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Journal of Physics: Conference Series
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Soft measurements in technological processes control
To cite this article: L P Vershinina and M I Vershinin 2020 J. Phys.: Conf. Ser. 1515 052023
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ICMSIT 2020
Journal of Physics: Conference Series
1515 (2020) 052023
IOP Publishing
doi:10.1088/1742-6596/1515/5/052023
Soft measurements in technological processes control
L P Vershinina1, 3 and M I Vershinin2
Federal state Autonomous educational institution of higher education "SaintPetersburg State University of Aerospace Instrumentation", Bolshaya
Morskaya, 67, letter A , Saint-Petersburg, 190000, Russia
2
Federal state budgetary educational institution of higher education "SaintPetersburg Mining University", 21st Line, 2, Saint-Petersburg, 199106, Russia
1
3
E-mail: [email protected]
Abstract. Intelligent information and measurement systems, microprocessor control of
measurement procedure cause increasing role of metrological aspect in technological process
control. The role of soft measurements in improving the methodological base of measuring
systems is shown. Examples of the implementation of the concept of soft measurements and
calculations in the development of mathematical support of automated technological process
control system for the production of radio electronic means are given.
The complexity of technological processes control in modern production is due to the large number
of controlled parameters, the uncertainty of knowledge about environmental factors that affect the
control object, and the incompleteness and inaccuracy of measurement information.
When organizing control in the automated control system, continuous metrological support of the
technological process is performed and the optimal modes of operation of the technological object
control are determined and then implemented.
One of the directions of improvement of methodological base of measuring systems is extending the
measurement functions, obtaining results in the form of knowledge, conclusions and recommendations
on the basis of available a priori and received information in the process of measurements. The need to
measure the properties of objects, expressed not in quantitative, but in qualitative form, attracted to the
measuring environment the methods of the theory of fuzzy sets and fuzzy logic, implementing the
concept of soft, or intelligent measurements.
Uncertainty of the measurement result reflects ignorance of the exact value of the measured value.
Traditional methods of metrology do not allow taking into account poorly formalized a priori
information about the measured values. Methods of fuzzy set theory make it possible to consider and
take into account such information.
The emergence of the soft measurement direction helped attract artificial intelligence to the
measurement environment. Currently, various measurement scales are being actively studied. The very
concept of "measurement" is used to determine the membership function and the degree of fuzzy of
various phenomena and processes [1].
Soft measurement technology is focused on solving control problems with weakly structured objects
using fuzzy set theory techniques. Today, however, traditional metrology methods are also can be
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1
ICMSIT 2020
Journal of Physics: Conference Series
1515 (2020) 052023
IOP Publishing
doi:10.1088/1742-6596/1515/5/052023
implemented within this theory. For example the work [2] shows the possibility of presenting with the
help of fuzzy variables traditional information on error in metrology.
The modern concept of soft measurements finds application in solving the most important practical
problems: continuous evaluation of product quality, evaluation and optimization of production systems
control, parametric and structural identification [3]. The methodology for solving such problems is
characterized by:
•
•
•
integration varied in form and to contents of information for increase or achievement of the
required quality of result of measurements;
realization of the principle of self-development of models of the objects of measurement on the
basis of adaptation in the course of soft measurements;
use of various types of measurement scales for increase in efficiency of measurements.
The linguistic scale used in soft measurements extends the idea of traditional scales of measurement
theory and is interfaced with the main scale by using a common metric carrier. Soft measurements are
based on the description of parameters of technological objects as fuzzy sizes [4, 5].
The concept of soft measurements and calculations was implemented by the authors in the
development of mathematical control models, which are part of the mathematical support of the
automated technological process control system for radio electronic means production.
Modern production of radio electronic means is characterized by high dynamism of development.
The product range and manufacturing technologies are changing rapidly. Frequent replacement and
adjustment of production equipment is required [6].
When changes in the technological process dominate over stationary production, as a rule, there is
not a sufficient amount of statistics. Incompleteness of statistical data does not allow correct application
of mathematical statistics methods to improve the technological process. Measurement errors
complicate the calculation of the management. In addition, the selected control often cannot be
implemented exactly on the production equipment.
These factors are characteristic of thermal technology processes, which occupy a significant place in
the production of radio electronic means. В модели управления тепловыми операциями входные и
выходные параметры рассматриваются как нечеткие переменные.
Let xij be the parameters of the object at the manufacturing stage, ui are technological modes, and yi
x
u
y
are output parameters. Fuzzy subsets  ij  F ( X j ),  i  F (U ),  i  F (Y ) correspond to the
variables xij, ui, and yi.
Let x = {xj }  F(X j ) be the initial state of the object. It is necessary to select the technological
modes u'  F(U) in such a way as to provide the required value of the output indicator y'  F(Y).
To calculate the control, we use - and -compositions. The control u' is selected from the interval

