New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems
The method of reliability and flexibility valuation for computer aided design and flexible manufacture interpreted as an indivisible purposeful system, which is based on purposeful automaton theory, automaton-game simulation of design and cluster analyses, developed by the authors, is also inves...
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Інститут проблем штучного інтелекту МОН України та НАН України
2011
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| Cite this: | New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems / V. Harbarchuk, N. Hots // Штучний інтелект. — 2011. — № 4. — С. 4-9. — Бібліогр.: 4 назв. — англ. |
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| author | Harbarchuk, V. Hots, N. |
| author_facet | Harbarchuk, V. Hots, N. |
| citation_txt | New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems / V. Harbarchuk, N. Hots // Штучний інтелект. — 2011. — № 4. — С. 4-9. — Бібліогр.: 4 назв. — англ. |
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| description | The method of reliability and flexibility valuation for computer aided design and flexible manufacture interpreted as
an indivisible purposeful system, which is based on purposeful automaton theory, automaton-game simulation of
design and cluster analyses, developed by the authors, is also investigated herein. The necessity to develop adaptable
self-training systems for the study of these units is grounded.
Розглядається новий метод оцінки надійності і гнучкості системи автоматизованого проектування і
виробництва як єдиної цілеспрямованої системи на основі синтезованих автоматно-ігрових моделей,
розроблених авторами, кластерного аналізу і векторних ігр.
Рассматривается новый метод оценки надежности и гибкости системы автоматизированного проектирования
и производства как единой целеустремленной системы на основе синтезированных автоматно-игровых
моделей, разработанных авторами, кластерного анализа и векторных игр.
|
| first_indexed | 2025-11-24T11:41:32Z |
| format | Article |
| fulltext |
«Искусственный интеллект» 4’2011 4
1H
UDC 681.03
Volodymyr Harbarchuk1, Nataliya Hots2
1Lublin University of Technology, Poland
2Lvov Polytechnic University, Ukraine
wig@cs.pollub.pl
New Automaton-Game Theory Method
for Modeling of Reliability and Flexibility
Valuation for CAD-CAM Systems
The method of reliability and flexibility valuation for computer aided design and flexible manufacture interpreted as
an indivisible purposeful system, which is based on purposeful automaton theory, automaton-game simulation of
design and cluster analyses, developed by the authors, is also investigated herein. The necessity to develop adaptable
self-training systems for the study of these units is grounded.
Introduction
Computer aided design (CAD) and flexile manufacturing systems (FMS) for
computer aided manufactory (CAM) are now considered to be of the highest engineering
level. Although the major part of the research in this field is divided into two separate
directions, concerning CAD and CAM. This fact contradicts the system theory approach.
In this paper same features of CAD-CAM, which determine their efficiency and
expedience, are discussed. The basic principles for this are: purposefulness, evolution ability,
system analysis, complexity and man-computer integration [1], [2], [3].
Task definition. Let general aim Fs to create system S, which has a number of
characteristics Hs as well as resources Rs and time-limit Ts, be formulated and besides
Fs = ( f 1 , … , fi. , … ,fn),
where fi is local aims (criteria ).
The aim Fs I Ts, Rs is achieved. If Ts* ≤ Ts , Rs* ≤ Rs ,
fi* = opt fi I ( Hs, Rs Ts) for all I = 1,…,n , (1)
where Ts*, Rs*, fi* are actual values for design-time, resources and local aims. Now
we want to select the factors, which first of all influence the task (1), expected to be solved
by CAD-FMS unit; further this unit is referred to as CAD-CAM.
Models and Methods
Automaton-game model. Let's observe the discrete process of designing and creating
system S. Design problem is described as purposeful finite discrete indeterminate auto-
maton functioning [1], [4]:
A1 = <X1, Y1, Z1, ξ1, ψ1, F1>, (2)
where X1, Y1 , Z1 are inputs, outputs and state factors,
New Automaton-Game Theory Method for Modeling of Reliability and Flexibility…
«Штучний інтелект» 4’2011 5
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ξ1 = X1 × Z1 × F1 => Z1 is transaction function, ψ1 = X1 × Z1 × F1 => Y1 –
outputs function, F1 is the aim of system S design, F1 belong to Fs .
The manufacturing problem can be given in the same way
A2 = < Y1, Y2, Z2, ξ2, ψ2, F2 > , (3)
where ξ 2 = Y1 × Z2 × F2 => Z2, ψ2 = Y1 × Z2 × F2 => Y2 .
