=Paper=
{{Paper
|id=Vol-3309/paper20
|storemode=property
|title=Analysis of a Dataset for Modeling a Transport Conveyor
|pdfUrl=https://ceur-ws.org/Vol-3309/paper20.pdf
|volume=Vol-3309
|authors=Oleh Pihnastyi,Anna Burduk
|dblpUrl=https://dblp.org/rec/conf/ittap/PihnastyiB22
}}
==Analysis of a Dataset for Modeling a Transport Conveyor==
https://ceur-ws.org/Vol-3309/paper20.pdf
Analysis of a Dataset for Modeling a Transport Conveyor
Oleh Pihnastyi 1 and Anna Burduk 2
1
National Technical University "Kharkiv Polytechnic Institute", 2 Kyrpychova, Kharkiv, 61002, Ukraine
2
Wroclaw University of Science and Technology, 27 W. Wyspianskiego, Wrocław, 50370, Poland
Abstract
The analysis of the works, which considered the use of neural networks for modeling a multi-
section transport conveyor, was carried out. The prospects for the use of neural networks for
the design of highly efficient control systems for the flow parameters of a multi-section
transport conveyor are studied. The problem that limits the use of neural networks for building
control systems for the flow parameters of a multi-section transport conveyor is considered.
The possibility of constructing generators for generating a data set for the process of training a
neural network is being studied. A method for generating a data set based on experimentally
obtained measurements of the instantaneous values of the input material flow as a result of the
operation of industrial transport systems is proposed. Using dimensionless variables, a
statistical analysis of a stochastic flow of material entering the input of the transport system
was performed. An estimate of the correlation time of a stochastic process characterizing the
input flow of material is given. The recommendations on choosing the type of correlation
function for the model of the input material flow were confirmed. It is demonstrated that the
input flow of material is a non-stationary stochastic process. Approximations for modeling the
input flow of materials of the operating transport system are considered.
Keywords 1
transport conveyor, neural network, non-stationary stochastic process, dataset generator
1. Introduction
Conveyor-type transport systems are widely used in the mining industry due to the low cost of
material transportation [1]. The unit cost of transportation is significantly affected by the length of the
transport route and the material load factor of the transport system. Within each section, to reduce the
specific energy consumption, belt speed control systems [2, 3, 4], material flow control systems [5, 6]
coming from the bunker to the section input, as well as control systems based on the energy management
methodology [7, 8]. One of the types of models that are used to design control systems for the flow
parameters of the transport conveyor and diagnose the state of the transport system are models based on
neural networks.
To diagnose the wear level of a conveyor belt, a neural network with the 13-5-1 architecture (13
nodes in the input layer, 4 nodes in the hidden layer, and one node in the output layer) was proposed [9].
The conveyor belt speed control algorithm is represented by a model based on a neural network with 3-
4-3 [10] and 3-10-1 [11] architectures. Transport system state models using a neural network are
presented in [12] (architecture 4-9-14) and [13] (architecture 4-20-1).
The control system of the flow parameters of a multi-section transport contains a model of a
conveyor section using a neural network with the 9-3-2 architecture [14]. It is shown that for the case
of the non-stochastic input flow of material for the transport conveyor, the control algorithm of the input
flow value has satisfactory accuracy.
ITTAP’2022: 2nd International Workshop on Information Technologies: Theoretical and Applied Problems, November 22–24, 2022,
Ternopil, Ukraine
EMAIL: pihnastyi@gmail.com (A. 1); anna.burduk@pwr.edu.pl (A. 2)
ORCID: 0000-0002-5424-9843 (A. 1); 0000-0003-2181-4380 (A. 2)
©️ 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)
A comparative analysis of the computational performance of the models is carried out, followed by
the conclusion that for transport systems with a large number of individual sections [15, 16, 17, 18], it
is advisable to use a neural network when building models of the transport conveyor. It is multi-section
transport conveyors with a large number of sections (several tens or hundreds of sections) that open up
prospects for the widespread use of models based on neural networks. Additionally, it should be pointed
out that models using a neural network scale well.
2. Problem statement
One of the problems that limit the use of neural networks for building control systems for the flow
parameters of a multi-section transport pipeline is the lack of a sufficient data set for training a neural
network. This circumstance is due, on the one hand, to the fact that under production conditions the
transport conveyor operates in a narrow range of flow parameters, which is determined by the
technological features of the material extraction process, on the other hand, the different structure of
the technological route, and, accordingly, the location and connection of the conveyor sections. It is
assumed that the flow of material (t ) , incoming into the transport system is subject to stochasticity
and can be described as a random process
( t ) d ( t ) s ( t ) , (1)
where d (t ) is a deterministic function of time t ; s (t ) is stationary centered ergodic process, which
is determined by the one-dimensional distribution density [18, 19, 20]
1 2
f ( ) exp ,
2 (2)
2 2
with mathematical average m 0 , standard deviation , and correlation function [20]
K () exp .