u  u  û , where
( ui  ( yi  y )), uˆ = (
u=
i
( ui  ( yi  y  )))  (
i
( ui ( yi  y  ))) ,
i
yi ={(y,(μ iy ) π )|(μ iy ) π =μ iy
 πi };
i =  ( xij | xj ) ,
j
“M” is a measure of the similarity of variables xij and xj [7].
It is known that the most advanced control is achieved when it is adequate in particular in complexity
and uncertainty to the controlled process. In this connection the issue of developing adaptive models of
technological processes control, which are adjusted and supplemented during process, becomes relevant.
Such models provide a definition and adjustment of control effects in the manufacturing process.
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ICMSIT 2020
Journal of Physics: Conference Series
IOP Publishing
doi:10.1088/1742-6596/1515/5/052023
1515 (2020) 052023
The need to adjust the process modes is also due to the heterogeneity of material characteristics,
especially in group processes [8].
Consider a technological process as a sequence of transitions from the initial state to the final state
along some trajectory:
X 0 → X 1 → X 2 → ... → X N .
The technological process states are represented by convex fuzzy subsets. Let the Xk state at the
 
k- th step of the technological process be determined by the vector of monitored parameters x j
Lk
j=1
.A
plurality of experimental data obtained by measurement is broken down into nk clusters corresponding
to nk possible technological process modes in the k-th stage.
Description of control process is based on fuzzy display:
f : X U → X ,
where X is the state space; U is the space of control strategies.
In space X  U  X we form fuzzy ratios Rk such that
X k+1 = Rk X k ,
where symbol  is the symbol of max-min operation.
For nk possible technological process modes at the k-th stage we determine the set
R 
nk
k,i i=1
, k = 0,..., N − 1 , for which
X k+1,i = Rk,i X k .
 
We determine the set X k,i
nk
i=1
of permissible states of the system at each stage, starting with XN and
ending with X0:
-1
X k,i = Rk,i
X k+1 ,
-1
where Rk,i is the ratio inverse to the relation Rk,i .
Let X is membership function of state Xk,i; C is membership functionsetting technological
restrictions for design parameters.
Then the admissible solution of Dk,i on k-th a stage is defined by membership function D =XC,
where symbol  is the symbol of some binary operation. The specific type of operation is determined
based on the characteristics of the technological process. Reallocation of design and process stocks
allows you to get a set of acceptable solutions Dk,i at each stage of the process:
D
0,i
|R0,i i=1 → D1,i|R1,i i=1 →
n0
→ Dk,i|Rk,i i=1 →
n1
nk
→ XN .
Let stage the real condition of a system on k-th technological process decide by fuzzy set Yk with the
corresponding membership function Y.
We define the permissible trajectory closest to state Yk and select the control action corresponding
to it. As a measure of proximity, we take the Hamming distance [9]:
(Yk ,Dk,i ) =
1
Lk
Lk

