The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability
The modeling is considered of behavior of metal structures with changing geometric characteristics, which functioning in aggressive external environments. Information about the parameters of the external environment is incomplete or inaccurate. To formalize this information proposed to use the mathe...
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| Zitieren: | The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability / L.I. Korotka, Y.A. Кorotka // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2017. — Вип. 16. — С. 64-71. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1338352020-12-08T14:42:57Z The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability Korotka, L.I. Korotka, Y.A. The modeling is considered of behavior of metal structures with changing geometric characteristics, which functioning in aggressive external environments. Information about the parameters of the external environment is incomplete or inaccurate. To formalize this information proposed to use the mathematical apparatus of the theory of fuzzy sets and interval analysis. The opportunities of the application of the ways have been examined. Розглянуто моделювання поведінки металевих конструкцій зі змінними геометричними характеристиками, які функціонують в агресивному зовнішньому середовищі. Інформація про параметри зовнішнього середовища є неповною або неточною. Для формалізації цієї інформації запропоновано використовувати математичний апарат теорії нечітких множин та інтервального аналізу. 2017 Article The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability / L.I. Korotka, Y.A. Кorotka // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2017. — Вип. 16. — С. 64-71. — Бібліогр.: 7 назв. — англ. 2308-5916 http://dspace.nbuv.gov.ua/handle/123456789/133835 004.8:004.94 en Математичне та комп'ютерне моделювання. Серія: Технічні науки Інститут кібернетики ім. В.М. Глушкова НАН України |
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The modeling is considered of behavior of metal structures with changing geometric characteristics, which functioning in aggressive external environments. Information about the parameters of the external environment is incomplete or inaccurate. To formalize this information proposed to use the mathematical apparatus of the theory of fuzzy sets and interval analysis. The opportunities of the application of the ways have been examined. |
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Korotka, L.I. Korotka, Y.A. |
| spellingShingle |
Korotka, L.I. Korotka, Y.A. The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability Математичне та комп'ютерне моделювання. Серія: Технічні науки |
| author_facet |
Korotka, L.I. Korotka, Y.A. |
| author_sort |
Korotka, L.I. |
| title |
The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability |
| title_short |
The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability |
| title_full |
The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability |
| title_fullStr |
The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability |
| title_full_unstemmed |
The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability |
| title_sort |
use of elements of computational intelligence in problems of forecasting of corroding constructions durability |
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Інститут кібернетики ім. В.М. Глушкова НАН України |
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2017 |
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http://dspace.nbuv.gov.ua/handle/123456789/133835 |
| citation_txt |
The Use of Elements of Computational Intelligence in Problems of Forecasting of Corroding Constructions Durability / L.I. Korotka, Y.A. Кorotka // Математичне та комп'ютерне моделювання. Серія: Технічні науки: зб. наук. пр. — Кам’янець-Подільський: Кам'янець-Подільськ. нац. ун-т, 2017. — Вип. 16. — С. 64-71. — Бібліогр.: 7 назв. — англ. |
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Математичне та комп'ютерне моделювання. Серія: Технічні науки |
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Математичне та комп’ютерне моделювання
64
UDC 004.8:004.94
L. I. Korotka*, Cand. of Tech. Sciences, Associate Professor,
Y. A. Кorotka**, Student
*Ukrainian State Chemical Technology University, Dnipro,
**Oles Honchar Dnipro National University, Dnipro
THE USE OF ELEMENTS OF COMPUTATIONAL
INTELLIGENCE IN PROBLEMS OF FORECASTING
OF CORRODING CONSTRUCTIONS DURABILITY
The modeling is considered of behavior of metal structures
with changing geometric characteristics, which functioning in ag-
gressive external environments. Information about the parameters
of the external environment is incomplete or inaccurate. To formal-
ize this information proposed to use the mathematical apparatus of
the theory of fuzzy sets and interval analysis. The opportunities of
the application of the ways have been examined.
Key words: fuzzy sets theory, interval analysis, modeling, fo-
recasting of construction durability, computational intelligence.
