Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks
The mathematical modeling method of the soil contamination based on the neural networks theory is developed. The method was tested based on the facts received during the geochemical research of the Halych district contamination. As the result of mathematical modeling, the isoconcentration lines are...
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irk-123456789-872432015-10-15T03:02:06Z Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks Horbiychuk, M.I. Khrabatyn, R.І. Bandura, V.V. Pasyeka, N.C. Samaniv, L.V. Приложения. Опыт разработки и внедрения The mathematical modeling method of the soil contamination based on the neural networks theory is developed. The method was tested based on the facts received during the geochemical research of the Halych district contamination. As the result of mathematical modeling, the isoconcentration lines are developed and drawn on the landscape map of the area. Разработан метод математического моделирования загрязнения грунта на базе теории нейросистем. Метод опробован на фактическом материале, полученном вследствие геохимических исследований загрязнения территории Галичского района. В результате получено семейство линий изоконцентраций, нанесенных на ландшафтную карту территории. Розроблено метод математичного моделювання забруднення ґрунтів на базі теорії нейромереж. Метод випробувано на фактичному матеріалі, отриманому внаслідок геохімічних досліджень забруднення території Галицького району. У результаті отримано сімейство ліній ізоконцентрацій, нанесених на ландшафтну карту території. 2015 Article Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks / M.I. Horbiychuk, R.І. Khrabatyn, V.V. Bandura, N.C. Pasyeka, L.V. Samaniv // Управляющие системы и машины. — 2015. — № 4. — С. 83–85. — Бібліогр.: 6 назв. — англ. 0130-5395 http://dspace.nbuv.gov.ua/handle/123456789/87243 504.06+004.032.26 en Управляющие системы и машины Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Приложения. Опыт разработки и внедрения Приложения. Опыт разработки и внедрения |
| spellingShingle |
Приложения. Опыт разработки и внедрения Приложения. Опыт разработки и внедрения Horbiychuk, M.I. Khrabatyn, R.І. Bandura, V.V. Pasyeka, N.C. Samaniv, L.V. Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks Управляющие системы и машины |
| description |
The mathematical modeling method of the soil contamination based on the neural networks theory is developed. The method was tested based on the facts received during the geochemical research of the Halych district contamination. As the result of mathematical modeling, the isoconcentration lines are developed and drawn on the landscape map of the area. |
| format |
Article |
| author |
Horbiychuk, M.I. Khrabatyn, R.І. Bandura, V.V. Pasyeka, N.C. Samaniv, L.V. |
| author_facet |
Horbiychuk, M.I. Khrabatyn, R.І. Bandura, V.V. Pasyeka, N.C. Samaniv, L.V. |
| author_sort |
Horbiychuk, M.I. |
| title |
Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks |
| title_short |
Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks |
| title_full |
Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks |
| title_fullStr |
Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks |
| title_full_unstemmed |
Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks |
| title_sort |
mathematical and computer modeling of soil contamination in halych district based on the theory of neural networks |
| publisher |
Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
| publishDate |
2015 |
| topic_facet |
Приложения. Опыт разработки и внедрения |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/87243 |
| citation_txt |
Mathematical and Computer Modeling of Soil Contamination in Halych District Based on the Theory of Neural Networks / M.I. Horbiychuk, R.І. Khrabatyn, V.V. Bandura, N.C. Pasyeka, L.V. Samaniv // Управляющие системы и машины. — 2015. — № 4. — С. 83–85. — Бібліогр.: 6 назв. — англ. |
| series |
Управляющие системы и машины |
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УСиМ, 2015, № 4 83
УДК 504.06+004.032.26
M.I. Horbiychuk, R.І. Khrabatyn, V.V. Bandura, N.C. Pasyeka, L.V. Samaniv
Mathematical and Computer Modeling of Soil Contamination in Halych District Based
on the Theory of Neural Networks
Разработан метод математического моделирования загрязнения грунта на базе теории нейросистем. Метод опробован на фактиче-
ском материале, полученном вследствие геохимических исследований загрязнения территории Галичского района. В результате по-
лучено семейство линий изоконцентраций, нанесенных на ландшафтную карту территории.
The mathematical modeling method of the soil contamination based on the neural networks theory is developed. The method was tested
based on the facts received during the geochemical research of the Halych district contamination. As the result of mathematical model-
ing, the isoconcentration lines are developed and drawn on the landscape map of the area.
Розроблено метод математичного моделювання забруднення ґрунтів на базі теорії нейромереж. Метод випробувано на факти-
чному матеріалі, отриманому внаслідок геохімічних досліджень забруднення території Галицького району. У результаті отри-
мано сімейство ліній ізоконцентрацій, нанесених на ландшафтну карту території.
