=Paper=
{{Paper
|id=Vol-3896/paper16
|storemode=property
|title=The selection of a structure of a neural network model for predicting the flow parameters of transport systems
|pdfUrl=https://ceur-ws.org/Vol-3896/paper16.pdf
|volume=Vol-3896
|authors=Oleh Pihnastyi,Georgii Kozhevnikov,Bohdan Fedorchak
|dblpUrl=https://dblp.org/rec/conf/ittap/PihnastyiKF24
}}
==The selection of a structure of a neural network model for predicting the flow parameters of transport systems==
https://ceur-ws.org/Vol-3896/paper16.pdf
The selection of a structure of a neural
network model for predicting the flow
parameters of transport systems
Oleh Pihnastyi1,†, Georgii Kozhevnikov1∗,†, Bohdan Fedorchak 1,†
1
National Technical University "KhPI", 2, Kyrpychova str., Kharkiv, 61002, Ukraine
Abstract
The selection of a structure of a model for predicting flow parameters of a distributed transport
system of the conveyor type is considered in this paper. The rationale for using a neural network to
model a transport system consisting of a large number of individual sections is given. The analysis of
transport conveyor models is carried out. It is shown that the model of a transport system, which is
based on a neural network, can be successfully applied to predict the flow parameters of a transport
system consisting of a very large number of sections. The architecture of the neural network and the
technique of forming a data set for its training are proposed. To train the neural network, the back
propagation method of error was used. A comparative analysis of models of conveyor-type transport
systems based on multilayer neural networks of different structures is carried out. Various neural
network structures were studied on various test tasks. An analysis of the neural network learning rate
with logistic and linear activation functions is given.
Keywords ⋆1
conveyor, distributed system, control
1. Introduction
One of the important problems of the leading enterprises of the mining industry is the reduction
of costs for the extraction and transportation of minerals. The conveyor type transport system is
the main method of transporting material [1–3]. The average share of the cost of transporting a
unit mass of material is 20% of the total cost of coal mining [4]. Costs are especially noticeable
for long multi-sectional transport systems and branched transport systems. As the length of the
transport system increases, transportation costs increase too. Uneven coming of material at the
input of the transport system leads to an uneven distribution of material along the
transportation route. It's the one of the main reason for the inefficient use of transport conveyor.
Reduced transportation costs is achieved by increasing the level of congestion with the
material of the transport system [1, 5]. To increase the level of congestion of the transport
⋆
ITTAP’2024: 4th International Workshop on Information Technologies: Theoretical and Applied Problems, October 23-
25, 2024, Ternopil, Ukraine, Opole, Poland
1∗
Corresponding author.
†
These authors contributed equally.
pihnastyi@gmail.com (O. Pihnastyi); Heorhii.Kozhevnikov@khpi.edu.ua (G. Kozhevnikov);
Bohdan.Fedorchak@khpi.edu.ua (B. Fedorchak)
0000-0002-5424-9843 (O. Pihnastyi); 0000-0002-6586-6767 (G. Kozhevnikov); 0009-0003-7335-9276 (B. Fedorchak)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
system, control the speed of the conveyor belt or the value of the output stream from the
accumulating hopper entering the input of a separate section is used [6-8]. The design of the
control system is simplified if the transport conveyor is divided into sections [1, 2]. In this case,
control of flow parameters can be carried out within a separate section. For the design of a
control system for flow parameters of the transport system, transport conveyor models are most
often used, which are based on the finite element method [3, 9-12] and the finite difference
method [13, 14]. For a qualitative analysis of the parameters of transport systems, equations of
system dynamics [7] and aggregated equations [15] are used.
2. Formal Problem Statement
Dividing a long transport conveyor into separate sections and using transport systems with an
extensive internal route containing a large number of converging and diverging sections
ensures an increase in the capacity and length of transport systems. However, in this case, the
use of finite element and finite difference methods for modelling conveyor-type transport
systems is not effective due to the large amount of calculations [2, 10, 13]. To model a transport
system consisting of a large number of sections, the analytical model of a transport conveyor
[16] can be successfully applied. An analytical model of the main multi-section conveyor is
presented in [17]. If the conveyor belt speed for each section of the transport system, consisting
of a very large number of sections, is constant, then this models are an excellent tool for
simulating such a transport system. If the speed of the conveyor belt changes over time, then the
analytical model will require significant computational resources. This circumstance imposes a
limitation on the maximum number of sections of the transport system, for the description of
which an analytical model can be used. The maximum number of sections is determined from
the condition that the calculation time should be less than the maximum permissible value. This
value is limited by the time allotted for controlling the parameters of the transport system. If the
number of sections reaches several dozen separate sections, then a more advanced model of the
conveyor is required to design an effective control system for the flow parameters of the
transport conveyor.