2
(3)
The correlation time kor
1
, (4)
kor
(ti t j ) .
depends on the method of organizing the production process, determines the characteristic time of the
process, at which the correlation between the sections of the random process ti and t j can be neglected.
Having performed experimental measurements of the values of the input (t ) and output 1 (t , Sd )
flows of material from sections of the transport conveyor with a length of Sd , under the conditions of
production activity, it is possible to form a data set for training a neural network, , on the basis of that a
model of the transport system is built. However, as already emphasized above, due to technological
limitations on the values of the belt speed a (t ) of the conveyor section and the input flow (t ) , as well
as significant differences between the length and branching of transport routes, the data set, constructed
in this way for training the neural network, will be very useful for optimizing the control system of the
existing transport conveyor. This method is not suitable for designing a control system for the flow
parameters of a new transport conveyor with a completely different material transportation route, both
in length and in branching.
Another way to build an exact correspondence between the flow parameters (t ) and 1 (t, Sd ) is to
use the analytical model of the conveyor section [21, 22], which allows you to calculate the value of the
output flow 1 (t, Sd ) from the known value of the input flow and the law of belt speed change. In [23]
], a method for generating a data set for training a neural network on the example of a branched eight-
section conveyor with a deterministic material flow for the input sections of the transport system
(t ) d (t ) ~ d 0 d 1 sin t , (5)
and conveyor belt speed
a(t ) ~ a0 a1 sin a t a , (6)
with arbitrarily given values of coefficients d 0 , d 1 , a 0 , a1 , angular velocities , a and angles ,
a . Further development of the research presented in [23] is to build a random value generator (t ) ,
based on the experimental data of the instantaneous values of the input material flow. This generator can
be used to form the required number of sets of input flows with specified properties (2), (3) with
subsequent calculations of the output flow values using an analytical model of the conveyor section.
This work is devoted to the first step in this study, namely, the use of a set of experimental data to
determine the form of a deterministic function of time d (t ) for a given stationary centered ergodic
process s (t ) , determined by a one-dimensional distribution density (2) and a correlation function (3).
3. Main material
Experimental data characterizing the dynamics of the flow of material incoming the transport system
input are presented in [24–30] and can be used to construct random process generators (t ) (1). To
determine the form of the deterministic function of time d (t ) let's use the results of [29, 31]. After
scanning a graphic image, a set of points i , ti for time values is obtained
ti tmin it , i 0..N , (7)
(t t )
t max min ,
( N 1)
where tmin , tmax are initial and final values of time; N 11591is number of sections i , ti used when
scanning a graphic image.
The tabular data set i , ti obtained as a result of scanning is shown in Fig.1.
Figure 1: Actual volume capacity for the SRs 2000 bucket-wheel excavator recorded in the Belchatow
surface lignite mine during the excavation of one terrace [29]
Let us introduce dimensionless variables
(t )
( ) , (8)
s (t )
s ( ) ,
(t )
d ( ) d ,
where
t t min
, (9)
t max t min
taking into account which the flow of material (t ) can be represented in a dimensionless form
( ) d ( ) s ( ) , (10)
where s () is a stationary centered ergodic process, which is determined by the one-dimensional
distribution density
1 2
f () exp , (11)
2 2
with mathematical average
m 0 ,
standard deviation
1 ,
and correlation function
K () exp ,
kor (12)
kor
kor ,
t max t min
( ti t j )
( i j ) . (13)
(tmax tmin ) (t max tmin )
Taking into account the introduced dimensionless variables, the implementation () takes the form
shown in Fig. 2
Figure 2: Implementation of a stochastic process
For a stochastic process () , known on the time interval [0,1] let's look for a deterministic time
function d () in the form of a Fourier series expansion of a function with period T=1
a0 2 2
d ( ) an cos n bn sin n , (14)
2 n 1 T n 1 T
1
a cos(2n)d 0 ,
0
n (15)
1
b sin(2n)d 0 .