Problems setting. The mathematical modeling
methods of soil contamination in Halych district,
offered by us, is based on neural networks theory
to provide more precise estimation of elements
content in soil in any point of the district. Among
the values of such estimates the main values are
the concentration or abnormality coefficients of
the chemical elements, the percentage abundance
of elements, summary contamination values etc.
The main research material
Average percentage abundance of elements in
crust is called clark. But in every separate region,
depending on the geological structure, soil type,
geographical zones and other factors, there will be
their own specific percentage abundances of ele-
ments. These specific values are called regional
background. Therefore, only the concentrations
which exceed the clarks and background can be
abnormal, and hazardous for normal geoecosys-
tems progress.
Abnormal concentration of the elements in, for
example, soil, is calculated using formula:
Ca = Ci – Ck – Cf , (1)
where Ck – average abundance of element in crust;
[1]; Cf – average element background.
Formula (1) contains undefined variable Ci –
concentration of element in soil for specified area.
To calculate the value of Ci in any point of the
chosen region we need to approximate the re-
search results with mathematical dependence
Ci = f (X, Y), (2)
where X and Y – the location coordinates of
sampling points.
The analysis of existing approximation points
showed that we should pay attention to the func-
tional approximation method using the neural
network theory [2].
As the result of representation Ci = f (X, Y) it is
necessary to provide the production of appropriate
signals according to the samples and possible signals
which were not included in the sample. The second
condition makes the sample generating very com-
plex. In general, this problem is not solved, but in
every single case we can find the particular solution.
The solution of the function approximation
problem (2) is grounded on the Hecht–Nielsen
Theorem, proving the possibility of an experimen-
tal data approximation by a function of many vari-
ables, possibility of quite a general view through a
two-layer network with full direct links. Such a
network has n neurons in the input layer, 2 1n
neurons in the hidden layer with pre-known acti-
vation functions and m neurons in the output lay-
ers with the unknown activation functions.
This theorem is non-constructive, as it defines
only presentation of any multivariate function of
several variables, using neural networks of fixed
size. The characteristics of the activation function
of hidden layer and the type of activation function
of output layer neurons still remain unknown.
In practice, the requirements of Hacht–Nielsen
theorem to the activation functions are satisfied in
the following way. In hidden layer neurons the
sigma activation functions are used, and for the
output layer the linear activation functions are
used. During the training the parameters of every
single neuron are specified.
84 УСиМ, 2015, № 4
One of the possible problems during the training
of neural network is non-perception. The problem is
when the neural network is good enough for training
sample and the standard deviation between the net-
work output and the experimental data is pretty
small, but when the new data which are not in the
training sample are presented, the error becomes
larger. One of the methods to avoid non-perception
is to increase network. The other is to regularize the
network [2]. Research showed that regularization
decreases the non-perception of network, but in-
creases the training time.
The radial basis networks are more effective to
avoid non perception [3], because they require more
neurons than back propagation neural networks.
In [4] the possibilities of neural networks as the
approximators of dependences (2) were analyzed.
This analysis was based on the precision of func-
tional dependences f (x) reproduced by neural net-
work. We did the analysis of neural networks, tak-
ing into account the non-perception of network,
therefore the network was trained on the given
approximation nodes; then the f (x) values were
calculated in nodes different from the training
samples. As the result of such analysis there was
made the conclusion that the general regression
network from radial basis networks class is the
best choice. Fig. 1 shows the results of depend-
ence (2) approximation using the radial basis neu-
ral network. The inputs were represented with
samples coordinates, which were given as dimen-
sionless quantities using the following formulas:
min
max min
i
i
X Xx
X X
, (3)
min
max min
i
i
Y Yy
Y Y
, (4)
where iX , iY – coordinates of i – th sample,
1i ,N ; minX , minY – minimal values of Xi and
iY ; maxX , maxY – maximum values of Xi and Yi;
N – sample size.
As the training sample the values of quicksilver
concentration in soil i
HgC , calculated as the re-
sults of sample analysis in coordinates Xi, were
used. This results were given as dimensionless
quantities as well:
min
max min
i
Hg Hg
i
Hg Hg
C C
z
C C
. (5)
а
b
Fig. 1. Results of mathematical modeling of quicksilver concentra-
tion in Halych district soils
The last stage of the model construction was
the adequacy testing, which consists of the given
model testing for usability to solve the problem
using the final result. As the adequacy criteria the
correlation coefficient was used [5]:
1
2 2
1 1
N
*
i i
i
zz N N
*
i i
i i
z z
K
z z
,
where *
iz , iz – are the results of modeling and
the real values of quicksilver concentration (in
relative values) for point i.