Introduction. In the different branches of industry and building one the
mechanical systems with changing characteristics are widely used, the actuali-
ty of the problem of modeling their behavior being caused by it. The example
of such systems can be constructions functioning in the external aggressive
mediums and corroding. One the peculiarities of this article is that the parame-
ters of aggressive medium (AM) are examined like quantities the information
of which are incomplete or inaccurate. If the parameter of aggressive medium
is examined as the corrosion rate when being absence of voltage it will be
obviously that its significance cannot be determined uniquely.
In the real conditions this parameter depends on the whole range of fac-
tors: medium temperature, its moisture, grade of saturation of different ele-
ments and others. On the one hand quantitative characteristics of all these fac-
tors are determined with difficulty, on the other hand — can change in the
wide range during the whole term of exploitation. When setting the task the
medium is known in the best case to have that or another grade of aggression
which can be described with help of linguistic variable [1, 4].
Statement of the problem. Traditionally for solving the task of fore-
casting of durability of corroding constructions the determinate method
has been used (corrosion rate was supposed given dotty quantity) and fol-
lowing statement (further the task in the precise setting) has been used:
1 2
*
* min , , , ,
: , 0, 1, ,
, 0, .
N
i i
j j
t t t t
t t c i N
t c j J
(1)
© L. I. Korotka, Y. A. Korotka, 2017
Серія: Технічні науки. Випуск 16
65
Here *t — the design value of the durability of the construction;
N — quantity of the elements in the system; J — quantity of the ele-
ments working on compression; — assumed voltage; ,i t c —
current voltage in i-element; * ,j t c — critical voltage of stability loss;
c — vector of the parameters of the aggressive environment, in this ca-
pacity, the paper considers 0v — corrosion rate of unloaded material.
When modeling corrosive process in the work the influence of the
mechanical voltage on the corrosion rate is taken into account, that results
in the appearance of the feedback in the scheme of solving the task of fo-
recasting of durability [2].
Solving the task of forecasting of durability in particular allows to de-
termine the predictable significance of durability of every element taking into
account changes of voltages in them and, therefore, in the whole system.
As it has been mentioned above, information about parameters AM is
incomplete and corrosion rate can be set by some interval 0 0 0[ ; ]v v v ,
levels of which are determined by the significance of the linguistic varia-
ble — «grade of medium aggression». This interval is treated as a large
number of possible significances which the parameter corrosion rate can
take in the process of modeling behavior of corroding construction (fig. 1).
Fig. 1. The scale of conditional partitioning into intervals of values linguistic
variable «degree of aggressiveness of the environment»
Then fuzzy setting task of forecasting of durability can be written:
1 2
0
*
0
* min , , , ,
: , 0, 1, ,
, 0, .
N
i i
j j
t t t t
t t v i N
t v j J
. (2)
The procedure of calculation of forecasting durability of the element li-
able to corrosion or determination of its the calculation of strained condition
(SC) in some moment of time supposes the joint using of some numeral
Математичне та комп’ютерне моделювання
66
method of calculation SC (in this work — method of final elements (MFE))
and numeral method of solving the Cauchy task for system of differential
equations (SDE) describing corrosion process. As a model of accumulation
of geometrical damages V. M. Dolynskiy model is examined [2]:
0 1i
i
d
v k
dt
, (3)
where i — depth of corrosion damage of i-element of the construction;
k — coefficient taking into account the influence of strained condition on
the corrosion rate.
Solving this SDE is possible only numerically, for example, by Euler
method [2, 3] at that solving the task SC is done in every unit of the tem-
porary net:
11 1
0 1
ss s s s
i i t ih v k
. (4)
Here s — number of iteration; th — step of integration.
Methods of formalization of incomplete information. It is obviously
that probabilistic stochastic method can be alternative to the determinative
method of solving tasks of forecasting durability at inaccurate data. However,
at that it is necessary to carry out rather non-trivial conditions (for example,
statistical stability, knowledge of distribution of laws of random quantity or
their parameters, information of which, as a rule, is absent). That’s why the
using of this method is connected with some difficulties.
