=Paper=
{{Paper
|id=Vol-3790/paper7
|storemode=property
|title=Neural network-based approach for predicting the flow material in transport systems
|pdfUrl=https://ceur-ws.org/Vol-3790/paper07.pdf
|volume=Vol-3790
|authors=Oleh Pihnastyi,Victoriya Usik,Georgii Kozhevnikov,Oleksii Matiash
|dblpUrl=https://dblp.org/rec/conf/icst2/PihnastyiUKM24
}}
==Neural network-based approach for predicting the flow material in transport systems==
https://ceur-ws.org/Vol-3790/paper07.pdf
Neural network-based approach for predicting the flow
material in transport systems
Oleh Pihnastyi1, , Victoriya Usik1 , Georgii Kozhevnikov1, and Oleksii Matiash1,
1
National Technical University "Kharkiv Polytechnic Institute", Kirpichova 2, 61002, Kharkiv, Ukraine
Abstract
This article addresses the problem of effectively training a neural network to predict parameters of the
output flow of a conveyor system. It discusses the problems of obtaining a complete set of data for complex
branched structures of multi-section conveyor systems with different section lengths. The problem of
generating a data set for training a neural network is solved using an analytical model of a transport system.
The input parameters for the model include approximations of the incoming material flow and conveyor
belt speed allowing to consider the oscillatory behavior of the transport system's parameters. The study
also examines the impact of peak loads on the material flow at the system's entry point. The findings
demonstrate that the predictive model enables effective analysis of dynamic changes in the transport
system's parameters, including peak flow values.
Keywords
control, PDE-model, distributed system, conveyor 1
1. Introduction
A transport conveyor designed for moving bulk materials is a complex dynamic system with a
transport delay [1 3]. The system includes many long conveyors [4 6] and accumulating bunker
located between them [7, 8]. The conveyor is an important component of the transport infrastructure
of a mining enterprise, offering versatility, easy of automation and high productivity. Transporting
bulk materials represent a significant proportion of the total cost of materials extraction [9, 10] and
increasing the efficiency of the transport conveyor provides a significant reduction in this cost. A
common method for reducing transport costs is to optimize the loading factor of bulk material on a
transport conveyor, based on the use of belt speed control systems [11 13] and regulation of the
volume of material flow coming from the accumulating bunker [14 17]. To construct a training data
set, this work uses an analytical model of the transport system [16]. The model reflects the oscillatory
nature of the system parameters and allows taking into account variable transport delay.
The novelty of this work lies in the integration of neural network techniques with traditional
conveyor system models, which enhances the ability to predict and optimize transportation systems
performance under varying conditions. This approach not only contributes to solving problems in
the field of transport systems, but also offers practical recommendations for the mining industry,
ensuring more efficient and cost-effective transportation of materials.
2. Formal problem statement
The process of transporting material on a belt conveyor is characterized by its complex and non-
linear nature and as a result, the mathematical models developed for this process consist of sets of
ICST-2024: Information Control Systems & Technologies, September 23-25, 2023, Odesa, Ukraine.
Corresponding author.
These authors contributed equally.
pihnastyi@gmail.com (O. Pihnastyi); usik.viktory@gmail.com (V. Usik); heorhii.kozhevnikov@khpi.edu.ua (G.
Kozhevnikov); oleksii.matiash@cit.khpi.edu.ua (O. Matiash)
0000-0002-5424-9843 (O. Pihnastyi); 0000-0002-3515-4849 (V. Usik); 0000-0002-6586-6767 (G. Kozhevnikov); 0009-0000-
3379-3260 (O. Matiash)
© 2024 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
highly complex and non-linear PDEs [18]. It requires highly complicated numerical techniques to
solve them. Therefore, these models are not suitable for control system design. Recently, researchers
in the field of conveyor systems have shown increased interest in neural network models due to their
advantages such as adaptation, fault tolerance and speed of operation. For example, authors in the
study [19] develops five artificial neural network models to predict conveyor belt damage using 11
parameters. In the paper [20] proposed a deep learning-based conveyor belt damage detection
method. An intelligent control system of transporting material on a belt conveyor utilizing the
capabilities of neuro-fuzzy systems is presented in the paper [18]. The papers [21, 22] are devoted to
the development of instrumental and methodological support for the study of conveyor transport
systems with neural network models. However, the authors of these and other articles do not
consider neural network models for branched multi-section conveyor systems.