This paper proposes the use of a neural network (NN) for modelling a multi-section
conveyor. It should be noted that the researchers of conveyor systems have already shown
interest in this class of models. Regression models [18-20] and NN models [21, 22, 23] were used
to analyse the strength characteristics of the transport conveyor. The feasibility of using the
regression model of the conveyor section for the design of the belt speed control system was
studied in paper [19]. In [21], a model based on NN is considered to control the speed of
movement of the conveyor belt. The advantage of these papers is that the regression model and
the model based on NN were built in accordance with the actual experimental measurement.
However, when designing multi-section transport conveyors, the ability to use an experimental
data set is associated with great difficulties. This greatly complicates the use of NN for modelling
a multi-section transport conveyor. This work is devoted to the construction of a model based
on NN to describe the state of the flow parameters of a multi-section conveyor and the following
analysis of these parameters.
3. An Analytical Model of the Conveyor Section
A conveyor is a type of production line [23]. Consider the approximation that the conveyor belt
is not extensible. For this assumption, the rock material moves along the transportation route at
the same speed equal to the speed of the belt. The system of equations for modelling the
movement of material along the transport route has the form [8, 16]:
∂ [ χ ]0 ( t,S ) ∂ [ χ ]0 ( t,S )
(S) (1)
∂t ∂S
[ χ ]1 (t,S)=a(t ) [ χ ]0 (t,S) (2)
under the initial conditions:
[ χ ]0 (t 0 ,S)=H (S)Ψ (S) , (3)
+∞
∫−∞ δ ( S ) ds=1 H(S)=¿ {0 ,S<0;¿¿¿¿
,
(4)
where the parameters[ χ ]0 ( t,S ) (t/m), [ χ ]1 (t,S ) (t/h) - the linear density of the rock and the
flow of the rock at time t (h) at the point of the route determined by the coordinate S (m),
S ∈ [ 0 , S d ] , S is the length of the conveyor line. Flow parameters [ χ ]0 ( t,S ) , [ χ ]1 (t,S ) are linked
d
coefficient a=a(t ) (m/h), which determines the conveyor belt speed of the conveyor line;
λ(t ) - the intensity of the arrival of the rock on the conveyor line at the point with the
coordinate S=0; δ ( S ) is Dirac function.
Let’s write the next expressions using dimensionless variables [16]:
t S
τ= ξ=
Td Sd
(5)
, ,
[ χ ]0 ( t,S ) Ψ ( S ) γ ( τ )=λ( t ) T d
θ 0 ( τ , ξ )= ψ ( ξ )= Sd Θ , (6)
Θ , Θ ,
T T
g( τ )=a(t ) d ϑ ( τ )=σ (t ) d Θ=max Ψ ( S ),
Sd , Sd Θ ,
λ(t )
a(t ) , { } (7)
δ ( ξ )=S d δ ( S ) , H ( ξS d )=H ( S ) . (8)
Rewrite the system of equations (1) – (3) in the dimensionless form:
∂ θ0 ( τ , ξ ) ∂ θ0 ( τ , ξ )
(ξ ) (9)
∂τ ∂ξ ,
θ 0 (0 ,ξ )= H(ξ )⋅ψ (ξ ) , (10)
where Td is the time during which the rock passes the entire transportation route, from the
moment it enters the conveyor belt and up to the point of unloading from the conveyor.
The system of equations (5), (6) corresponds to a system of characteristics:
dξ
=g( τ ) ξ| =β (11)
dτ , τ=0 ,
dθ 0 ( τ , ξ ) γ(τ )
=δ ( ξ ) (12)
dξ g( τ ) , θ 0 ( 0 , β )= H( β )⋅ψ ( β ) .