Two directions can be noted for formalization of incomplete information
which have appeared practically simultaneously, these are the mathematical
device of the fuzzy sets theory (FST) and the device of classical interval anal-
ysis (IA). They can be used depending on solvable tasks and problems. Let’s
examine the possibility of their using when solving this kind of tasks.
The interval analysis and its methods have a value in the tasks where
ambiguities appear from the very beginning and are the essential pats of set-
ting tasks [6, 7]. Let’s note that using the intervals doesn’t require knowledge
of the laws or parameters of distribution of random quantity. The interval
quantity can have and can’t have the distribution on interval. Moreover all
points of the interval are «equitable» (but it doesn’t mean that they are distri-
buted on the interval equally, if, of course, there is no statistical information).
When solving the tasks of forecasting of durability in the statement
(2) the device of interval analysis has been used. Since the parameter AM
is examined as interval quantity so it is reasonable to use interval methods
for solving SDE. For this purpose a wide range of double and interval me-
thods can be used [7]. In this case double solving of the task of forecasting
of durability of corrosive constructions can be received.
Серія: Технічні науки. Випуск 16
67
However, it ought to take into account a range of peculiarities of
these methods, for example, so called effect of Moor overspeeding or ef-
fect of unpacking which is connected only with inside properties of inter-
val methods regardless of mistakes of numeral solvents [7].
In the most cases guaranteed marks of the error of the result are ne-
cessary. Then a posteriori marks of the numeral solvent, for example,
based on the majorizing function by Lozinckiy.
It should be noted not going into detailed describing these methods
that in this article for the construction of double solvent of Cauchy task for
SDE type (3) with the parameter given by interval the task was being
solved approximately with using the method by Runge-Kutta of the first
order. As a result the interval solvent of Cauchy task has been received
min max 0 0[ * ; * ] [ *( ); *( )]t t t v t v , the width of which, when it is neces-
sary, can be accurated.
Obviously, the using interval analysis allows to formalize incomplete
information about AM parameters and receive the interval of numeral sol-
vent of the task of the forecasting of durability. However, there are some
specific peculiarities of using of the interval numeral methods, which are a
feature of the class of differential equations systems describing corrosion
wear (3). For determination in the quality of corrosive element let’s ex-
amine a rod of a circular section at the monoaxial loading. These problem
aspects are described in sufficient detail in [3].
If there is a possibility of the construction of the belongings function
of the corrosion v rate it is reasonable to use the device FST. For for-
malizing fuzzy data -level principle of summarizing is used [4]. In the
article the construction of the belongings function is made with using di-
rect expert marks [4, 5].
Using levels of the sets allows to receive not only the interval of
changing the significance of the durability but also its significance defuzzy
[5] simultaneously with corresponding significance of the belongings
function t .
Using interval numeral methods or the device of the fuzzy sets theory
at SDE solvent, describing the process of the accumulation of the geome-
trical damages, allows to take into account fuzzy character of the medium
parameter, however, it is mated with large calculating inputs. Especially
this problem becomes actual in the case when the task of forecasting of the
durability is a part of more general task — the determination of optimal
parameters of corrosive constructions, when limit functions suppose the
determination of the durability of the construction and the solvent of the
task of nonlinear mathematical programming at every step.
Procedures for representing the corrosion rate as a fuzzy value in the
form of a tuple of its values, as well as converting a fuzzy set of longevity
Математичне та комп’ютерне моделювання
68
values into a clear number are well known [1, 4]. Naturally, their implementa-
tion does not represent any computational complexity and does not have a
significant effect on the speed of the algorithm. Significantly greater com-
plexity from this point of view is the task of determining the values of the
tuple of longevity, corresponding to the values of the tuple of corrosion rates.
From the analysis of the formulas of the analytical formulas [2] follows
that there is a relationship between the rate of corrosion 0
iv and the value it .
Therefore, for any value 0
iv , the value it can be determined by the formula:
0
0
i
j i
j
v
t t
v
. (5)
Then it is possible to use this relationship to calculate all values of
the tuple of longevity using only one known solution it . There will be no
significant increase in computing costs in this case.
Unfortunately, this approach turns out to be applicable only for stati-
cally determinate systems.