0
n
The expansion coefficient a0 is determined from the condition of ergodicity of a stationary centered
process s ()
1 k
k
m lim
s ( )d 0 , (16)
k 0
whence, taking into account (15), it follows
1 1
a0 a0
0 ( )d 0 2 d 2 , (17)
Let's write the expression for the correlation function
1 k
K d (, an ) lim
k
( ) d ()( ) d ( )d
k 0
1 1 1
( ) ( )d ( ) d ( ) d ( ) d d ( ) d ( )d ,
1
1 0
(18)
0 0
Let's make preliminary simplifications
d ( ) d ( ) a0 bn sin 2n( ) sin 2n( ) a0
n 1
2 cos2nan cos2n bn sin 2n . (19)
n 1
1 2 1
() d ( ) d ( )d 2 an cos2n ( ) cos2nd
a0
0
2 n 1 0
1
2 bn cos2n ( ) sin 2nd . (20)
n 1 0
a0
d ( ) an cos2ncos2n sin 2nsin 2n
2 n 1
bn sin 2ncos2n cos2nsin 2n . (21)
n 1
By virtue of the fulfillment of the identity (15)
1 2
a0 a0
0 2 d ( ) d
4
, (22)
1 2
an cos2n d ( )d cos2n n n sin 2n ,
an ab
(23)
0
2 2
1 2
sin 2n n cos2n .
an bn b
0
bn sin(2n) d ( )d
2 2
(24)
Let's substitute the prepared expressions (20), (22)–(24) into (18) and obtain the form of the
correlation function
K d (, an ) A0 An cos2n Bn sin 2n , (25)
n 1 n 1
where
1 2
1 a
A0
1 0
( ) ( )d 0 ,
4
1 1
a bn
2 2
An 2 an ( ) cos2nd bn ( ) sin 2nd n ,
0 0
4
Bn an bn .
The coefficients a n are determined from the equality equating the coefficients for the same
expansion harmonics
K () K d (, an ) . (26)
where K () is the given function (12) represented by the Fourier series.
4. Analysis of results
Consider the form of the correlation function in the zeroth approximation
1 2
1 a0
1 0
K d (, a0 ) A0 ( ) ( ) d . (27)
4
The distribution density f s ( ) of a random variable s next to the distribution density f ( ) (11) is
shown in Fig.3. To construct the diagram, 50 intervals were selected in accordance with the
recommendations [32, 33] with the number of elements in the histogram N 11591.
Figure 3: The density of distribution f s ( ) of a random variable
For the process (t ) let's define the values
t
max
1
(t )dt ms 4663
t max t min tmin
(28)
tmax 1743.76 ,
tmin 1685.825
t max
1
(t ) ms 2 dt s 2 14702 (29)
t max t min tmin
whence the form for a random process () in the zeroth approximation can be represented by the
equation
a 4663
d ( ) 0 3.2 (30)
2 1470
( ) 3.2 s ( )
An analysis of the distribution histogram presented in Fig. 3 shows that the zero approximation is not
enough to simulate a random input material flow [29]. To describe the non-stationarity of a random
process [29], additional terms of expansion (25) are needed.
For the zero approximation, the correlation function K d (, a0 ) (27) of the random process can be
calculated (30). The chart of the function K d (, a0 ) is shown in Fig.4.
Figure 4: Correlation functions K d (, a0 ) and K ()
For comparative analysis, a monotonically decreasing function K () has been added to the Fig.4
K () exp (31)
kor
with correlation time kor =1/20. Analysis of the results in Fig. 4 shows that the random process, as
expected, has a fairly short correlation time. Adding non-stationary terms to series (14) will make it
possible to smooth the correlation functions K d (, a0 ) .
5. Conclusion
The quality of the neural network training process, and accordingly the accuracy of the multi-section
pipeline model based on the neural network, directly depends on the data set used for training. In this
regard, the formation of a data set for training a neural network is an important practical and theoretical
task, the solution of which is directly related to the development of the theory of control systems for
the flow parameters of a multi-section conveyor. As a method for solving this problem, this paper
considers the construction of generators of a random process that simulates the input flow at the
incoming to the transport system. The solution to this problem is complicated by the fact that for the
existing transport systems the incoming material flow is characterized not only by stochasticity but is
also a non-stationary flow. Thus, the method of constructing an input material flow generator based on
a set of experimental data will allow taking into account these features in close relationship with the
technological features of production. Generators of this kind will make it possible to form the required
number of data sets for high-quality training of neural networks in multi-sectional conveyor models. In
addition, one and the same input data set can be converted into different output data sets depending on
the structure of the transport route and the law of interaction between sections of the transport conveyor.
In this paper, the implementation of a random process is analyzed, which is supposed to be used to
construct a generator of the input material flow. The stochastic process is represented by the canonical
expansion of the non-stationary part in a Fourier series. A statistical analysis of the implementation of
the input material flow is carried out and a model of the input material flow in the zero approximation
is presented. The recommendation to use the correlation function in exponential form for modeling the
input material flow has been confirmed.
The prospect of further research is to improve the accuracy of approximation of the statistical
characteristics of the generator to the input material flow for the available sets of experimental data. An
additional task is to determine the law of distribution of the value of the input cargo flow of material
entering the input of the transport system per unit time.
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