Integration of the system of equations (11), (12) allows to obtain a general solution in the
form:
γ (τξ)
θ 0 ( τ , ξ )=[ H ( ξ )−H (−G( τ ξ )) ] + H (−G( τ ξ ))ψ (−G( τ ξ )) (13)
g( τ ξ ) ,
τ
G(τ )=∫ g(ω)dω (14)
τ ξ =G−1 (G( τ )−ξ )=τ−Δτ ξ , 0 ,G
−1
(G(τ ))=τ ,
where
Δτξ is the value of the transport delay.
The obtained solution (13) allows to determine the output parameters of the single
conveyor's section. For a conveyor's section whose length is ξ=1 , the output parameters can be
calculated using the following formulas:
γ ( τ−Δτ ξ )
θ 0 ( τ ,1)=( 1−H ( 1−G( τ )) ) +H (1−G( τ ))ψ (1−G( τ )) (15)
g( τ−Δτ ξ ) ,
γ ( τ−Δτ ξ )
θ1 ( τ ,1)=( 1−H ( 1−G( τ )) ) g( τ )+H (1−G( τ ))ψ (1−G( τ ))g( τ ) (16)
g( τ−Δτ ξ ) .
For the steady-state mode, expressions (15) and (16) have a simpler form:
γ ( τ −Δτ ξ )
θ 0 ( τ ,1)= (17)
g( τ −Δτ ξ ) ,
γ ( τ−Δτ ξ )
θ1 ( τ ,1)= g( τ ) (18)
g( τ−Δτ ξ ) .
In the initial period of movement of the conveyor belt ( 1−G( τ )) >0 the output parameters of
the conveyor section are determined by condition (10):
θ 0 ( τ ,1)=ψ (1−G( τ )) , (19)
θ 1 ( τ ,1)=g( τ )ψ (1−G( τ )) . (20)
The obtained expressions for calculating the output parameters θ 0 ( τ ,1) and θ 1 ( τ ,1) of the
conveyor section (17) – (20) will be used to form a data set for training NN of a multi-section
conveyor.
4. Conveyor Section Model Using a Neural Network
The conveyor-type transport system provides directional movement of material from the place
of mining to the place of processing or the point of loading for subsequent transportation. The
route diagram of a branched conveyor system consisting of several dozen separate sections is
given in [24]. Constructing a model of a transport conveyor using NN, let's use a simplified
diagram of the transport route shown in Figure 1.
Figure 1: Diagram of a branched conveyor transport route.
The transport route diagram contains four input conveyors (section m = 1,2,4,5) and two
output conveyors (section m = 7,8). The material coming from the previous section into the
bunker instantly leaves it and enters the next section. The bunker only provides the required
direction of movement of the material. Regulation of the value of the material flow is carried out
with a change in the speed of the conveyor belt (18), (20). The model under consideration, as will
be shown below, can be expanded without any problems to an arbitrary number of sections,
which allows to simulate transport routes of a rather complex configuration.
To describe the functioning of a separate conveyor section of the transport system, we use
dimensionless variables (5)–(8) of the model (9), (10), which allow to determine the state of the
γ ( τ ) is the intensity of the
flow parameters of the individual conveyor section at a time τ : m
g ( τ ) is conveyor belt speed;ξ m is length of the m –th transport section.
input flow of material; m
Δτ ξm
An additional parameter of the section may be the value of the transport delay :
τ
ξ m= ∫ g(ω)dω (21)
τ−Δτ ξm
.
However, the measurement of the transport delay in production conditions is associated
with a number of difficulties. As a result, the calculation of the value of the transport delay is
performed by measuring the value of the conveyor belt speed, which is equivalent to solving
(21). But solving (21) leads to the fact that the advantage of using a model based on NN is lost in
comparison with the analytical model. It is the cost of computing resources associated with
solving (21) that makes it difficult to use an analytical model to describe a transport system
consisting of a large number of sections and opens the prospects for using a model based on NN.
Therefore, if in real production conditions it is not possible to directly measure the amount of
transport delay, this parameter is not advisable to include in a set of parameters for an individual
section. Similar considerations can be given for the parameters of the input material flow
γ m ( τ )=θ1m ( τ ,0) and the material output flow θ1m ( τ ,1) for the inner sections (17), (20), the
Δτ ξm
values of which are determined through the value of the transport delay . In addition, it
should be pointed out that for calculating the parameters m 1m γ ( τ )=θ ( τ ,0) θ ( τ ,1)
, 1m of the
inner sections, the information should be stored on their values and values of the conveyor belt
g (τ )
speed m for the time interval ( ).