On the whole the constructing of S is realized by the automaton Ao :
Ao = A1 U A2,
or
Ao= < X 1, Y2 , Z , ξo, ψo , Fs >, (4)
Z= Z1 U Z2, ξo = X1 × Z × Fs => Z, ψo = X1 × Z × Fs => Y2.
The Ao-automaton processes data, energy and materials, therefore it consists of
three local automata Ai , Al, Am described in (1), (2):
Ao = Ai U Al U Am. (5)
The models (2)-(5) formulate the whole engineering problem in terms of purposeful
technological designer activity. The structure of automaton (2) examples the set of sub
automata A1d , A1r , A1c, which represent supervisor, computer and controller, fig.1.
Figure1. A common model of automata ergamat, where Ad is subautomata
supervisor, Ar- subautomata is computer, Ac is subautomata-controller, F is aim of system
Thus, the automata (2), (3) possess all general features of actual control systems;
that's why model (2) can simulate the CAD and (3) can simulate the FMS-CAM-systems.
Hence, figure (4) is the model of CAD-CAM. The functions ξo , ψo are the most complex
members in the automaton Ao. For their playing models of vector-games (V-games) are
used [2]. In general a V-game is defined as follows
G = < {Ik}, {Nk}, {Fk}, {Rk}, π >, (6)
where Ik is any gambler from the set {Ik} which has it’s own vector-strategy Nk, aim
Fk and resource Rk; π is game rules. The local aims Fk in a complex hierarchical man-
computer CAD CAM-system are not collinear, but subordinate to general purpose Fs.
Therefore approaching the aim Fs under conditions (1) (or evolution of the automata (2), (3),
(41, (5) ) can be interpreted as running of the finite V-games set (6), defined on some net
X
d
Yd
Yr
Ad Ar
Ac
F
Harbarchuk V., Hots N.
«Искусственный интеллект» 4’2011 6
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structure of Ao-automaton [1], [2]. After that follows ξo ≈ Gξ, ψo ≈ Gψ, where Gξ, Gψ are
V-games, which causes changing the state Z and outputs Y2 for Ao then figure (4) shows
Ao = < X1, Y2, Z, Gξ, Gψ, Fs >. (7)
The model (7) is called automaton-game model (AG-model) for CAD-CAM. The
aims Fx, which appear in Ao , are vectors too, that is Fk = (fk1 , ... , fkn). Some reasons of
conflicts among the members of Ao have been investigated earlier [2]. For a couple of
gamblers Ik, Il) I Fk, Fl the antagonism can be introduced
akl(G) = (n - no)/n, 0 ≤ akl ≤ 1,
where no is the set amount for those components fki belong to Fk and fil belong to
Fe, whose interests are collinear, no ≤ n . Obviously, any game is fully antagonistic, if no =
O or if no = n, then it is completely non-conflict. That’s why akl can indicate the reliability
and flexibility of A1·, A2, Ao, and the control strategy for CAD-CAM is how to obtain akl
~minimum at each design step and time discrete ti belong to Ts .
Reliability characteristics definition. Let the system S be a Bs composition of members bj,
Bs = {bj}, j = 1,., m.
Then we divide Bs into three clusters using the following conditions: Bα is α-cluster,
if any single failure of member by α belong to Bα, Bα belong to Bs, causes the S-failure
as a whole. Bβ is β-cluster, if any single by β-failure inside the time interval [0, tjβ], bjβ
belong to Bβ, Bβ =Bs\ (Bα belong to Bs) only decreases the S-efficiency. Bγ is γ-cluster, if
no single by γ -failure within [o, tγ] influences the S-efficiency at all, but all the by γ -
failure inside [0, tγ] or even single one within [tγ,ts] decreases S-efficiency. The
components by α belong to Bα cover the basic structure of S-system. To design some
objects from Bα, Bβ, Bγ there are correspondent clusters α1, β1, γ1 of subautomata
A1α, A1β, A1γ for A1 and the same are α2, β2, γ2 of A2α, A2β, A2γ for A2.
These clusters realize the design decisions obtained on A1α, A1β, A1γ. Let T1 be
time interval for S-design, T2 be the interval of design realization on A2, T2 = Ts - T1.
