Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters
In our study, the detection of an extremum for estimates of a set of ATC criteria in a preferred scalar with certain constraints will be understood as optimization.
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| Datum: | 1985 |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
1985
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irk-123456789-1828972022-01-23T01:27:19Z Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters Grishko, V.G. Scientific-technical section In our study, the detection of an extremum for estimates of a set of ATC criteria in a preferred scalar with certain constraints will be understood as optimization. 1985 Article Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters / V.G. Grishko // Проблемы прочности. — 1985. — № 8. — С. 1175-1180. — Бібліогр.: 5 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/182897 62-50.001.5 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Scientific-technical section Scientific-technical section Grishko, V.G. Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters Проблемы прочности |
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In our study, the detection of an extremum for estimates of a set of ATC criteria in a preferred scalar with certain constraints will be understood as optimization. |
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Grishko, V.G. |
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Grishko, V.G. |
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Grishko, V.G. |
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Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters |
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Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters |
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Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters |
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Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters |
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Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters |
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systems approach to problems of the design of automated test complexes. report 2. determination of system parameters |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Systems approach to problems of the design of automated test complexes. Report 2. Determination of system parameters / V.G. Grishko // Проблемы прочности. — 1985. — № 8. — С. 1175-1180. — Бібліогр.: 5 назв. — англ. |
| series |
Проблемы прочности |
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AT grishkovg systemsapproachtoproblemsofthedesignofautomatedtestcomplexesreport2determinationofsystemparameters |
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2025-07-16T02:09:54Z |
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2025-07-16T02:09:54Z |
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1837767642304217088 |
| fulltext |
SYSTEMS APPROACH TO PROBLEMS OF THE DESIGN OF AUTOMATED
TEST COMPLEXES.
REPORT 2. DETERMINATION OF SYSTEM PARAMETERS
V. G. Grishko UDC 62-50.001.5
At the present time, sufficient experience has been accumulated in the development of
automated test complexes (ATC). Howsoever large the practical successes in developing ATC
of some classes of investigations involving the mechanical properties of materials (MPM),
they should not exclude the fact that furtber effective development of ATC is possible with
the condition that the final design theory, which does not have well-defined formulations
at the present time even with respect to basic positions, is created.
In familiar literature sources, problems of ATC design are treated as problems involving
the engineering design of test machines, measuring systems, ASP, and systems for automated
data processing independently of one another. Where, in this case, rational (in some sense)
parameters are selected from some of these systems, this problem does not arise with other
systems. One usually speaks of the selection of a serviceable system without a quantitative
estimate of its quality. In those cases where optimization is accomplished, it is usually
done so, as a rule, with a single dominating criterion. This approach gives rise to signifi-
cant loss of efficiency as compared with the potentially possible efficiency.
In our first report, we proposed a method of selecting a rational ATC structure.
Optimization of ATC parameters, which is carried out from the position of a multicri-
terial evaluation within the framework of the solution of the following problem, is con-
sidered below:
the selection of a large number of criteria serving to estimate the ATC
D = {a~, d2 . . . . . dN}, D =/= ~ ;
the formation of a large number of quality-lntensity levels for D criteria
Qa~o = {qx, q= . . . . . qm}, Q =/= ~ ;
reflection of the quality-intensity levels in a large number of estimates
6 : Q ~ O,whe~ 0 = {o~, ~ . . . . . o.}, 0 =#= ~ ;
and, determination of the optimality principle and derivation of ATC parameters that
satisfy this principle.
The problem of selecting rational (optimal) ATC parameters consists in defining a
variant of the o ~ system in terms of a multicriterial estimate:
0 (~) = {0 (r ( I )
From the mathematical standpoint, the problem of multicriteriaZ optimization is incor-
rect if the detection of an extremum is understood for the optimization, since the attain-
ment of an extremum for a single criteria does not make it possible to find an extremum for
the remaining criteria [i]. The optimization concept must therefore be defined more precisely.
In our study, the detection of an extremum for estimates of a set of ATC criteria in a
preferred scalar with certain constraints will be understood as optimization. The latter is
attained by solving the above-indicated problems.
Selection of Criteria. A large number of ATC-estimate criteria can be ordered in a
hierarchic structure, one of the variants of which is shown in Fig. i. The first level is
represented by the criteria d,, d2, and ds, which characterize the universality of the test-
ing machines that enter into the ATC (d,), the level of improvement in technical and program
Institute of Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev. Trans-
lated from Problemy Prochnosti, No. 8, pp. 116-120, August, 1985. Original article submitted
August 14, 1984.
