=Paper=
{{Paper
|id=Vol-3842/paper7
|storemode=property
|title=Determination of heterogeneity of composite materials of shell structures by conductometric method
|pdfUrl=https://ceur-ws.org/Vol-3842/paper7.pdf
|volume=Vol-3842
|authors=Andrii Sverstiuk,Taras Dubyniak,Volodymyr Nevozhai,Andrii Remez,Mykola Poshyvak
|dblpUrl=https://dblp.org/rec/conf/bait/SverstiukDNRP24
}}
==Determination of heterogeneity of composite materials of shell structures by conductometric method==
<pdf width="1500px">https://ceur-ws.org/Vol-3842/paper7.pdf</pdf>
<pre>
                                Determination of heterogeneity of composite
                                materials of shell structures by conductometric
                                method
                                Andrii Sverstiuk1,2,†, Taras Dubyniak2,∗,†, Volodymyr Nevozhai2,†, Andrii Remez2,† and
                                Mykola Poshyvak2,†
                                1
                                    I. Horbachevsky Ternopil National Medical University, Maidan Voli, 1, Ternopil, 46002, Ukraine
                                2
                                    Ternopil Ivan Puluj National Technical University, Rus'ka str. 56, Ternopil, 46001, Ukraine



                                                   Abstract
                                                   The paper proposes an approach to simulation modeling of the inhomogeneity of composite
                                                   materials of shell structures based on the conductometric method. The object of research is the
                                                   control of the inhomogeneity of composite materials used for the shell structures of mirror
                                                   antennas by the conductometric method. The information and measuring system for determining
                                                   the inhomogeneity of composite materials by the conductometric method is presented. Typical
                                                   designs of devices for measuring the inhomogeneity of composite materials by the conductometric
                                                   method are analyzed. The shell structure of mirror antennas (mirror reflector or aperture array) is
                                                   used as a control object. For the actuators that ensure the operation of the system, a structural
                                                   calculation and a description of the operating principle are given. A Petri net is presented to display
                                                   the process of verification for the presence of composite inclusions and the probabilistic distribution
                                                   of the time spent by the test material at the working positions P1, P2, P3, P4. The state of the
                                                   working positions of the measuring unit during the control process and the computer program and
                                                   results of visualization of the internal structure of the composite are presented. The errors of the
                                                   measuring channels are analyzed and the permissible values of parameters and operating modes are
                                                   selected. Assumptions about the development of the object of study in the search for optimal design
                                                   characteristics of the device for analyzing and calculating the measurement and study of radio
                                                   engineering characteristics of mirror antennas in the form of standing wave coefficient, gain, and
                                                   radiation pattern at a constant frequency range are predicted.

                                                   Keywords
                                                   antenna mirror, electric arc spraying, composite materials, conductometric method1



                                1. Introduction
                                The development of measuring equipment aimed at providing solutions to the problem of
                                automating the control of various processes (technological, testing, research, diagnostic, etc.)



                                1
                                  BAIT’2024: The 1st International Workshop on “Bioinformatics and applied information technologies”, October 02-04,
                                2024, Zboriv, Ukraine
                                ∗
                                  Corresponding author.
                                †
                                  These authors contributed equally.
                                    sverstyuk@tdmu.edu.ua (A. Sverstiuk), d_taras@ukr.net (T. Dubyniak), v.nevo1971@gmail.com (V. Nevozhai),
                                filvasoxz@gmail.com (A. Remez), claruspuer01@gmail.com (M. Poshyvak)
                                    0000-0001-8644-0776 (A. Sverstiuk), 0000-0003-1529-6951 (T. Dubyniak), 0009-0004-2003-4280 (V. Nevozhai),
                                0009-0005-4846-4650(A. Remez), 0009-0009-9655-4123 (M. Poshyvak)
                                                © 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
is accompanied by a rapid growth in the variety of types of measurements with a steady
expansion of measurement ranges and an increase in speed and accuracy.
   The main prerequisite for expanding the functionality and a fundamental feature of
modern measuring equipment is the introduction of programmable computing power into the
measuring chain, mainly in the form of a microprocessor device or computer.
   The transition from digital measuring instruments and devices to processor-based
measuring instruments has led to the fact that the measuring device has two parts -
hardware and software, since a significant part of the measuring procedure in them is
realized in digital form, i.e., by means of measuring transformations of digital arrays.
Measuring transducers, as measuring instruments designed to convert physical quantities
into output signals convenient for measurement or further transformation, are becoming
increasingly used both in measuring equipment and in automatic process control systems.
   It should be noted that most test methods were developed long ago and over time, only the
equipment for their implementation has improved. The conductometric method of
measurement, which is often used to control composite materials to determine the
inhomogeneities and depth of surface cracks, was used.