In fact, two factors influence the change in stresses in the elements of
a statically indeterminate truss: the change in the cross-sectional area of
the rod and the change in internal forces due to a change in the stiffness of
all elements, which in turn depends on the rate of corrosion. This fact is
confirmed by the following graphic illustration, shown in fig. 2.
Obviously, the described situation can lead to a deliberately wrong
decision, that is, not only the form of the durability property function, but
also the boundaries of the fuzzy set itself, in this case [ ; ]i jt t changes sig-
nificantly. Thus, the hypothesis that, knowing the tuple of the corrosion
rate, one can use formula (5) and obtain the corresponding tuple of longev-
ity, is refuted by numerical experiments.
Fig. 2. Tuples of durability for the FE (1) and FE (3)
Серія: Технічні науки. Випуск 16
69
The results are given for two finite elements (FE): FE (1) and FE (3).
In this case, proposed to use the representation of the durability of the con-
struction as a fuzzy set in the following form:
2 11
1 1 1
&
k kNk i j
k k
k k ki j
t t
t
t t
, (6)
where , [ ; ], 1 1; 2 2k k
i j i jt t t t k N
, k1 — is the number of the
element of the tuple in which the functions that determine its limiting
state change.
In order to avoid such situations in the calculation of the constraint
functions that determine the limiting state of the construction, it is neces-
sary to calculate all the elements of the tuple of longevity.
Thus, the determination of the durability of corrosive structures in-
volves calculating the longevity for all points in the tuple of corrosion rate.
Consequently, the use of α-levels leads to a multiple increase in computa-
tional costs, and the problem of improving the efficiency of the computa-
tional algorithm acquires an independent value.
In order to improve the efficiency of computational methods using
FST, it is proposed to use several neural networks that allow us to deter-
mine the rational parameters of numerical procedures for a system of dif-
ferential equations of the form (3).
Numeral results. For numeral illustration the solvent of the task of
forecasting of the durability of the rod stretched by the force Q is ex-
amined. Initial data: 12Q kN ; limiting voltage 240 MPa ; starting
external 2,5 cmR and inner 1,25r cm ; integration step 0,5;3th ;
coefficient of influence of voltages 10,003k MPa ; given limiting sig-
nificance of error of the numeral solvent 5 6 % .
When solving the task of the forecasting of durability to avoid men-
tioned above supernumerary situations [3]. Euler method has been used.
The quantity of α-levels was taken equal to six.
Dephased significance of the durability deft when using the fuzzy
sets theory has been obtained by the centroid method [4, 5]; avt average
significance of the interval of the durability min max* ; *t t .
For bigger obviousness the author deliberately gives a quantity avt to
demonstrate an impossibility of using an average mark of the significance
of the durability (table 1).
Математичне та комп’ютерне моделювання
70
Table 1
The results of solving the problem of forecasting in various productions
0v , cm/year *t ,
years
min max ,
2av
t tt
years
_ ,av tuplet
years
deft ,
years
Different statements
0,1 5,16 – – –
Precise statement (IA)
[0,90; 0,11] [4,62; 5,68] 5,15 – –
[0,06; 0,14] [3,63; 8,56] 6,09 – –
Fuzzy statement (FST)
[0,09; 0,11] [4,69; 5,74] 5,22 5,19 5,08
[0,06; 0,14] [3,69; 8,61] 6,15 5,52 5,97
Where the mean for all elements of the tuple:
2 1
1
_ 2 1
N
i
i
av tuple
t
t
N
.
Note that in order to obtain a tuple of durability (Fuzzy statement), the
problem was solved for all points of the velocity tuple [4, 5] and point values
(defuzzy) values were obtained: 0 0,1 cm/ yeardefv ; 1,42323 year;th
5,97425 yeardeft 0,9455deft ; 0,05638def .
On the base of the analysis of the numeral experiments it should be
noted that given methods allow to obtain and estimate the result at the pre-
cise or fuzzy data. At its bottom the method of the interval analysis is for-
malized and algorithmed well enough. Using set levels allows to obtain the
defuzzy significance of the durability with its function of belonging t ,
which allows to establish the grade of belongings deft to the fuzzy set t .