τ − Δτ ; τ
ξm
Taking into account the above arguments, as the nodes of the input layer of NN, we choose
the intensity of the input stream of the material and the speed of the conveyor belt of the input
sections (m = 1,2,4,5). The values of the nodes of the output layer of NN will correspond to the
values of the output flow for the final sections (m = 7, 8).
γ2( τ )
=const (22)
γ3( τ ) , γ 3 ( τ )≠0 .
The architecture of NN for constructing an aggregated model is a feed-forward, a full-
connected and three layer. We introduce the notation for the parameters of the input layer of
NN:
x 3 m−2=γ m ( τ ) , x 3 m−1=g m ( τ ) , x 3 m =ξ m , μ=1,…,M. (23)
where m is the number of the conveyor section (Figure 1). For the model of the transport
γ ( τ ) , gm ( τ ) , ξ 1 of the input sections m = 1,2,4,5
system, we will use the input parameters m
(Figure 1).
Let's introduce the notation for the parameters of the output layer of NN:
y 1=θ 17 ( τ , ξ 7 ) , y 2=θ 18 ( τ , ξ 8 ) . (24)
y y
The output parameters 1 and 2 correspond to the output material flows for sections m = 7,
8 of the transport system of Figure 1. The parameter system (23), (24) is an example of a set of NN
parameters for a transport system of eight sections. Using a similar approach, we can determine
the input and output parameters for an aggregated model of a transport system with an
arbitrary number of sections.
5. Results
Two types of activation functions were used for the selection of a structure of NN model [25]:
the linear or ReLU (25) and the logistic (26):
f ( x )=bx ,
{f(x)=a, if x≥a/b,¿{f(x)=bx, if a/b>x>0, ¿ ¿ (25)
a
f ( x )= (26)
1+exp(−bx ) .
Within one layer, for all nodes, the same activation function is set with coefficients fixed for
each node of the layera ,b . For different layers, the form of the activation function and the
coefficients that determine it may differ.
For the transport system we had considered two models a multilayer NN with structure 13–
N L L –2, containing L-hidden layers and N L nodes in each layer: 13-8-8-2 and 13-5-5-5-2. The
considered structures contain approximately the same number of hidden nodes
N h =N L L ~ 15 with the number of weights
N w =( N i + N o ) N L + ( L−1 ) N 2 (27)
L ,
that determine the computational complexity of the learning algorithm. When analyzing
structures with the same number of neurons in the input N i , output N o and hidden layers
N h the formula that determines the number of weight coefficients for the structure
N i −N L L−N o (Figure 2) takes the form
N 2
N w =( N i + N o ) N L + ( L−1 ) N 2=
L L
h
( 1 N +N
1− + i o
L Nh ) .
(28)
a) b)
Figure 2: The neural network structure: a) 13-8-8-2; b)13-5-5-5-2
With an increase in the number of hidden layers L the value of the function
N w ( L) decreases
for L>1. The sign of the derivative of the function
N w ( L) is determined by the expression:
( )
∂ Nw 2 N i+ N o+ N h
~ − <0 (29)
∂L L Nh
, for L>1.
N N N
Thus, at constant values of i , o , h the complexity of the computational algorithm for
determining the values of the output flow parameters of the transport system in accordance
with (28) is inversely proportional to the number of hidden layers. The main characteristics of
NN used to build a model of the transport system are presented in Table 1.
Table 1
Characteristics of neural networks for modelling the transport system
Speed learning
Coeff. "b" (HL)
Coeff. "a" (HL)
Coefficient "a"
(hidden layer)
(output layer)
Number of
Activation
id
Structure
function
epochs
MSE
711 8-8 Logistic 2,0 1,0 2,0 10-4 0,39 103
712 8-8 Logistic 2,0 1,0 4,0 10-4 0,19 1,2*103
713 5-5-5 Logistic 2,0 1,0 4,0 10-4 0,51 1,2*103
911 8-8 Linear (ReLU) 100 0,1 4 10-4 0,08 68*103
9112 8-8 Linear (ReLU) 100 0,1 4 10-3 0,05 78*103
921 5-5-5 Linear (ReLU) 2,0 1,0 2,0 10-4 0,41 28*103
9212 5-5-5 Linear (ReLU) 2,0 1,0 2,0 10-3 0,08 28*103
Each option is represented by the same and constant learning rate km which allows
α =10−4
you to compare the training durations of NN used to build different models of transport systems.