2. Analysis of available research
Manufacturing and calculation of mirror antennas on the initiative and direct participation of
Professor Oleg Shabliy and Associate Professor Andriy Rudnyk began at Ivan Pului Technical
University and continues to this day with the search for a technology for forming surfaces
with specified geometric properties and increased accuracy of the shape of the reflective
surface. In particular, as one of the options, the method of forming a reflective surface of a
given profile by electric arc spraying was considered [1]. It was supposed to manufacture a
reflective surface from a mesh material blank placed on a punch by applying an electric arc
spray coating on it, which would reduce the overall dimensions of the shell in terms of
thickness and weight. It should be noted that in order to maintain uniform application, it is
important to correctly position the working unit in relation to the punch surface, i.e., to move
it at a constant distance and orient it normally to each point on the surface.
    Scientists from Ukraine and abroad have been involved in the design, production, and
development of the mirror, which is reflected in [2, 3]. The mirror is intended to fully reflect
the electromagnetic waves incident on it (Fig. 1). Therefore, its surface is made of highly
conductive metals. The surfaces of hard metals are 2-3 times thicker than the thickness of the
reflective layer and have the best reflectivity (the distance at which the amplitude of the
electromagnetic field decreases several times). Solid reflectors are made in the form of metal
sheets or films (foils) that are applied to a lightweight dielectric base of foam or fiberglass.
                                 a)                                        b)
Figure 1: Reflectors in the form of a paraboloid of rotation (a) and a parabolic cylinder (b):  -
distance from the focus to the observation point;  - is the angle between the reflector axis
(FO) and the direction to the observation point.

   To reduce weight and wind load, the reflective surface is sometimes made in the form of
perforated sheets, one- or two-line mesh of round or rectangular wire. In the case of an
inconsistent reflector, part of the electromagnetic energy leaks through it, creating unwanted
back radiation and reducing the antenna gain. To reduce leakage, the characteristic holes
should not exceed (0.1  0.2).., where  is the radio wavelength [4].
   Formation of shells by electric arc spraying and application of composite material. The
formation of mirror antennas (aperture arrays) consists of several stages. The first stage is
deformation of the two-dimensional mesh and fixing of the nodes by electric arc spraying
with aluminum (Fig. 2). The second stage, after sputtering on the punch, is to obtain a surface
with a high temperature and apply a composite material such as polystyrene. Polystyrene is a
polymeric material used in the manufacture of various products due to its unique properties.




Figure 2: Electric arc spraying method for mesh material.

   Depending on the complexity of the structure of the substance, the state in which it is
located, and the corresponding level of technology [5, 6], the methods used to assess the
composition and structure of composite materials are divided into:
   - chemical;
   - structural and mechanical;
   - physical and chemical, including electrochemical (potentiometry, conductometry);
thermoanalytical (differential thermal analysis, calorimetry; X-ray (X-ray diffraction and X-
ray phase); spectral (molecular spectroscopy, photoelectric method, flame photometry,
electron and nuclear magnetic resonance spectrophotometry, infrared and ultraviolet
spectroscopy); optical (light microscopy, reflected light microscopy, refractometry, electron
and scanning microscopy).
   For our case, it is sufficient to use the conductometric measurement method, which is often
used to control composite materials [7]. The conductometric method is a method for
determining the electrical conductivity of electrolytes (systems with an ionic type of
conductivity, which are represented by aqueous and non-aqueous solutions, colloidal systems,
suspensions, pastes, and melts).
   Conductometric analysis allows not only to determine the electrical conductivity of
colloidal systems (e.g., binders, sludge glass), but can also be used to study the degree of
saturation of capillary-porous bodies or the kinetics of hydrolysis, hydration, and dissolution
processes that occur during the curing of binders. By measuring electrical conductivity, it is
possible to control the processes of accelerated curing of building materials (for example,
during steaming or autoclave processing).