Conclusions. The methods of formalization of inaccurate or in-
complete information about parameters of external aggressive medium
with the help of the mathematical analysis of the fuzzy sets theory and
interval analysis are suggested. The possibilities of their using and some
problem aspects when solving tasks of the forecasting of the durability
of corrosive constructions are examined. When using the mathematical
apparatus of the theory of fuzzy sets with the aim of increasing the effi-
ciency of computational methods, it is suggested to use artificial neural
networks. The use of neural networks allows us to obtain rational para-
meters of numerical procedures.
Серія: Технічні науки. Випуск 16
71
References:
1. Zadeh L. The concept of linguistic variable and its using to the adoption of
approximate solvents / L. Zadeh — Moscow : MIR, 1976. — 163 p.
2. Zelentsov D. G. The calculation of constructions with changing geometrics in
the aggressive mediums. Rod systems / D. G. Zelentsov. — Dnepropetrovsk :
USCTU, 2002. — 168 p.
3. Zelentsov D. G. The methods of increasing efficiency of the numeral solvents
of some types of differential equations systems / D. G. Zelentsov, L. I. Korot-
kaya // Modern problems of mathematics, mechanics and programming. Col-
lected articles / under the editorship of N. N. Kizilova, G. N. Zholtakevich. —
Kharkov, 2011. — P. 234–241.
4. Korotkaya L. I. Fuzzy modelling of the behavior of the elements of the chemi-
cal equipment / L. I. Korotkaya // Eastern-European magazine of the progres-
sive technologies. — 2013. — № 2/4 (62). — P. 12–15.
5. Korotkaya L. I. Selection of parameters of numerical procedures for forecast-
ing problems solution of durability of prone to corrosion / L. I. Korotkay,
N. Y Naumenko // Bulletin Kherson national Technical University. —
2014. — № 3(5). — P. 56–61.
6. Shariy S. P. The finite-dimensional interval analysis / S. P. Shariy. — Publish-
ing house «XYZ», 2010. — 597 p.
7. Shokin Yu. I. Interval analysis / Yu. I. Shokin. — Novosibirsk : Science,
1981. — 112 p.
Розглянуто моделювання поведінки металевих конструкцій зі
змінними геометричними характеристиками, які функціонують в аг-
ресивному зовнішньому середовищі. Інформація про параметри зов-
нішнього середовища є неповною або неточною. Для формалізації ці-
єї інформації запропоновано використовувати математичний апарат
теорії нечітких множин та інтервального аналізу.
Ключові слова: теорія нечітких множин, інтервальний аналіз,
моделювання, прогнозування довговічності конструкцій, обчислюва-
льний інтелект.
Отримано: 11.05.2017
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/RUS <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>
>>
/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
>>
<<
/AllowImageBreaks true
/AllowTableBreaks true
/ExpandPage false
/HonorBaseURL true
/HonorRolloverEffect false
/IgnoreHTMLPageBreaks false
/IncludeHeaderFooter false
/MarginOffset [
0
0
0
0
]
/MetadataAuthor ()
/MetadataKeywords ()
/MetadataSubject ()
/MetadataTitle ()
/MetricPageSize [
0
0
]
/MetricUnit /inch
/MobileCompatible 0
/Namespace [
(Adobe)
(GoLive)
(8.0)
]
/OpenZoomToHTMLFontSize false
/PageOrientation /Portrait
/RemoveBackground false
/ShrinkContent true
/TreatColorsAs /MainMonitorColors
/UseEmbeddedProfiles false
/UseHTMLTitleAsMetadata true
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/BleedOffset [
0
0
0
0
]
/ConvertColors /ConvertToRGB
/DestinationProfileName (sRGB IEC61966-2.1)
/DestinationProfileSelector /UseName
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements true
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MarksOffset 6
/MarksWeight 0.250000
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PageMarksFile /RomanDefault
/PreserveEditing true
/UntaggedCMYKHandling /UseDocumentProfile
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [600 600]
/PageSize [419.528 595.276]
>> setpagedevice
|