The value of the coefficient “b” for the output layer is equal to 1,0 for all studied cases. In model
711 with structure 13-8-8-2, the same activation function is defined for each node. The results of
predicting the output flow 17
θ ( τ ,3/2)
using this model are presented in Figure 3. The quality of
the prediction is estimated at MSE = 0,390. A doubling of the scale factor in the activation
function of the output layer led to a halving of the MSE value (MSE = 0,197) with the same
number of learning epochs.
Figure 3: Predicted material output flow 17
θ (τ ,1.5) , Model 711.
Subsequent migration from 13-8-8-2 (Model 712) to 13-5-5-5-2 (Model 713) did not result in a
decrease in MSE. The reason is explained by the development of instability in the learning
process of NN. The next step of the study was the transition in model 712 from the logistic
activation function (1) to the linear activation function (2). With the value of the coefficients for
the hidden layera=4 , b=1 and for the hidden layera=4 , b=1 the learning process was not
stable. When changing the coefficients for the hidden layer a=100 , b=0 ,1 the learning
process became stable. The learning process lasted ~68*103 epochs and was stopped with
−7
MSE~0,08 and Δ MSE ~ 7⋅10 . Then, to speed up the learning process, the learning rate was
α =10−4
increased from a value km
α =10−3
to a value km for all nodes. This made it possible to
continue the learning process in an accelerated mode, reaching ~78*103 epochs with an
MSE~0,053. Further training was interrupted due to the development of instability in the
training process. At the same time, the value MSE~0,390 and MSE~0,197 was reached at ~6*103
and ~15*103 epochs, respectively. This allows one to compare the training required by the three
for logistic activation function and linear activation function (ReLU) for the given parameters
for NN (Table 1) as a ratio of ~10 : 1.
The final stage of the study was the transition from structure 13-8-8-2 (Model 911) to
structure 13-5-5-5-2 (Model 921), Table 1. The presence of an additional hidden layer did not lead
to a decrease in the MSE value in model 921 compared to the 911. However, it is worth noting
the presence of oscillatory processes of the MSE value relative to value ~ 0,082. The results of
prediction the output flow parameters 17
θ (τ ,1.5) θ (τ ,0.6)
, 18 of the transport system are
presented in Figure 4, Figure 5. Comparison of the prediction results shows that the use of the
ReLU activation function for training NN makes it possible to obtain a more accurate forecast of
stream parameters with a lower MSE value than when using the Logistic activation function. A
significant disadvantage of using the Linear activation function (ReLU) compared to using the
Logistic activation function is a significant increase in the time that needs to be spent on training
NN. A comparative analysis of the prediction quality criterion for those considered in this work
is shown in Figure 6.
Figure 4: Predicted material output flowθ 17 ( τ ,3/2) : a) model 711; b) model 721; c) model 911; d)
model 721.
θ (τ ,0.6) : a) model 711; b) model 721; c) model 911; d)
Figure 5: Predicted material output flow 18
model 721.
Figure 6: Prediction quality criterion.
Multilayer NN based on linear (ReLU) demonstrated a more robust learning process and gave
lower MSEs than NN based on logistic activation functions. An increase in the number of hidden
layers with a constant number of neurons in them led to the emergence of instabilities during
the learning process of NN for the logistic activation function and the appearance of oscillatory
processes in the case of using the ReLU activation function. It should be noted that an increase in
the number of hidden layers, on the one hand, leads to a decrease in the quality of the forecast
(an increase in the MSE value), on the other hand, it makes it possible to obtain a significant
increase in the accuracy of predicting the peak values of the flow parameters of the transport
system, which is clearly shown in Figure 4, Figure 5.
6. Conclusion
A model using NN can be a fairly good tool for predicting the state of the output flow
parameters of a branched transport system consisting of a large number of individual sections.