3. Description of the created information system
Mathematical modeling of an information and measuring unit for controlling the internal
structure of a composite. The control of the internal structure of a composite includes a
number of methods and techniques for evaluating and analyzing its composition, size and
organization of components. The main methods of controlling the internal structure of
composites include:
    Optical microscopy: It is used to study the structure at the micro level, to assess the size and
shape of inclusions, and to evaluate the homogeneity of the material.
    Electron microscopy: Includes scanning electron microscopy (SEM) and transmission
electron microscopy (TEM), which provide high-resolution images for studying structure at
the nanoscale.
    X-ray diffraction: It is used to analyze the crystal structure of materials, to detect the
presence of crystalline phases and determine their structure.
    Thermal Analysis: Includes Differential Scanning Calorimetry (DSC) and
Thermogravimetric Analysis (TGA) to study the thermal properties and changes in material
structure when heated.
    Nuclear magnetic resonance: Used to study the molecular and atomic structure of a material.
    Ultrasonic inspection: Used to detect defects and assess material uniformity.
    These methods help to study the structure of composites at different levels, from the nano-
to the macro-level, which is important for understanding their properties and improving their
production processes.
    Inhomogeneities in composite materials in shell structures can be caused by various factors
and have different characteristics. Some of the most common types of inhomogeneities in
composites include:
    Inclusions: Small particles or areas of other material that are embedded in the main matrix
material. These inclusions can be random or regular in size and shape.
    Porosity: The presence of pores beneath the surface of a composite that can occur during
the manufacturing process or as a result of mechanical damage.
    Manufacturing defects: Irregularities that occur during the manufacturing process, such as
cracks, bubbles, wrinkles, etc.
    Property variations: Material properties that do not match in different directions or in
different parts of the structure.
    Various methods can be used to model such inhomogeneities, including computational
methods, finite element analysis, analytical models, and experimental methods. In addition, for
each type of inhomogeneity, specific methods can be used to evaluate and predict their impact
on the properties and behavior of composite materials in structures.
    Conductometry is a technique that uses the measurement of a material's conductivity (or
resistance) to determine its properties. To determine inhomogeneities in composite materials
of shell structures, the conductometric method can be used to:
    Pore Detection: Porosity in composites typically has a higher resistivity than the composite
material itself, so measuring the resistivity can help detect the presence of pores.
    Measurement of inclusion concentration: If inclusions have different electrical properties
than the base material, their presence can affect the conductivity. Conductometry can help
determine the concentration of such inclusions.
    Detection of manufacturing defects: Cracks or other defects in a composite can alter its
electrical conductivity, which can be detected by conductometry.
    Assessment of material homogeneity: Different inhomogeneities in a composite can lead to
changes in its conductivity. Conductometry can be used to evaluate material homogeneity.
    To determine the inhomogeneities of composite materials in shell structures, the
conductometric method requires careful analysis of the measurement results and may require
specialized equipment and techniques.
    Different approaches and methods can be used to mathematically model the information
and measurement system for controlling the internal structure of a composite. Here are some
possible stages of creating such a model:
    Define composite parameters: Set parameters that characterize the internal structure of the
composite, such as inclusion sizes, distribution, concentration, material type, etc.
    Selecting the inspection method: Selection of internal structure inspection methods, such as
radiography, ultrasonic inspection, thermal imaging inspection, acoustic inspection, etc. Each
method may require appropriate mathematical models for data analysis and interpretation.
    Development of a mathematical model of the control method: Create a mathematical model
for the selected inspection method. For example, for ultrasonic inspection, a model of the
propagation and reflection of ultrasonic waves in a composite can be created.
    Simulation and analysis of results: Application of the created mathematical model to
simulate the control of the internal structure of the composite and analysis of the results. This
allows us to evaluate the effectiveness of the chosen method and optimize the control setup.
    Model validation: Checking the developed mathematical model against experimental data to
confirm its accuracy and correctness.
    This approach makes it possible to systematically develop and improve the information
and measuring equipment for controlling the internal structure of the composite.
   The digitized data set on the structure of a composite may contain information on various
parameters that characterize its internal structure. Here are some possible parameters and
methods for digitizing them:
   Inclusion sizes: The size of inclusions in a composite can be estimated by processing images
from microscopes. The data can be digitized by measuring the area or diameter of the
inclusion.
   Inclusion distribution: A histogram can be used to evaluate the distribution of inclusions,
where each column corresponds to the number of inclusions within a certain size range.
   Component organization: You can use parameters such as component spacing, angular
relationships, etc. to describe the organization of the composite components.
   Material homogeneity assessment: To evaluate material homogeneity, indicators can be
measured that indicate the degree of inclusion diversity in different areas of the composite.
   Defects and damage: Assessment of defects and damage may include measurement of their
dimension and distribution in the composite.