The purpose of this study is to build an effective model for predicting the values of the output
flow parameters of a branched conveyor transport system. Analysis of experimental studies [23-25]
allows us to make the assumption that, with a sufficient degree of accuracy, the input flow of the
material can be represented in the form of a Fourier series expansion with a limited number of terms
of the series [26]. To ensure a quasi-constant fill factor of the conveyor, it is necessary to synchronize
the value of the input material flow and the belt speed [27]. It follows from this that the value of the
input material flow and the value of the belt speed must be proportional. This allows us to represent
the speed of the belt in the form of an expansion in a Fourier series with the same limited number of
terms in the series. To simplify the demonstration of the analysis of results, the input material flow
and belt speed are presented in the form of a series limited by one term. This approximation of the
flow parameters of the transport system is the basis for the formation of the input parameters of the
analytical model. The use of an analytical model allows for each series of values of input parameters
to calculate a series of values of output parameters of the transport conveyor. Accordingly, it possible
to generate a data set for training a neural network in the model for predicting the flow parameters
of the transport conveyor. The input parameters are represented by harmonic functions containing
the phase shift. This approach is used to model situations when peak values of material flow occur
in a transport system. Special attention is paid to the analysis of these situations in this study. The
proposed model makes it possible to predict the occurrence of such situations that leads to increased
load on the conveyor belt and its gradual destruction.
3. Preparation of a data set for training a neural network
A set of training data is needed for supervised training of a neural network. In our case, these
data represent examples of input data and their corresponding outputs for solving specific problems
of managing an existing transport system. It is difficult to obtain such a data set in the conditions of
real operation of transport systems. This is due to the following reasons: 1) each transport system is
unique in design and sections of one transport system have different lengths; 2) the functioning of
the transport system is carried out in a narrow range of flow parameters, in which economic
feasibility is ensured, but the training data set must be generated in a wide range of values; 3) lack
of measuring sensors in the required places of the transport route; 4) confidentiality of production
information. Therefore, to generate a data set for training a neural network, we use an analytical
model of the transport system [16]. To build this model, we used a simplified transport route diagram
presented in Figure 1. The transport route diagram contains four input conveyors (section m = 1,2,4,5)
and two output conveyors (section m = 7,8). Also, for simplicity, we assume that for a node that
contains an input material stream and two outgoing material flows, the ratio of the values of the
output flows is constant (Figure 2).
Consider such values of the parameters of the transport system:
m ( ) is the intensity of the
g ( )
input flow of material and m is conveyor belt speed. This values are oscillatory in nature and
limited by the minimum and maximum values. The experience of using periodic functions to analyze
the accuracy of approximation of predicted results using a neural network is described in [28-30].
Figure 1: Diagram of a branched conveyor transport route.
Figure 2: Schemes for calculating the balance of flows in the nodes of the conveyor transport route:
a) converging node; b) diverging node.
( ) g ( )
Given this experience flow parameters m , m , that determine the state of the transport
system, and initial condition , that determine the initial distribution of material along the length
of the section, were represented as:
m 3+ m
m ( ) = 0 m + 0 m sin m − , 0m = , (1)
4 24
g m 3+ m
g m ( ) = g0 m + 0 m sin m + , g0 m = , (2)
2 3 8
m 3+ m
m (t ) = 0 m + 0 m sin m + , 0m = . (3)
4 24
The values ) and of the input sections m shown in
Figure 3 and Figure 4.
Figure 3: The intensity of material flow m ) incoming to m th section.
Figure 4: The belt speed gm for m th section.
The data set for training the neural network is generated by using the analytical model [16]. The
data set satisfies the transport route in Figure 1. Le
output flow 1m ( , m ) describes as:
m ( − m )
1m ( , m ) = g m ( ) , m Gm ( ) , (4)
g m ( − m )
1m ( , m ) = g m ( ) m ( m − G ( )) , m > Gm ( ) , (5)
tr m ~ m
were m is the length of the m-th section; m Gm ( ) is an end point
is the transport delay time;
of the transition mode of the m-th section of the conveyor line. The values the material output flow
1m for sections m = 1,2,4,5 is shown in Figure 5. This behavior of the output flow of the material 1m
is explained by the presence of a transition period during which the value of the output flow is
determined by the distribution of the material with a linear initial density m along the m-th
section. The arrows indicate the point in time when the transition period is completed m = Gm .
Figure 5: The material output flow 1m ( , m ) for m-th section.
