1: Network metrics value (MAE) for the fully-connected perceptron with one hidden layer
Figure 1 shows, that the best MAE value of this model is 59.85% and we can see that after 10th
epochs the value remained constant during the whole learning process of the fully-connected perceptron
with one hidden layer.
Figure 2: Network metrics value (MSE) for the fully-connected perceptron with one hidden layer
Figure 2 shows, that MSE value gradually declined and after 20th epoch it stayed almost the same
and equals 6785.
Figure 3 and Figure 4 shows the work results of a fully-connected perceptron with two hidden layers.
Figure 3: Network metrics value (MAE) for the fully-connected perceptron with two hidden layers
Figure 3 shows, that MAE value of the model equals 40.98 and, after 20th epoch, remained constant
during the whole learning process of the fully-connected perceptron with two hidden layers.
Figure 4: Network metrics value (MSE) for the fully-connected perceptron with two hidden layers
Figure 4 shows that value steadily go down between 10 and 15 epochs, reaches local minima and
equals 5795. The further decreasing of the network mistakes says that minima mistake is local.
Figure 5 and Figure 6 shows work results of a fully-connected perceptron with two hidden layers
and the genetic method with adaptive mutation.
Figure 5: Network metrics value (MAE) for the fully-connected perceptron with two hidden layers and
the genetic method with adaptive mutation
Figure 5 shows that MAE results for the fully-connected perceptron with two hidden layers and the
genetic method with adaptive mutation equals 23.95 and, starting from 5th epoch stayed almost the
same. So, we can say, that during the training the model reached its mistake minima and the network is
considered to be trained.
Figure 6: Network metrics value (MSE) for the fully-connected perceptron with two hidden layers and
the genetic method with adaptive mutation
Figure 6 shows that value of the mistake slightly decreased. During 20th epoch it stayed almost the
same and equals 3253.
There was a comparison exercise of developed models results with the methods as follows: linear
regression, polynomial regression, logistic regression, nearest neighbour algorithm, random forest, ant
colony optimization algorithm. The criterion of estimation were Mean Absolute Error (MAE), Mean
Squared Error (MSE) and runtime (Table 1).
Table 1
Comparison exercise of developed method for prediction the flue gas desulfurization efficiency
Method MAE MSE Runtime, seconds
Linear regression 79.24 9103 363
Polynomial regression 77.84 9031 401
Logistic regression 78.56 9041 374
Nearest neighbour algorithm 75.76 7421 428
Random forest 74.15 7201 469
Ant colony optimization algorithm 73.89 7523 393
Multilayer perceptron with one hidden layer 59.85 6785 864
Multilayer perceptron with two hidden layers 40.98 5795 964
Multilayer perceptron with two hidden layers 24.95 3253 564
and the developed genetic algorithm
Table 1 shows, that the use of neural networks gives more accuracy than the use of regression
models. For example, the average absolute mistake values of the multilayer perceptron with one or two
hidden layers respectively equal 59.85 and 40.98. Meanwhile, the average absolute mistake values of
linear and logistic regression respectively equal 79.24 and 78.56. So, neural networks can achieve more
accuracy in prediction than regression models as they can better process a non-linear behaviour. But
neural networks need more runtime to stop working. The runtime of the multilayer perceptron with one
hidden layer equals 864 seconds while the runtime of the polynomial regression equals 401 seconds.
To solve this problem, the modified genetic method with adaptive mutation was developed. It allows to
increase the accuracy of prediction and to reduce the time needed for neural network learning. While
testing, it showed the lowest MSE value, that equals 3253. It is 54% less than the random forest method
has and 43% more than the multilayer perceptron with two hidden layers has. Also, the runtime of the
multilayer perceptron with two hidden layers and the genetic algorithm equals 564 seconds, that is 34%
less than the multilayer perceptron with one hidden layer has and 41% more than the multilayer
perceptron with two hidden layers has. According to the results, we can sum up that it is perspective to
use evolutionary algorithms for ANN learning, as using them can reduce learning time and achieve
more deeper minima of ANN learning mistake.
6. Conclusion
The work described the solution to optimization problem of flue gas desulfurization process strategy
using heuristic methods. The modified genetic method for prediction of flue gas desulfurization based
on the created neural network was developed. The vital difference between this developed genetic
method and other similar methods is in using adaptive mutation, that uses the level of population
development in working process. It means that less important genes will mutate in chromosome more
probable than high suitability genes. The worse an individual is adapted the far it is located from the
optimum which means it has more possibility to mutate, in which case it will move far away from the
current non-optimal location. The proposed genetic method can completely explore a searching area,
avoid local extrema on the genetic searching step and successfully use found ‘good’ decisions (in other
words, it can improve results steadily using intermediate decisions). Also, it represents the influence of
time series characteristic on factual efficiency of desulfurization and increases its precision of
prediction. There was a comparison exercise of the proposed method and others. During the work, it
was found that the developed method gives the smallest prediction mistake in prediction of SO2
composition in the outlet after flue gas desulfurization (MAE equals 24.95 and MSE equals 3253, what
is less comparing to other models built on different methods) and also has smaller runtime (learning
time of the model equals 564 seconds). The practical use of the developed method can increase the
efficiency of flue gas desulfurization process and decrease SO2 emissions into the atmosphere.