3.1. Petri net as a mathematical apparatus for studying information processes
To process the results of measuring the current strength using current electrodes, it is
necessary to have its nominal static characteristic, on the basis of which the desired current
strength can be calculated from the measured current value and the appropriate corrections
made.
    When analyzing measurement results, it is often necessary to find an analytical expression
that relates some variables. Such an expression allows you to draw conclusions not only about
the nature of the relationship between these factors, but also to quantify the value of one of
them for a given value of another.
    In some cases, the form of the relationship between variables may be known based on
certain theoretical considerations.
    However, there are often situations when the nature of the relationship between variables
is not known in advance and it is necessary to find a mathematical expression of the
relationship between them based on the experimental data.
    If the nature of the relationship between the variables is known, the problem is reduced to
determining the constant coefficients in the relationship equation using the least squares
method.
    A Petri net is a graphical and mathematical tool for modeling systems and processes. As a
rule, Petri nets are used to model parallel (synchronous and asynchronous) systems and
processes.
    Originally proposed in Karl Petrie's doctoral dissertation, they were further developed in
the works of such scholars as Tadao Murata, Kurt Jensen, Vitaly Kotov, and Anatoly Sleptsov
[8, 9].
    In recent years, an annual conference "Applications and Theory of Petri Nets" has been
held, the Petri Net Newsletter is published in Bonn, several hundred modeling systems for
various hardware and software platforms are known, and implementations of Petri net
processors exist. Areas of application of Petri nets include the study of telecommunication
networks, network protocols, computing systems and computing processes, production and
organizational systems.
3.2. Petri nets as a means of modeling systems and processes
Petri nets are a structure defined by a set of input and output transactions. Modeling systems
using Petri nets.
   Simple Petri nets contain only three basic elements: nodes, transitions, and markers.
Therefore, building models of complex dynamic systems with a large number of interacting
parallel and asynchronous processes and many information and material flows becomes a
rather complicated and cumbersome procedure.
   This significantly narrows the class of system models that can be built on the basis of
simple Petri nets. In such cases, extensions of simple Petri nets are used, which make it
possible to significantly simplify the construction of complex models and their graphical
representation.
   Expanding the capabilities of nodes during modeling.
   Further expansion of the capabilities of Petri nets for modeling tasks is associated with the
transition from the use of nodes with markers and transitions to the use of data warehouses (a
node with a certain data structure) and data streams [10, 11].
   It was mentioned above that in a Petri net, all possible states of the model are indicated by
nodes with markers. In general, nodes act as data stores of a given size, and transitions act as
data flows.
   The capabilities of Petri nodes can be greatly expanded by assigning different types of data
to tokens, such as character strings, integers or real numbers, sets, structures, as is done in
programming languages.
   Display nodes with such markers, you need to specify the types of data and determine the
maximum number of markers of each type that can be in a node. Another way to expand the
functions of mode of access to tokens, i.e., to specify how tokens (data) are received by nodes
and how they are removed from them.
   This allows you to create token queues in nodes in a similar way to how requirements
queues are created in the CMO.
   The choice of queueing and token removal modes depends on the sequence in which you
want to check tokens in nodes. Therefore, it is hardly possible to give general advice on which
access modes to use.
   In simple Petri nets, random access mode is automatically used (the order in which tokens
are queued and the order in which they are removed does not matter to them).
   Extending the capabilities of Petri nodes is a very convenient tool for modeling material
and information flows in production systems.
   Petri net rules and methods of description [12, 13].
   Expanding the possibilities of transitions during modeling.
   Transitions are active network elements that can be triggered in parallel. Whether a
transition can be triggered in parallel or whether it will be triggered earlier than other
transitions must be specified in the transition definition during the simulation.
   The order in which transitions are triggered is determined by the simulation control
program. In order to reproduce the dynamics of the system being modeled, transitions must
be triggered at the appropriate moments in the simulation time.
   A transition can only be excited if the excitation rules are met. To do this, the simulation
control program searches for markers at the input nodes of each transition to check whether
the rules defined by the input arcs are met.
   If the required set of markers in the input nodes of a transition is found, it is triggered. A
transition is triggered when all four conditions are met:
   - the parallelism bandwidth is still not exhausted (i.e., how often a time-dependent
transition can be triggered in parallel with itself);
   - the input nodes of the transition contain a sufficient number of markers with the
necessary attributes that correspond to the expressions of the input arcs;
   - the logical conditions formulated for the attributes of node markers can be fulfilled;
   - the throughput capacity of the output nodes of this transition is such that they are able to
include as many tokens as can be specified by the numbers of the throughput capacity of the
output arcs, i.e., the numbers that determine the number of tokens that will get to the output
nodes.
   Then, the simulation program checks the markers in the input nodes that are destroyed at
the current moment of the model time (for input arcs, a later marker destruction time can be
set), and the markers that will be created for the output nodes are generated after the
transition time has expired (for output arcs, the time on the arc relative to the transition time
can be set).
   Consider the Petri net shown in Fig. 3 (black markers are marked with the symbol #).
When viewing the set of markers in the left part of the network, the simulation control
program checks the excitation rule of the T1 junction. The transition can be triggered by
removing three black tokens from the input node P1, generating one black token at the output
node P2, and five black tokens at the output node P3. The next set of tokens does not allow the
transition T1 to be triggered again, because node P1 must have at least three black tokens.
Such a set of markers can occur, for example, when a transition for which node P1 is the
source node is triggered.
   Transitions that are triggered in model time.
   In order to model dynamic systems, you need to be able to associate the moments of
transition triggering with the model time. There are several types of transitions:
instantaneous, exponential, and deterministic. An instantaneous transition is not associated
with a moment in time, and its switching is performed as described above. This type of
transition is usually displayed on a Petri dish diagram as a line or a narrow rectangle.