If a single task from α1-cluster is unsolved w1thin T1, then the whole project
iconsidered be not realized. If the same takes place for β1-cluster, the project is not
optimal. Now the project is not realized if no tasks at all from β1-cluster are solved inside
T1. What’s else, we specify the whole project as not-realized, if at least one single task
from γ1 -cluster remained unsolved in TS. The system S is considered be not-operational if
a single decision at least from cit-cluster is not realized through the subautomata α2 within
T2. The S is not considered optimal if any one decision from β1 has been unaccomplished
by the β2-subautomata in T2, and S is un operational if all the decisions from β1 are not
implemented in T2. At last, the S 1s not optima 1f all the γ1-decisions are not realized in
T2 or even one of them during the test maintenance within the time discrete Δt belong to ts.
The probability P(Fs} of the aim Fs achievement under conditions (1) depends on the
A1 -, A2 -reliability:
P{Fs) = P(A1) .P(Az), (8)
where P(A1) is non-failure probability for A1 in [o,T1], P(A2) for A2 in [T1, Ts].
New Automaton-Game Theory Method for Modeling of Reliability and Flexibility…
«Штучний інтелект» 4’2011 7
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According to the concepts of reliability theory we take the consequent way of subautomata
connection and the parallel one for the clusters. Then the probabilities of subautomata norm l
functioning indicate
P(α1) = ∏ P(A1α1), P(β1 } = ∏ P(A1β2), …, ∏ P(A2γ6)
and now
P(A1) = 1 ((1-P(α1)) (1-P(β1)) (1-P(γ1)) (9)
P(A2) = 1 - ((1 - P(α2)) (1 - P(β2)) (I - P( γ2)). (10)
The A1 mainly transforms the input data X1 into the output Y1. Therefore it’s more
relevant to Ai' in (5), and now
P(A1) = P(Ai).
The A2 takes data Y1,the aims F2, Fs and then transforms energy and materials,
approaching to S. That’s why the A2 is to be described as Al U Am and P(A2) ~ P(Al U
Am). From this point of view we shall select factors which have the strongest influence
on P( Ai) and P( Al U Am) .
Considering (6), (7) the CAD-CAM functioning can be approximated by the
purposeful general exercising of the V-games set, where the P(Fs)-factor somehow
depends on the values of akl for any couple of interconnected subautomata in A1 , A2 , on
a12 for the couple (A1 , A 2) and on ao1, a02 while automata A1 ,A2 performs V-games
with nature-partner (external actions). To solve such games the efficient principle of pat
tern strategy has been developed. Obviously, antagonism degree of akl considerably
influences the task solving probability for the subautomata of alI the clusters. Thus all the
members
P(α1), ... , P( γ2),
are functions of all in their own clusters. '!he general strategy of Ao-functioning
demands completely to eliminate antagonism each step of making decisions. Now if for
some couples of subautomata in α1 or in α2 cluster is valid
aklIα1 =1 or aKllα2=1 then P(A1) = 0 or P(A2) =0
what in any case gives P (Fs)≠ 0. The results in clusters β1, β2, γ1, γ2 are defined in
the same way, but herein P (Fs) ≠ 0 except the above mentioned case. The problem of
antagonism degree elimination in CAD-CAM is under investigated and its research is now
very important; this causes new problem of artificial intellect in CAD-CAM.
CAD-CAM readiness. Let's define the factor maintenance-readiness of A1 as
K(A1) = (T1 – ∑c tc ) / T1, c = 1, ... ,6,
where t1 is the time interval necessary for conflicts to be eliminated, which may
appear as a consequence of incorrect tasks, indefinite aims or function distribution, t2 is
period within the automaton is waiting for instructions, t3 is delay time determined by
computers and peripheries, t4 is pauses because of hard- and software defects, t5 is time
spent to locate and prepare the data, t6 is time for project coordination. For A2 is valid
K(A2) = ( T2 - ∑ t'c ) /T2, c = 1,…, 6.
t3 is time lost because of hardware; t4 is time lost, because of the defects appeared in
the software of computer controlled machinery and robots, involved in manufacturing
Harbarchuk V., Hots N.
«Искусственный интеллект» 4’2011 8
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system S; t5 is time extent necessary for decision correction and mistakes elimination; t6 –
preparation time for the task YI received from A1.
Then
K(Ao) = (Ts - ∑ tc - ∑ t'c ) / Ts .