7. References
[1] S. Liu, L. Sun, S. Zhu, J. Li, X. Chen, W. Zhong, Operation strategy optimization of desulfurization
system based on data mining, Applied Mathematical Modelling 81 (2020) 144-158. doi:
10.1016/j.apm.2019.12.004.
[2] Z. Shao, F. Si, D. Kudenko, P. Wang, X. Tong, Predictive scheduling of wet flue gas
desulfurization system based on reinforcement learning, Computers & Chemical Engineering 141
(2020) p. 107000. doi: 10.1016/j.compchemeng.2020.107000.
[3] J.A.J. Alsayaydeh, W.A.Y. Khang, W.A. Indra, V. Shkarupylo, J. Jayasundar, Development of
smart dustbin by using apps, ARPN Journal of Engineering and Applied Sciences 14 (2019) 3703-
3711.
[4] X. Li, Q. Liu, K. Wang, F. Wang, G. Cui, Y. Li, Multimodel Anomaly Identification and Control
in Wet Limestone-Gypsum Flue Gas Desulphurization System, Complexity 2020 (2020) 1-17. doi:
10.1155/2020/6046729.
[5] J. Fu, H. Xiao, T. Wang, R. Zhang, L. Wang, X. Shi, Prediction Model of Desulfurization
Efficiency of Coal-Fired Power Plants Based on Long Short-Term Memory Neural Network, in:
2019 International Conference on Internet of Things (iThings) and IEEE Green Computing and
Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and
IEEE Smart Data (SmartData), 2019, pp. 40–45. doi.
10.1109/iThings/GreenCom/CPSCom/SmartData.2019.00030
[6] D.Adams, D. Oh, D. Kim, C. Lee, M. Oh, Prediction of SOx–NOx emission from a coal-fired CFB
power plant with machine learning: Plant data learned by deep neural network and least square
support vector machine, Journal of Cleaner Production 270 (2020) p. 122310. doi:
10.1016/j.jclepro.2020.122310.
[7] Z. Qiao, X. Wang, H. Gu, Y. Tang, F. Si, C. Romero, X. Yao, An investigation on data mining and
operating optimization for wet flue gas desulfurization systems, Fuel 258 (2019) p.116178. doi:
10.1016/j.fuel.2019.116178.
[8] J.A.J. Alsayaydeh, W.A.Y. Khang, W.A. Indra, J.B. Pusppanathan, V. Shkarupylo, A.K.M. Zakir
Hossain, S. Saravanan, Development of vehicle door security using smart tag and fingerprint
system, ARPN Journal of Engineering and Applied Sciences 9 (2019) 3108-3114. doi:
10.35940/ijeat.E7468.109119.
[9] G. Uddin et al., Artificial Intelligence-Based Emission Reduction Strategy for Limestone Forced
Oxidation Flue Gas Desulfurization System, Journal of Energy Resources Technology 142 (2020)
1-16. doi: 10.1115/1.4046468.
[10] Y. Guo et al., Modeling and optimization of wet flue gas desulfurization system based on a hybrid
modeling method, Journal of the Air & Waste Management Association 69 (2019) 565-575. doi:
10.1080/10962247.2018.1551252.
[11] J.A.J. Alsayaydeh, W.A.Y. Khang, A.K.M.Z Hossain, V. Shkarupylo, J. Pusppanathan, The
experimental studies of the automatic control methods of magnetic separators performance by
magnetic product, ARPN Journal of Engineering and Applied Sciences 15 (2020) 922-927.
[12] Z. Kong, Y. Zhang, X. Wang, Y. Xu, B. Jin, Prediction and optimization of a desulphurization
system using CMAC neural network and genetic algorithm, Journal of Environmental Engineering
and Landscape Management 28 (2020) 74-87. doi: 10.3846/jeelm.2020.12098.
[13] I. Fedorchenko, A. Oliinyk, A. Stepanenko, T. Zaiko, S. Shylo, A. Svyrydenko, Development of
the modified methods to train a neural network to solve the task on recognition of road users,
Eastern European Journal of Enterprise Technologies 98 (2019) 46–55. doi: 10.15587/1729-
4061.2019.164789.
[14] E. Pardo, J. Blanco-Linares, D. Velázquez, F. Serradilla, Optimization of a Steam Reforming Plant
Modeled with Artificial Neural Networks, Electronics 9 (2020) 1923. doi:
10.3390/electronics9111923.