Figure 3: Petri net for displaying the process of checking for composite inclusions.

   If the response time of a transition is distributed according to an exponential law, then
such a transition is represented by an unpainted rectangle, and if the response time of a
transition is deterministic, then it is represented by a painted rectangle. A Petri net in which
the response time of transitions is given by a probability distribution is called a stochastic
Petri net [14].
   Parallel triggering of transitions.
    With a sufficient number of tokens in the input nodes, transitions can be triggered several
times in parallel until they run out of tokens. This allows you to describe quite complex real-
world processes and systems. The number of transitions is set by the parallelism value in the
system being modeled. For example, the standard value of parallelism in POSES++ systemis
232, that is, it can vary from 1 to 4294967295, which is sufficient to achieve practical goals.
    Transition T1 is triggered three times simultaneously because the parallelism limit is not
defined. If you set the parallelism value for transition 2, it could only be triggered twice in
parallel. The parallelism limit does not affect transitions that do not have a trigger time
specified. When this time is defined (for example, a fixed time of 10 s), the functioning of the
transition is noted in the statistics of the simulation results, for example: "At time 0, two
triggering events start simultaneously and last for 10 s". At the simulation time of 10 s, the
third triggering starts and continues for 10 s (until the simulation time reaches 20 s).
    Transition priorities.
    Since a transition needs to check the excitation rules to be triggered, a situation arises
when individual transitions compete with each other for the possession of markers. As long as
no priorities are set, competing transitions solve problems randomly, i.e., a random number
generator determines which of them should be checked first with the same probability for all
transitions. If a rule is fulfilled for this transition, it is triggered before those that could also be
triggered.

3.3. Petri net that reproduces the process of composite verification
The transition triggering time can be fixed or calculated. It depends on the time scale used in
the model and the time tick that the model developer determines [15].
   The simulation time is advanced with some fixed value of the time tick, for example, every
second. Time rounding errors do not affect accuracy if the simulation time is specified as an
integer data type Fig. 4.




Figure 4: Probabilistic distribution of the time spent by the test material on the working
positions P1, P2, P3, P4.
     The deterministic value of the triggering time can be directly assigned to the transition
 attribute, while the arbitrary value of the time must be determined (or rather calculated)
 during the modeling process, since it may depend on the values of the marker [16].
     Status of the working positions of the measuring unit during the control process Fig. 5.




 Figure 5: Status of the working positions of the measuring unit during the control process.

    Thus, a new arbitrary time value for the transition is set for each beat of the model time,
 just as for the triggering of the transition.

 4. Program and results of visualization of the internal structure of
    the composite
 Calculation program

      clear all
      %generation of random numbers according to a given    if ((q(i)<Q)&(i>1))
law                                                              s2=s2+1;
      N=10;                                                 end
      Q=0.3;                                                 p4(i)=s1;
      M1=25;                                                  p5(i)=s2;
      D1=5;                                                        tt=tt+T(i);
      t1=normrnd(M1,D1,1,N);                                       t(i)=tt;
       M2=15;                                                       tii=[0:T(i)/50:T(i)];
      D2=7;                                                 n =length(tii);
      t2=normrnd(M2,D2,1,N);                                i2=i2+n;
       M3=22;                                                  p1(i1:i2)=0;
      D3=11;                                               p2(i1:i2)=0;
      t3=normrnd(M3,D3,1,N);                               for j=1:n
       M4=17;                                                  if (tii(j)>=t1(i))&&(tii(j)<(t2(i)+t1(i)))
      D4=8;                                                     p1(j)=1;
      t4=normrnd(M4,D4,1,N);                                   end
       q=rand(1,N);                                            if (tii(j)>=(t1(i)+t2(i)))&&(tii(j)<(t2(i)+t3(i)+t(1)))
        % distribution density functions                         p2(j)=1;
       x=[0:.1:30];                                            end
       f1=normpdf(x,M1,D1);                                           end
       f2=normpdf(x,M2,D2);                                 P1(i1:i2)=p1(1:n);
       f3=normpdf(x,M3,D3);                                   P2(i1:i2)=p2(1:n);
  f4=normpdf(x,M4,D4);                                    i1=i2+1;
 subplot(4,1,1)                                       end
  plot(x,f1), grid                                    nP1=length(P1);
 subplot(4,1,2)                                       nP2=length(P2);
   plot(x,f2), grid                                   figure
   subplot(4,1,3)                                     ti=[0:t(N)/k:t(N)];
  plot(x,f3), grid                                    Ni1=interp1(t,Ni,ti,'nearest');
  subplot(4,1,4)                                      p11=interp1((1:nP1),P1,ti,'nearest');
 plot(x,f4), grid                                     p21=interp1((1:nP2),P2,ti,'nearest');
  % positions P0 P1 P2 P4 P5                          p41=interp1(t,p4,ti,'nearest');
 k=100;                                               p51=interp1(t,p5,ti,'nearest');
 tt=0;                                                 subplot(5,1,1)
  s1=0;                                               stem(ti,Ni1,'o')
 s2=0;                                                grid
 i1=1;                                                subplot(5,1,2)
 i2=0;                                                stem(ti,p11,'o')
 for i=1:N                                            grid
    T(i)=t1(i)+t2(i)+t3(i)+t4(i);                     subplot(5,1,3)
      Ni(i)=N-i+1;                                    stem(ti,p21,'o')
              if ((q(i)>=Q)&(i==1))                   grid
          s1=1;                                       subplot(5,1,4)
       end                                            stem(ti,p41,'o')
       if ((q(i)>=Q)&(i>1))                           grid
       s1=s1+1;                                       subplot(5,1,5)
       end                                            stem(ti,p51,'o')
             if ((q(i)<Q)&(i==1))                     grid
          s2=1;
    end