The change in the linear material density at the output of a section (m = 1,2,4,5) describes as:
m ( − m )
0m ( ,m ) = , m Gm ( ) , (6)
g m ( − m )
0m ( , m ) = m ( m − Gm ( )) , m Gm ( ) . (7)
The changes are shown in Figure 6 and Figure 7. Arrows in Figure 6 and Figure 7 indicate the
point of separation of the time interval into two parts, the left part of which corresponds to the
transitional mode of the conveyor line m Gm ( ) , the right part of which often corresponds to the
established mode of the conveyor line m Gm ( ) . The profile of the linear density 0 m ( , m ) is
formed by two parameters, intensity in-coming material flow m ( ) and the speed g m ( ) separated
section. The value of the output flow 1m ( , m ) determines the value of the input flow m ( ) for the
next section.
Figure 6: The linear density 0 m ( , m ) at the output of the first and second sections.
Figure 7: The linear density 0 m ( , m ) at the output of the fourth and fifth sections.
The duration of the transition period tr m is determined by the speed gm of the conveyor belt
and the length of the section m
tr m
m =
g ()d .
0
m (8)
In the case under consideration (Figure 6, Figure 7), the maximum duration of the transition
period has section number one, tr 1 ~ 2 . For the transition period, the output flow of the material
with the conveyor section 1m ( , m ) is not related to the input flow of the material m ( ) and the
speed of the belt g m ( ) . The transition period of the m-th section is characterized by the average
transport delay time tr m ~ m for this section (Figure 8). The transition period for the considered
transport system (Figure 1) can be estimated by the value
tr ~ max (max( tr 1 , tr 2 ) + tr 3 , tr 4 , tr 5 ) + tr 6 + max( tr 7 , tr 8 ) . (9)
Substituting the values tr m ~ m in (9) allows us to obtain the transition period for the
transport system
tr ~ tr 1 + tr 3 + tr 6 + tr 7 5 (10)
.
The values of the parameters of the transport system of the time interval 0 tr that
corresponds to the time of the transition period should be excluded from the data set intended for
training the neural network. The reason is that during this period of time the output material flow
1m ( , m ) is determined by the initial distribution of the material m ( ) along the transport route
[16], and not by the parameters m ) and gm , when the output flow of the transport system is
independent of the initial distribution of the material. The value of the output flow for m=1, 2, 4, 5
of the section is shown in Figure 9. It should be noted that the value of the output flow of the 5-th
section has pronounced peak values, which are determined by expressions (4), (5).
Figure 8: Transport delay value m ( ) for the m th section, tr .
The appearance of peak values is a consequence of the periodic nature of the supply of raw
materials to the input of the section and the periodic law of change in the speed of movement of the
conveyor belt. Thus, peak loads can occur not only as a result of an uneven random cargo flow of
material incoming to the entrance of the transport system. They can also form inside the transport
system itself. Peak loads in the transport system can occur when the material flows smoothly into
the transport system by virtue of equation (4). The presence of peak values in the data set complicates
the training of the neural network.
Figure 9: The output flow 1m ( , m ) for the m th section, tr .
The transport system (Figure 1) is a distributed system. Such a system is characterized by
transport delay. Transport delay in a distributed system plays an important role in generating output
m ( )
values of flow parameters. The value of the transport delay for the m th section depending
on the time is shown in Figure
considered constant. Thus, the absence of transport delay in the data set for training the neural
network should not lead to a significant error.
4. Prediction model analysis
For training the neural network, a data set was used, which was formed in accordance with the
provisions of the previous partition. This data set is pushed in [31]. Figure 3, Figure 4, Figure 7, Figure
9 demonstrate that the values of training the neural network are presented in a wide range of values.
The neural network is built in accordance with the architecture based on a model from article [32].
To calculate the weight coefficients of the neural network, the back propagation method of error
was used. The updated weight value for each era is calculated based on its old value and error
determined by the parameters of the output layer
W j , k , n +1 = W j , k , n − E j , k , n , (11)
where the learning rate is equal = 10 .