So the main factors that determine CAD-CAM readiness are: management, efficiency,
data- and software quality, machinery reliability.
CAD-CAM flexibility. We want to study the flexibility concept in two aspects: in
local and general. We define the loca1 flexibility we define as automaton Ao feature to
provide an optimal output Y2 in [O,Ts] inspire of X1 and (or) Fs changes, while the Ao-
structure is constant. This is functional Ao-flexibility. We understand the general flexibility
as automaton ability quickly tune on the new aim F's in Δ τ-time and (or-) on the new input
X'1 to get corresponding output Y'2 inside the subject oriented sphere of aims Δ Fs . This
is structure functional flexibility of Ao .
To provide the local Ao-f1exibility it is necessary to, develop and use the discrete
adaptive self-training system methods known before. Apparently, the general flexibility
expects the local one. To study general flexibility we observe CAD-CAM as a queuing
system. Here the successive connected A1 and A2 are servants. The inputs for A1 are X1,
Fs. The service manner is determined by the aim F1 C Fs and restricted by T1, Hs, R1
belong to Rs. The inputs for A2 are Y1, F, S; the service is also specified by F2 C Fs and
restricted by T2, Hs, R2 C Rs. The Fs has major priority among the inputs of A1, A2. Both
inputs are non-stationary. The system A1 starts service actions according F's after result Y1
has been obtained, and A2 starts after Y2. Considering the complexity of automata A1, A2
structure (whose automata are service subsystems), and man-computer relations of those
automata as well, we note following theses (which are not detail discussed in this paper).
1. The functioning of A1-input subautomata, which percept X1 (from surroundings,
can be specified as Markov’s process in [0, τ].
2. In [τ,τs]-interval this process transforms itself into non-Markov’s because of:
a) iterate character of A1, A2 and loops in their connections;
b) multicriterial of project decisions and their starting-point compromise indicate the
influence on the whole process of project realizing until the end-point Y2│Fs because of
incorrect task and (or) aim formulation.
The automata A1, A2, Ao reliability can be estimated in two meanings as follows.
1. Let t's be the time interval within the aim Fs of creating and maintenance new
system S' is constant, e.g. S' is in a constant demand; T's is the interval necessary to create S'
using Ao; t'' is the interval for tuning Ao on the new aim F's. Then the flexibility factor is
L(Ao) = (t's - T's – t''s)/ t's.
If T's ≥ t', t''s ≥ t's and L(Ao) is negative, then Ao can’t manufacture computable
production. The Ao is worth if O < L(Ao) < 1 Factors L (A1) , L (A2) are defined the same
way. These factors determine the functional flexibility of Ao.
2. The structure of automaton Ao can be covered by oriented sectioned net
N (A o) == (V1, ... , Vn, Ѳ),
Where V1,...,Vn are sections of the net-knots representing the subautomata Ao from
clusters α1, α2 , Ѳ - the set of oriented connections [2], [4];
n is the number of knot sections. The entrance-section V1 from A1 takes the input
data X 1 I Fs the aims of subautomata in V1,…, Vn are determined by Fs-decomposition;
the exit- section Vn" outputs Y2 I Fs according to (1).
New Automaton-Game Theory Method for Modeling of Reliability and Flexibility…
«Штучний інтелект» 4’2011 9
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Thus N(Ao) is the structure-functional model of CAD-CAM studied as a queuing
system. The N(Ao) can be used for realizing some nets of structures W: anyone of them is
able to provide some output Y2i while floating X1 in ΔX1 -interval and (or-) Fs in Δ Fs
but considering (1). The structure transformation from Wi ( N (Ao)) into W K ( N (Ao)) is
supposed to occurs in jump-manner when the aim Fs-change quantum is greater then Δ*Fs
and (or) input X1-change is greater the Δ*X1. From this point of view the structure
flexibility of Ao can be indicated by the set power of W - L*(Ao) = 1, then Ao shoes only
the local flexibility.
Conclusion
Methodological basis of CADM simulation as automata target aimed systems and
methods of determining their reliability, readiness and flexibility are proposed. It is how
that investigation of CADM attar aimed queuing systems is worthy of note. The proposed
method of α, β, γ-clustering for CADM tasks and functions allows to classify demands
upon CADM reliability, readiness and flexibility in part1cular by paying main attention for
creating optimum readjust able basic composition.
In our opinion problems of CADM flexibility are actual, but they are more fully
reflected in terms of CADM adaptation and self-organizing as power controlling systems.