5. Visualization of the digitized data set on the composite structure
To conduct simulation modeling of the digitized data set on the composite structure, a
MATLAB program code was developed and four random samples `t1`, `t2`, `t3` and `t4` of
size `N=10` each were generated using a normal distribution with different parameters `M`
(mean) and `D` (standard deviation) for each sample. The probability density of the
distribution is then calculated for each sample using the `normpdf` function to display a
distribution density plot.
   Using ``subplot (4,1,1)`` to ``subplot (4,1,4)`` creates four plot windows, each plotting the
density of the distribution for the corresponding sample. Each plot is located on the
corresponding row of the subplot grid, with the `subplot` arguments indicating the row
number, the number of rows in the grid, and the number of subplots per row.
   The results of the measurement data are digitized and visualized in the information block
for easier interpretation.
   A digitized data set on the structure of a composite may contain information on various
parameters that characterize its internal structure.
   The digitized data can be presented in the form of a table, where each row corresponds to a
specific composite sample, and the columns represent various parameters characterizing its
structure. This allows for further analysis and modeling of the composite structure. To
visualize the measurement data, the information block uses a graphical interpretation in the
form of a color map, and a function with an offset of 40 is used to construct a contour plot. It
should be noted that the conductive cathode is located in the center of the material, and their
anodes are usually somewhat spaced along the edge of the mirror.
    The resulting graphical representations in Fig. 6 (a,b,c) allow us to draw conclusions about
the structure of the composite material. We can say that the material is suitable for use
without negative inclusions and surface cracks. It is of higher quality in the center, and closer
to the edge it has fewer non-conductive inclusions.




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                                    a) monochrome representation;
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                                        b) color representation;
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             40



             30
                                                                                              15


             20

                                                                                              10
             10


                                                                                              5
                  1     2         3   4   5    6      7           8        9        10   11


                                c) refractive representation;
Figure 6: Processing of measurement data in the information block at l - length, and s - depth.
with a current measurement from 0 to 40 mA:
   a) monochrome representation of the structure of the composite material;
   b) color representation of the structure of the composite material;
   c) refractive representation of the composite material structure.

   All this is depicted graphically and can be seen in the visualization program.

6. Visualization of the digitized data set on the composite structure
Program for visualizing the internal structure of a composite