УСиМ, 2015, № 4 85
The threshold of correlation coefficient is when
the *
i iz z is equal to 1. For the given case which
shows the high degree of the experimental data
equality to the modeling results (Fig 1, a). Quicksil-
ver concentration change (in relative values) as the
function of coordinates x and y is shown on Fig 1, b,
which shows that space surface has signified peaks,
which tells us about the heterogeny of the quicksil-
ver distribution in soils of Halych district.
The trained general regression neural network
gives an opportunity to calculate the quicksilver
concentration in the soil in any part of Halych dis-
trict. To do this we need to calculate the coordinates
using the map and calculate the non-dimensional
values xi and using formulas (3) and (4). The results
are given to the neural network inputs. As the output
of the network we receive the quicksilver concentra-
tion *
iz in non-dimensional quantities. Using for-
mula (5), we can calculate the quicksilver concentra-
tion in soil in dimensional quantity (mg/kg)
min max mini *
Hg Hg i Hg HgC C z C C .
The received value i
HgC gives a possibility to
calculate the abnormal quicksilver concentration in
chosen region of Halych district using formula (1).
The developed method can be used to calculate
the abnormal concentration of other elements in
soil (Pb, As, Cu, F , Mg etc.).
To estimate the usability of soils to breed the
pollution-free production the eco-techno-geoche-
mical maps [6] of specified element dispersion
can be recommended. They are built by drawing
the harmful chemical elements is concentration
lines on the area map. The weak point of this
method is that it gives just an average concentra-
tion values calculated with the certain step.
The more detailed is the map, the less is the
step of isoconcentrations and the bigger is the
volume of the real material required for the con-
struction. Also there is the danger to miss the con-
centration altitudes and this can cause the distor-
sion of eco-techno-geochemical maps.
Conclusions
The developed method of chemical elements
concentration estimation in soils gives an oppor-
Fig. 2. Isoconcentration lines in Halych district soils
tunity for automation of mathematical modeling
process by construction of real concentration
isolines, not their average values. The amount of
such lines is unlimited. This makes possible to
calculate more precise and fairer eco-techno-
geochemical maps. As the example, Fig. 2 shows
the quicksilver isoconcentration lines drawn on
the Halych district map.
1. Vinogradov A.P. The average content of elements in
the earth's crust. // Geochemistry. – 1962. – N 7. –
P. 555–557.
2. Kruglov V.V., Borisov V.V. Artificial neural networks.
Theory and practice. – M.: Hotline – Telecom, 2001. –
382 p.
3. Osovsky S. Neural networks for information process-
ing. – M.: Finance and Statistics, 2004. – 344 p.
4. Horbiychuk M.I., Kohutiak N.I., Kuznetsov E.A. Identi-
fication of static characteristics of technological objects
based on neural networks. // Measuring and computing in
industrial processes. – 2002. – 2, N 9. – P. 139 – 145.
5. Handbook of standard simulation programs. / A.G. Ivakh-
nenko, U.V. Kopp, V.S. Stepashko et al. / Ed. Ivakhnen-
ko A.G. – K.: Technique, 1980. – 184 p.
6. Adamenko O.M., Rud'ko G.I., Konsevych L.M. Ecological
mapping. – Ivano-Frankivsk: Polumya, 2003. – 584 p.
Поступила 30.12.2014
E-mail: ksm@nung.edu.ua, romankhr@yahoo.com,
vikaban@gmail.com, leuro@list.ru
© М.И. Горбийчук, Р.И. Храбатин, В.В. Бандура,
Н.С. Пасека, Л.В. Саманив, 2015
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/HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 5.0 i kasnijim verzijama.)
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/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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/UKR <FEFF04120438043a043e0440043804410442043e043204430439044204350020044604560020043f043004400430043c043504420440043800200434043b044f0020044104420432043e04400435043d043d044f00200434043e043a0443043c0435043d044204560432002000410064006f006200650020005000440046002c0020044f043a04560020043d04300439043a04400430044904350020043f045604340445043e0434044f0442044c00200434043b044f0020043204380441043e043a043e044f043a04560441043d043e0433043e0020043f0435044004350434043404400443043a043e0432043e0433043e0020043404400443043a0443002e00200020042104420432043e04400435043d045600200434043e043a0443043c0435043d0442043800200050004400460020043c043e0436043d04300020043204560434043a0440043804420438002004430020004100630072006f006200610074002004420430002000410064006f00620065002000520065006100640065007200200035002e0030002004300431043e0020043f04560437043d04560448043e04570020043204350440044104560457002e>
/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|