[15] J.A. Alsayaydeh, M. Nj, S.N. Syed, A.W. Yoon, W.A. Indra, V. Shkarupylo, C. Pellipus, Homes
appliances control using bluetooth, ARPN Journal of Engineering and Applied Sciences 14 (2019)
3344-3357.
[16] S. Stajkowski, D. Kumar, P. Samui, H. Bonakdari, B. Gharabaghi, Genetic-Algorithm-Optimized
Sequential Model for Water Temperature Prediction, Sustainability 12 (2020) 5374. doi:
10.3390/su12135374.
[17] A. Oliinyk, S. Skrupsky, S. Subbotin, Experimental research and analysis of complexity of parallel
method for production rules extraction, Automatic Control and Computer Sciences 52 (2018) 89-
99. doi: 10.3103/S0146411618020062.
[18] Z. Erzurum Cicek, Z. Kamisli Ozturk, Optimizing the artificial neural network parameters using a
biased random key genetic algorithm for time series forecasting, Applied Soft Computing 102
(2021) 107091. doi: 10.1016/j.asoc.2021.107091.
[19] A. Zaji, H. Bonakdari, H. Khameneh, S. Khodashenas, Application of optimized Artificial and
Radial Basis neural networks by using modified Genetic Algorithm on discharge coefficient
prediction of modified labyrinth side weir with two and four cycles, Measurement 52 (2020)
107291. doi: 10.1016/j.measurement.2019.107291.
[20] H. Cheng, J. Xie, Study on the application of recurrent fuzzy neural network in PH control system
of absorption tower, in: 2017 Chinese Automation Congress (CAC). doi:
10.1109/cac.2017.8243850.
[21] A. Oliinyk, I. Fedorchenko, A. Stepanenko, M. Rud and D. Goncharenko, Combinatorial
optimization problems solving based on evolutionary approach, in: 2019 15th International
Conference on the Experience of Designing and Application of CAD Systems (CADSM), Polyana,
Ukraine, 2019, pp. 41-45. doi: 10.1109 / CADSM.2019.8779290.
[22] X. Wang, L. Yang, X. Chen, J. Han, J. Feng, A Tensor Computation and Optimization Model for
Cyber-Physical-Social Big Data, IEEE Transactions on Sustainable Computing 4 (2019) 326-339.
doi: 10.1109/tsusc.2017.2777503.
[23] Z. Yang et al., Predicting particle collection performance of a wet electrostatic precipitator under
varied conditions with artificial neural networks, Powder Technology 377 (2021) 632-639. doi:
10.1016/j.powtec.2020.09.027.
[24] I. Fedorchenko, A. Oliinyk, A. Stepanenko, T. Zaiko, S. Korniienko, N. Burtsev, Development of
a genetic algorithm for placing power supply sources in a distributed electric network, Eastern-
European Journal of Enterprise Technologies 5 (2019) 6-16. doi: 10.15587 / 1729-
4061.2019.180897.
[25] F. Wang et al., Application of genetic algorithm-back propagation for prediction of mercury
speciation in combustion flue gas, Clean Technologies and Environmental Policy 18 (2016) 1211-
1218. doi: 10.1007/s10098-016-1095-1.
[26] J.A.J. Alsayaydeh, W.A. Indra, W.A.Y. Khang, V. Shkarupylo, D.A.P.P. Jkatisan, Development
of vehicle ignition using fingerprint, ARPN Journal of Engineering and Applied Sciences 14
(2019) 4045-4053.
[27] Z. Kong et al., Error prediction and structure determination for CMAC neural network based on
the uniform design method, Expert Systems 38 (2020). doi: 10.1111/exsy.12614.
[28] A. Oliinyk, I. Fedorchenko, A. Stepanenko, A. Katschan, Y. Fedorchenko, A. Kharchenko, D.
Goncharenko, Development of genetic methods for predicting the incidence of volumes of
pollutant emissions in air, in: 2019 2nd International Workshop on Informatics and Data-Driven
Medicine (IDDM), 2019, pp. 340-353. ISSN: 16130073.
[29] I. Fedorchenko, A. Oliinyk, О. Stepanenko, T. Zaiko, A. Svyrydenko, D. Goncharenko, Genetic
method of image processing for motor vehicle recognition, in: 2nd International Workshop on
Computer Modeling and Intelligent Systems, CMIS 2019, CEUR Workshop Proceedings,
Zaporizhzhia, Ukraine, 2019, pp. 211-226. ISSN: 16130073.
[30] Q. Li, J. Wu, H. Wei, Reduction of elemental mercury in coal-fired boiler flue gas with
computational intelligence approach, Energy 160 (2018) 753-762. doi:
10.1016/j.energy.2018.07.037.
[31] H. Jang, X. Shuli, S. So, Analysis the Compressive Strength of Flue Gas Desulfurization Gypsum
Using Artificial Neural Network, Journal of Nanoscience and Nanotechnology 20 (2020) 485-490.
doi: 10.1166/jnn.2020.17235.