 clear all
 F=[1 1 1 0 0 0 0 1 1 1 1;                                0 0 0 1 0 0 0 0 0 0 0;
    1 1 2 1 1 1 1 0 0 0 0;                                0 2 0 0 0 0 0 0 0 0 0;
    0 1 1 1 0 0 0 0 0 0 0;                                 1 3 4 0 0 20 23 0 4 0 1;
    0 1 3 7 14 0 16 8 1 1 3;                               1 3 0 0 0 33 29 19 8 3 2;
    0 2 3 0 21 28 25 16 6 1 1;                             1 4 0 0 0 30 27 18 0 3 1;
    1 3 4 0 0 0 0 0 10 2 0;                                1 3 5 0 0 19 18 12 5 1 0;
    1 3 4 0 27 0 0 20 9 1 0;                               0 2 3 4 6 8 7 4 1 0 0;
    1 2 4 14 17 19 17 11 4 0 0;                            0 0 1 1 2 2 2 0 0 0 1;
    0 1 2 5 6 7 5 2 0 0 0;                                 0 0 0 3 2 1 0 0 0 2 3;
    0 0 0 0 0 1 1 0 0 0 1;                                 0 0 0 0 0 0 0 1 1 1 1;
    0 0 0 0 0 0 1 2 1 1 1;                                 0 0 0 1 1 1 1 0 0 0 0;
 % 1 1 1 2 2 1 1 0 0 0 0;                                  0 1 2 1 0 0 0 0 0 0 0;
 % 0 1 1 1 1 1 1 0 0 0 0;                                  0 1 1 8 14 19 15 6 0 0 1;
 % 0 0 0 0 0 0 0 0 0 0 0;                                  0 1 2 16 22 26 22 12 4 1 2;
 % 0 1 1 7 0 16 12 4 0 0 3;                                1 2 3 24 29 32 28 18 8 3 3;
 % 0 1 2 13 0 0 0 14 4 0 0;                                1 3 4 22 26 30 27 18 9 3 1;
 % 1 2 3 0 0 0 04 23 10 1 0;                               0 2 4 12 16 19 18 12 5 1 0;
 % 1 3 4 0 0 0 0 0 11 1 0;                                 0 1 3 3 5 8 8 5 2 0 0;
 % 0 2 4 14 18 21 20 14 6 0 0;                             0 0 1 0 1 3 3 2 0 0 0;
 % 0 1 3 6 7 8 7 4 1 0 0;                                  0 0 1 1 2 2 1 1 1 1 1;
 % 0 0 1 1 1 1 1 0 0 1 2;                                  0 0 0 0 0 0 0 1 1 1 1;
 % 0 0 1 0 0 0 0 0 0 1 2;                                  0 1 1 1 1 1 1 0 0 0 0;
    0 0 0 0 0 0 0 1 1 1 1;                                 0 2 3 1 0 0 0 0 0 0 0;
    0 0 0 1 1 1 1 0 0 0 0;                                 0 1 3 4 1 1 1 0 1 0 0;
   0 0 1 1 0 0 0 0 0 0 0;                              0 2 3 0 1 0 0 15 5 1 1;
   0 1 1 8 14 19 0 7 1 1 4;                            1 3 4 0 30 0 0 20 9 3 1;
   0 1 2 15 22 27 0 1 6 2 2;                           1 3 4 0 0 0 0 0 9 3 0;
   1 2 3 22 29 35 0 0 0 2 0;                           1 2 4 0 0 0 20 13 6 0 0;
   1 3 4 22 27 31 0 0 9 1 0;                           0 1 2 3 6 8 8 5 1 0 0;
   0 2 4 15 0 0 0 0 4 0 0;                             0 0 0 0 0 1 1 0 0 0 0;
   0 1 3 6 7 7 4 1 0 0 1;                              0 0 0 0 0 0 0 0 0 1 2;
   0 0 1 0 1 1 0 0 0 0 1;                            %
   0 0 1 0 0 0 1 1 1 1 1;                            % 0 0 0 0 0 0 0 1 1 1 1;
   0 0 0 0 0 0 0 1 1 1 1;                            % 0 1 1 1 1 1 1 0 0 0 0;
   0 0 0 1 1 1 1 0 0 0 0;                            % 0 2 3 1 0 0 0 0 0 0 0;
   0 1 2 1 0 0 0 0 0 0 0;                            % 0 1 3 6 12 10 16 8 2 2 5;
   0 1 1 5 0 0 14 6 0 0 1;                           % 0 2 3 13 0 27 25 16 7 2 2;
   0 1 2 0 0 0 0 10 5 0 0;                           % 1 3 4 20 0 0 0 23 10 2 0;
   1 2 3 0 0 3 0 0 10 2 0;                           % 1 3 4 0 0 0 0 20 9 1 0;
   1 3 4 0 0 0 0 12 5 1 0;                           % 1 2 4 14 0 0 17 11 4 0 0;
   0 1 3 6 8 8 6 3 1 0 1;                            % 0 1 2 6 7 7 5 2 0 0 0;
   0 0 1 0 1 1 1 0 0 0 1;                            % 0 0 0 1 1 2 1 0 0 0 0;
   0 0 1 0 0 0 1 1 1 1 1;                            % 0 0 0 0 0 1 2 1 0 0 0;
   0 0 0 0 0 0 0 1 1 1 1;                            %
   0 0 0 1 1 1 1 0 0 0 0;                            % 0 0 0 0 0 1 1 1 1 0 0;
   0 0 2 1 0 0 0 0 0 0 0;                            % 0 0 0 0 0 1 2 2 1 0 0;
   1 0 0 2 9 14 12 5 0 0 3;                          % 0 1 2 0 0 1 2 2 1 0 0;
   1 1 1 0 0 0 2 1 4 2 3;                            % 0 1 3 5 12 17 14 6 0 0 1;
   1 2 2 2 2 3 2 18 8 4 3;                           % 0 2 3 12 0 0 24 15 5 0 0;
   1 2 3 2 2 3 27 18 9 3 1;                          % 1 3 4 0 27 0 0 23 11 3 0;
   1 2 3 1 1 2 1 1 5 0 0;                            % 1 3 4 0 0 0 30 22 11 4 0;
   0 1 2 3 5 8 8 5 1 0 0;                            % 1 2 4 14 17 20 18 12 6 2 1;
   0 0 1 0 0 1 1 0 0 0 0;                            % 0 1 2 6 8 8 6 3 1 0 1;
   0 0 0 0 0 0 0 0 0 0 0;                            % 0 0 0 2 2 3 2 0 0 0 0;
   1 0 0 1 1 1 1 1 1 1 1;                            % 0 0 0 0 1 2 2 1 0 0 0;
   0 0 0 2 2 2 1 1 1 1 1;                              1 1 2 1 1 1 1 0 0 0 0;
   0 0 0 2 2 1 1 1 1 1 1;                              0 1 2 0 0 0 0 1 1 1 1;
   0 1 1 6 0 0 0 5 0 0 2;                              0 0 1 0 0 0 0 0 1 1 1;
   0 1 2 0 0 0 0 0 4 0 0;                              0 1 3 9 0 0 17 8 0 0 2;
   1 2 3 0 0 0 0 0 10 2 0;                             0 2 3 0 0 0 26 16 6 1 0;
   1 3 4 0 0 0 0 0 10 2 0;                             1 3 4 0 0 0 33 0 10 2 0;
   0 2 4 0 0 0 0 0 5 2 1;                              1 3 4 0 0 0 0 0 0 2 0;
   0 1 3 7 8 8 5 2 0 1 2;                              1 2 4 0 16 0 0 11 5 1 0;
   0 0 1 1 1 1 0 0 0 1 2;                              0 1 2 5 6 7 5 2 0 0 1;
   0 0 1 0 0 0 1 1 1 1 1;                              0 0 0 0 1 1 1 0 0 0 0;
   0 0 0 0 0 0 0 1 1 1 1;                              0 0 0 0 0 1 2 1 0 0 0]
   0 0 0 1 1 1 1 0 0 0 0;                            contourF(40-F)