However, the accuracy of such a model depends on many factors, including the architecture and
the structure of such a model.
In this work, a comparative analysis of transport conveyor models based on multilayer NN is
carried out. The main focus is on NN with the logistic activation function and the ReLU
activation function. NN with a logistic activation function demonstrated a shorter learning time
for equal MSE values, which is explained by the distributed form of nonlinearity and high
connectivity. However, it should be noted that the learning process of NN with and linear
(ReLU) activation function is more stable, which allows achieving lower MSE values in the
learning process. The influence of the structure of NN on the duration of their training was also
studied.
The work touches upon many issues that are important from the point of view of
constructing models of conveyor-type transport systems. The estimation of the method of
initialization of the weight coefficients providing the connection between the nodes of NN is
carried out and the rationale for the preparation of a normalized data set for training NN is
given. The importance of the last question is emphasized by the fact that the values of the nodes
of the input and output layers are positive, which leads to a simultaneous increase or decrease in
the weight coefficients that ensure the connection of the nodes of the input layer with the nodes
of the hidden layer, and, as a consequence, to the occurrence of oscillatory processes.
A method for increasing the accuracy of the learning process as a result of removing values
from the data set is demonstrated, which characterize the transient mode of operation of the
transport system.
This article does not discuss the importance of hidden neurons as detectors of factors that
determine the behavior of the flow parameters of the transport system. Also, the problem of
reducing the order of a multilayer NN with losing the quality of the model prediction is not
considered.
References
[1] SIMINES for conveyors. Siemens. 2024.
URL: https://new.siemens.com/global/en/markets/mining-industry/transport/conveyor-
systems.html.
[2] Conveyorbeltguide Engineering: Conveyor components. 2024.
URL: http://conveyorbeltguide.com/examples-of-use.html.
[3] M. Alspaugh, “Longer Overland Conveyors with Distributed Power. In: Overland
Conveyor Company,” Lakewood, USA, 2005.
URL: http://www.overlandconveyor.com/pdf/Longer_Overland_Conveyors_with_Distrib
uted_Power.pdf
[4] Ju. Razumnyj, A. Ruhlov and A. Kozar, “Povyshenie jenergojeffektivnosti konvejernogo
transporta ugol'nyh shaht,” Gіrnicha elektromehanіka ta avtomatika. vol. 76, pp. 24–28,
2006. URL: https://docplayer.ru/64655888-Povyshenie-energoeffektivnosti-konveyernogo-
transporta-ugolnyh-shaht.html
[5] A. Semenchenko, M. Stadnik, Belitsky P., Semenchenko D. and Stepanenko O., “The impact
of an uneven loading of a belt conveyor on the loading of drive motors and energy
consumption in transportation,” EasternEuropean Journal of Enterprise Technologies, vol.
4/1(82), pp. 42–51, 2016. URL: https://doi.org/10.15587/1729-4061.2016.75936
[6] E. Wolstenholm, “Designing and assessing the benefits of control policies for conveyor belt
systems in underground mines,” Dynamica. vol. 6(2), pp. 25–35, 1980.
[7] H. Lauhoff “Speed Control on Belt Conveyors – Does it Really Save Energy?,” Bulk Solids
Handling Publ. vol. 25(6), pp. 368-377, 2005.
[8] O. Pihnastyi and V. Khodusov, “Model of conveyer with the regulable speed,” Bulletin of
the South Ural State University. Ser.Mathematical Modelling, Programming and Computer
Software vol. 10, pp. 64–77, 2017. URL: https://doi.org/10.14529/mmp170407.
[9] L.K. Nordell and Z.P. Ciozda, “Transient belt stresses during starting and stopping: Elastic
response simulated by finite element methods,” Bulk Solids Handling vol. 4(1), pp. 99–104,
1984. URL: http://www.ckit.co.za/secure/conveyor/papers/troughed/transient/transient-
belt-stresses.htm
[10] D. He, Pang Y., Lodewijks G. and X. Liu “Determination of Acceleration for Belt Conveyor
Speed Control in Transient Operation,” International Journal of Engineering and
Technology, vol. l.8(3), pp. 206–211, 2016. URL: http://dx.doi.org/10.7763/IJET.2016.V8.886
[11] B. Karolewski and Ligocki P., “Modelling of long belt conveyors. Maintenance and
reliability,” vol. 16 (2), pp. 179–187, 2014.