−5
The error E j ,k ,n was distributed between the nodes in proportion to the values of the weight
coefficients. For analysis, the process of training a neural network, the data order for training was
unchanged. This allowed to lead multiple repetitions of training with various network parameters
and compares the effect from changing parameters. Weight coefficients were initialized with random
values in the range 0.0;1.0 with uniform distribution density. For some parameter options, the
learning process reached 300,000 eras. As the input nodes of the neural network for modelling the
transport system, the characteristics m ( ) , g m ( ) of the input sections 1,2,4,5 on the interval
0 Tk = 100 are used. The prediction of the values of the output flow parameters 1m ( ,m ) for
sections m=1, 2, 4, 5 is shown in Figure 10. The results obtained correspond to a neural network
with an architecture of 3 10 1 (the input layer contains three nodes with values 1, g m ( ) , m ( ) ;
the output layer contains one node 1m ( , m ) ; the hidden layer contains 10 nodes). The prediction
error is estimated by the indicator
Nr
MSEm =
1
Nr (z − y ) ,
r =1
m, r m, r
2 (12)
where N r = 9000 is the amount of data for testing a neural network. The indicator value is
{MSE1; MSE2 ; MSE4 ; MSE5} = {10 -3;0,009 ;10 -3;0,0173} .
MSE5 value is significantly higher than MSE1 , MSE 2 , MSE 4 .
A high value MSE5 corresponds to the presence of peak values of the output flow 15 (Figure
10). Figure 11 and Figure 12 show the prediction of the output stream from the transport system, m
= 7.8. The prediction error is MSE78 = 0,22 . A model provides a satisfactory prediction for peak
values of the output flow of the material 18 ( ,1) . For the output flow 17 ( ,1) , the model averages
the peak small values of the function, while trying to repeat the behavior of the function for peak
maximum values.
Figure 10: Prediction of the output flow of material 1m ( , m ) , m=1, 2, 4, 5.
We explain the difference in the prediction for flow 17 ( ,1) and 187 ( ,1) by the fact that the
output flow 17 ( ,1) has a significant spread between the height of the group of maximum peak values
and the group of minimum peak values.
Figure 11: Prediction of the output flow of material 17 ( ,1) .
Figure 12: Prediction of the output flow of material 18 ( ,1) .
The approximation of the output flows 13 ( ,1) , 16 ( ,1) is fairly well presented, for the
intermediate sections m = 3 and m = 6. The prediction results are given in Figure 13 and Figure 14.
The prediction error MSE3 is 0,022 and MSE3 is 0,25. The value MSE for each subsequent section
increases by one order of magnitude. The exception is the last sections. For these sections, the
prediction error remains at the same level as the prediction error of the previous section. We attribute
this fact to the fact that the flows after the sixth section diverge, and the total prediction error also
decreases.
Figure 13: Prediction of the output flow of material 13 ( ,1) .
Figure 14: Prediction of the output flow of material 16 ( ,1) .
5. Conclusion
The results of the analysis the model using a neural network show that the neural network is a good
enough tool for predicting the value of flow parameters of an industrial transport system, which
consists of a very large number of divided sections. The prediction model allows us to determine the
peak values of the parameters of the transport system. An important consequence of the analysis of
the PiKh model of the transport system [16] is that peak loads in the transport system also arise for
the case of a smooth change in the magnitude of the incoming material flow m ( ) and the speed
g m ( ) of the conveyor belt. The peak value is many times bigger than the amplitude of the
background wave. The simplest explanation of the peak value effect can be built on the analysis of
the simple superposition of the waves different length. This effect increases in case periodical change
of the value of the belt conveyor. The occurrence of this effect is one of the causes of damage to
transport systems. One of the problems in studying the influence of the appearance of peak values
on the parameters of the transport system is the difficulty of obtaining them under industrial
conditions due to the unpredictable nature of the occurrence. The prediction model allows you to
identify these situations and ensure their elimination by controlling the flow parameters of the
transport system, for example, conveyor belt speed. To reduce the prediction error in the formation
of the data set for training the neural network, the data that corresponds to the transition mode
should be excluded. In this paper, the technique is given for the estimate the value of the duration
transitional mode for the many sections transport system. The analysis of the transport system model
shows that the reduction of prediction errors can be achieved by including as an additional node into
the input layer the flow parameter, which is the speed of the conveyor belt. An important result of
the conducted research is the conclusion that for transport systems with a high frequency of
oscillation of the conveyor belt speed, the oscillation amplitude of the transport delay value is
significantly less than the average value of the transport delay. This allows us to consider the
duration of the transport delay as a constant value and, accordingly, to conclude that this parameter
has a negligible effect on the prediction results. Such an assumption provides a reason why transport
delay is optional for inclusion in the set of parameters of the input layer of the neural network. The
assumptions obtained in this paper determine the prospects for further research.
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