    The significant results obtained in the simulation of the heterogeneity of composite
materials of shell structures using the conductometric method are the basis for their use in
instrumentation and radio engineering [17-20] and cyber-physical biosensor systems [21-23].
As an example, for the rapid and reliable transmission of information and data to specialized
clinics of the results of assessment and prediction of medical indicators of human health,
which is especially relevant for the transmission of data and diagnostic information in
telemedicine systems or other systems.

7. Conclusions
An important task for the instrumentation industry is to provide production, control, and
repair facilities with high-quality and reliable instruments. Different industries are closely
interconnected, and therefore, to fulfill the above task, the metallurgical and metalworking
industries are faced with the task of improving the quality of metal materials and alloys. To
evaluate mechanical properties due to a wide variety of operating and processing conditions,
tests are carried out that to some extent simulate these conditions. At the same time, for the
most reliable prediction of serviceability in a structure, a set of mechanical properties
determines the performance.
    In the course of the work, the methods of manufacturing antenna systems and
manufacturing reflective surfaces based on new technological and design ideas are considered.
The process of formation of shells from mesh material that can be used for the manufacture of
axisymmetric and non-axisymmetric reflectors or individual elements of mirror antennas is
investigated.
    One of the tasks investigated in shell formation is to find the position of the mesh elements
after deformation, which in our case is reduced to finding the position of the mesh nodes after
deformation. finding the position of the mesh elements after deformation, and applying the
composite material.
    It should be noted that most test methods were developed long ago and over time, the
equipment used to conduct them has only improved. The conductometric method allows us to
draw conclusions about the suitability of the material and is effective for identifying
inhomogeneities or surface cracks.
    Designing embedded systems on a modern element base significantly increases
development efficiency by reducing time, miniaturizing power consumption, and increasing
speed and reliability. Today, the task of acquiring skills in the development of information and
control devices based on microcontrollers and programmable logic devices that allow the
implementation of algorithms of high complexity is relevant. Carry out automated collection,
display and transmission of measurement information to a computer and automated
processing of data on the results of the experiment in order to assess the quality of the
technological process of its manufacture.

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