URL: http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.baztech-ce355084-3e77-
4e6b-b4b5-ff6131e77b30
[12] R. Pascual, V. Meruane and G. Barrientos, “Analysis of transient loads on cable-reinforced
conveyor belts with damping consideration,” In: Proceedings of the XXVI Iberian Latin-
American Congress on Computational Methods in Engineering CILAMCE 2005, pp. 1-15.
[13] C.A.Wheeler, “Predicting the main resistance of belt conveyors,” In International Materials
Handling Conference (Beltcon), Johannesburg, South Africa, pp. 1-16, 2003.
URL: https://login.totalweblite.com/Clients/doublearrow/beltcon%202003/8.predicting%20
the%20main%20resistance%20of%20belt%20conveyors.pdf
[14] T. Mathaba and X. Xia, “A parametric energy model for energy management of long belt
conveyors,” Energies vol. 8(12), pp. 13590–13608, 2015.
URL: https://doi.org/10.3390/en81212375
[15] M. Stadnik, D. Semenchenko, A. Semenchenko, P. Belytsky, S. Virych, and V. Tkachov,
Improving energy efficiency of coal transportation by adjusting the speeds of a combine
and a mine face conveyor. Eastern-European Journal of Enterprise Technologies, 1/8(97)
(2019), 60-70. URL: https://doi.org/10.15587/1729-4061.2019.156121
[16] O. Pihnastyi, G. Kozhevnikov and T. Bondarenko, “The information controlling model
transport system during transient conditions,” In: Proceedings of the 2019 international
scientific-practical conference Problems of infocommunications, Science and Technology
(PIC S&T), Kyiv, Ukraine: pp. 197–201, 2019.
URL: https://doi.org/10.1109/PICST47496.2019.9061214
[17] O. Pihnastyi and V. Khodusov, “Model of a composite magistral conveyor line,” In:
Proceedings of the 2018 IEEE International Conference on System analysis & Intelligent
computing (SAIC), Ukraine, Kyiv, pp.68–72, 2018.
URL: https://doi.org/10.1109/saic.2018.8516739
[18] M. Andrejiova and D. Marasova, “Using the classical linear regression model in analysis of
the dependences of conveyor belt life,” Acta Montanistica Slovaca, vol. 18(2), pp. 77–84,
2013.
[19] Ya. Lu and Q. Li, “A regression model for prediction of idler rotational resistance on belt
conveyor,” Measurement and Control, vol. 52(5), pp. 441–448, 2019.
URL: https://doi.org/10.1177/0020294019840723
[20] A. Kirjanow, “The possibility for adopting an artificial neural network model in the
diagnostics of conveyor belt splices,” Interdisciplinary issues in mining and geology, vol. 6,
pp. 1–11, 2016.
[21] L. Xinglei and Yu. Hongbin, “The design and application of control system based on the BP
neural network,” In:Proceedings of the 3rd International Conference on Mechanical
Engineering and Intelligent Systems (ICMEIS), pp. 789–793, 2015.
URL: https://doi.org/10.2991/icmeis-15.2015.148
[22] P. Xi and Y. Song, “Application research on BP neural network PID control of the belt
conveyor,” JDIM, vol. 9(6), pp. 266–270, 2011.
URL: https://www.questia.com/library/journal/1G1-338602055/application-research-on-
bp-neural-network-pid-control
[23] N. Selcuk and Y. Birbir, “Application of artificial neural network for harmonic estimation in
different produced induction motors,” Int. J. of Circuits, Systems and Signal Processing, vol.
4(1), pp. 334–339, 2007.
URL: https://pdfs.semanticscholar.org/ba2f/6d5ea4c91720be4044e0f3544efb60fd6bb4.pdf
[24] O.M. Pihnastyi, “Statistical theory of control systems of the flow production,” LAP
LAMBERT Academic Publishing, p. 436, 2018.
[25] P. Parmar, L. Jurdziak, A. Rzeszowska and A. Burduk, “Predictive Modeling of Conveyor
Belt Deterioration in Coal Mines Using AI Techniques,” Energies, vol. 17, pp. 3497-3527,
2024. URL:https://doi.org/10.3390/en17143497