Received results are perspective for developing and use CADM in theory. Limited volume
out this paper does not allow us to consider problems of CADM shaping as a queuing
system with non-Markov’s process of functioning. These problems demand special investi-
gations as they are raised for the first time.
References
1. Harbarchuk V.I. Mathematical design of complicated ship systems. Leningrad: Shipbuilding. 1982.
2. Harbarchuk V.I. Modeling of complicated processes and systems. Scientific Thought. Kiev. 1985.
3. Garbarczuk W. Projektowanie systemów ochrony informacji. Polska: Politechnika Lubelska, Lublin.
2006.
4. Harbarchuk V. Modeling and Optimization. Poland: Lublin Polytechnic. 2010.
Володимир Гарбарчук, Наталія Гоц
Новий автоматно-ігровий метод моделювання надійності і гнучкості автоматизованих систем
проектування і виробництва
Розглядається новий метод оцінки надійності і гнучкості системи автоматизованого проектування і
виробництва як єдиної цілеспрямованої системи на основі синтезованих автоматно-ігрових моделей,
розроблених авторами, кластерного аналізу і векторних ігр.
Владимир Гарбарчук, Наталия Гоц
Новый автоматно-игровой метод моделирования надежности и гибкости автоматизированных
систем проектирования и производства
Рассматривается новый метод оценки надежности и гибкости системы автоматизированного проектирования
и производства как единой целеустремленной системы на основе синтезированных автоматно-игровых
моделей, разработанных авторами, кластерного анализа и векторных игр.
Статья поступила в редакцию 21.06.2011.
|
| id | nasplib_isofts_kiev_ua-123456789-60241 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1561-5359 |
| language | English |
| last_indexed | 2025-11-24T11:41:32Z |
| publishDate | 2011 |
| publisher | Інститут проблем штучного інтелекту МОН України та НАН України |
| record_format | dspace |
| spelling | Harbarchuk, V. Hots, N. 2014-04-12T16:32:58Z 2014-04-12T16:32:58Z 2011 New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems / V. Harbarchuk, N. Hots // Штучний інтелект. — 2011. — № 4. — С. 4-9. — Бібліогр.: 4 назв. — англ. 1561-5359 https://nasplib.isofts.kiev.ua/handle/123456789/60241 681.03 The method of reliability and flexibility valuation for computer aided design and flexible manufacture interpreted as an indivisible purposeful system, which is based on purposeful automaton theory, automaton-game simulation of design and cluster analyses, developed by the authors, is also investigated herein. The necessity to develop adaptable self-training systems for the study of these units is grounded. Розглядається новий метод оцінки надійності і гнучкості системи автоматизованого проектування і виробництва як єдиної цілеспрямованої системи на основі синтезованих автоматно-ігрових моделей, розроблених авторами, кластерного аналізу і векторних ігр. Рассматривается новый метод оценки надежности и гибкости системы автоматизированного проектирования и производства как единой целеустремленной системы на основе синтезированных автоматно-игровых моделей, разработанных авторами, кластерного анализа и векторных игр. en Інститут проблем штучного інтелекту МОН України та НАН України Штучний інтелект Концептуальные проблемы создания систем искусственного интеллекта New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems Новий автоматно-ігровий метод моделювання надійності і гнучкості автоматизованих систем проектування і виробництва Новый автоматно-игровой метод моделирования надежности и гибкости автоматизированных систем проектирования и производства Article published earlier |
| spellingShingle | New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems Harbarchuk, V. Hots, N. Концептуальные проблемы создания систем искусственного интеллекта |
| title | New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems |
| title_alt | Новий автоматно-ігровий метод моделювання надійності і гнучкості автоматизованих систем проектування і виробництва Новый автоматно-игровой метод моделирования надежности и гибкости автоматизированных систем проектирования и производства |
| title_full | New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems |
| title_fullStr | New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems |
| title_full_unstemmed | New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems |
| title_short | New Automaton-Game Theory Method for Modeling of Reliability and Flexibility Valuation for CAD-CAM Systems |
| title_sort | new automaton-game theory method for modeling of reliability and flexibility valuation for cad-cam systems |
| topic | Концептуальные проблемы создания систем искусственного интеллекта |
| topic_facet | Концептуальные проблемы создания систем искусственного интеллекта |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/60241 |
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