j=1
 Y (x j ) −  D (x j ) , 0    1 .
3
ICMSIT 2020
Journal of Physics: Conference Series
1515 (2020) 052023
IOP Publishing
doi:10.1088/1742-6596/1515/5/052023
We define a valid solution D*k,i from the condition min d(Yk ,Dk,i ), i = 1,..., nk .
The control determined by the ratio R*k,i corresponding D*k,i is taken as optimal.
In general, the formulation and algorithms for solving the problem of optimization of technological
process control depend significantly on the types of uncertainty available in the task setting:
uncertainty of conditions due to interference; incompleteness and measurement errors; uncertainty due
to fuzzy target and limitations, etc. [10].
Let present the technological process as a multi-stage process:
X i +1 = f ( X i , ui ) ,
i = 0,1,..., N − 1 ,
where symbol  is the symbol of fuzzy operator, Xi = {(xi, mi(xi))}, xiX, uiU; mi(xi) is membership
function of fuzzy state Xi. Let i(ui) is membership function of fuzzy restrictions Ci={(ui,i(ui))}of the
technological process control.
In this case, one of the most appropriate control optimization strategies is a sequential optimization
strategy. Dynamic programming allows such a strategy to be implemented.
The sequence of controls ui (i=0,1,…,N-1), satisfying constraints Ci, and the sequence of states
X1,…XN, for which the quality indicator G takes the maximum value, we find from the system of
recurrent equations:

M N (X N ) = max (mN (xN )  mNG (xN )),
xN


M N −ν (X N −ν ) = max (μN −ν (u N −ν )  M N −ν +1 (X N −ν +1 )),
uN −ν


X N −ν +1 = f(X N −ν ,uN −ν ), ν = 1, ,N
.
Here MN-(XN-) is degree of membership of XN- to the purpose of GN-; {xN} are elements of set XN
; mNG (xN ) is membership function of fuzzy set X NG . Membership function values are degrees of
membership of the element xN to the purpose GN.
The strategy of step-by-step optimization is implemented in models of optimal management of
typical processes of radio electronic means production [11].
All developed models function under conditions of parameter variation characterizing physical and
chemical properties of manufactured products, incomplete and inaccurate measurement information,
drift of process equipment parameters.
Metrological support of the technological process using adaptive models is an actual direction of
development of measurements in automated production. The developed models are adaptive to change
of operation conditions and characteristics of the technological process and can be corrected during the
process and its metrological support.
References
[1] Zvyagin L S 2018 Soft measurements and calculations 11(12) 15-20
[2] Semenov K K 2012 Computer science and its applications 6 102-12
[3] Prokopchina S V 2018 Soft measurements and calculations 9 4-33
[4] Shopin A G 2002 Proc. of the Samara scientific center of the Russian Academy of Sciences 4(1)
178-84
[5] Solopchenko G N 2007 Measuring equipment 2 3-7
[6] Vershinina L P and Vershinin M I 2019 IOP Conf. Ser.: Mater. Sci. Eng. 537 042014
[7] Dyubua D and Prad A 1989 Capacity theory. Application to knowledge representation in
computer science (Moscow: Mir) p 286
[8] Vershinina L P and Vershinin M I 2017 Issues of radio electronics 10 82-5
[9] Borisov V V, Kruglov V V and Fedulov A S 2007 Fuzzy models and networks (Moscow:
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ICMSIT 2020
Journal of Physics: Conference Series
1515 (2020) 052023
IOP Publishing
doi:10.1088/1742-6596/1515/5/052023
Goryachaya liniya–Telecom) p 284
[10] Diligenskiy N V, Dymova L G and Sevastyanov P V 2004 Fuzzy modeling and multicriteria
optimization of production systems in conditions of uncertainty: technology, economics,
ecology (Moscow: Mashinostroenie-1 Publ) p 397
[11] Vershinina L P and Vershinin M I 2017 Modeling and situational quality management of complex
systems (Saint-Petersburg: GUAP) 4-10
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