0039-2316/85/1708-1175509.50 �9 1986 Plenum Publishing Corporation 1175
Fig. i. Hierarchy of ATC-estimate criteria: d~) universality of ATC;
Id~) mechanical loads; Id=) thermal loads; Ids) chemical effects; Id~)
radiation effects; ~di_~) dynamic range of test loads; Idi-2) range of
loading rates; d~ level of improvement in technical and program facil-
ities of ASNI; ds) degree of automation of control exercised over test-
ing apparatus; =dl (3di)) data losses; 2dI-~ (3dl-z)) error generated
by measurement conver=ers; ~d~-a (~dz-~)) computational error; 2d~-3)
error generated by method of data processing (inadequacy of model);
3dI-3) ASP error; ad~ (3d=)) operational properties; =d=-~, 3d=-I) pro-
duction losses due to poor component reliability; =d2-2 (3d=-=)) proba-
bility of repeat run of algorithm; ~d3 Cds)) economic indicators;
2d3-~ (3d3-~)) cost of technical facilities; =d3-= (3d3-2)) cost of
special software; =d3-3 (3d3-,)) cost of ATC reconfiguration with emer-
gence of new research problems; 2d3_~ (3d3_~)) operating expense; =d4)
correspondence between ASNI parameters and characteristics of process
under investigation; 2d~-~) average value during which requirement
should expect accommodation in turn; 2d~_~) average value of number of
requirements in system at any point in time.
facilities of the automated data-processlng system for the ATC (d=), and the degree of im-
provement in the automated-control system for the loading conditions of the testing machines
ASP (d,).
These criteria are detailed on the second and third levels of the hierarchy. The
second level of criteria can be represented in the form of the following groups.
The criterion d~, which determines the testing machine's potential in conducting in-
vestigations, is partitioned into elements:
mechanical effects (Zd~), which are subdivided into uniaxial, biaxial, and triaxial ef-
fects in view of the stressed state in the specimen. In each stressed state, there are basic
(tension, compression) and combined effects, which are derivatives of the basic effects
(bending, shear, etc.) ;
physical effects (Id~), which include the effect of thermal stresses and electromagnetic
radiation;
the external medium (Ids), which in terms of its own chemical properties is subdivided
into chemically neutral, acidic, basic, and special (vapors of hydrogen, nitrogen, carbon,
etc.) parts; and,
reactor radiation ('d~): y-radiation and neutron radiation.
The criteria d~ and ds include the following elements:
data losses 2d I and Sdl;
1176
operational properties =d= and Sd~;
economic indicators 2ds and Sds; and,
correspondence between the ASNI parameters and the characteristics of the process under
investigation =d~.
Components of the second-level criteria are determined on the third level of the hier-
archy.
Thus, each of the forms of energy effects can be characteized by two independent indi-
cators: the dynamic range of the test loads (*di-,) and the range of variation in the load-
ing rate (*di-~).
The error generated by the measurement converters (2d,-,, 3dx_x), the computational
error (2d,-2, Sd,-2), the error induced by the data-processing method (=d,-s), and the ASP
error (Sdx-s) will be treated as components of the criteria 2d~ and ~d,.
The operational problems can be evaluated from two components: productivity losses
owing to poor component reliability (2d~-,, Sd=_,), and the probability of a repeat run of
the algorithm(2d~-~, Sd~-2).
The economic indicators include: the cost of technical facilities (ads-z, Sds-,), the
cost of special software (=ds-~, Sds-2), the cost of ATC reconfiguration with the emergence
of new research problems (2ds-s, Sds-s), and operating expenses (2d~-a, 3ds-~).
Correspondence between the ASNI parameters and the characteristics of the process under
investigation: the average time during which a requirement should expect accommodation in
turn (2d~-,); and, the average value of the number of requirements in the system at any point
in time (=d~-2).
Construction of Criteria Scale. Practical use of the criteria under consideration is
coupled with the need to determine the allowable transformations, which are solved for each
criteria. The type of allowable transformations should therefore be considered in construc-
ting the scales. The values of the criteria d,, d=, and ds can be represented as discrete
ordinal scales. As we know, the principle of superposition is invalid for an ordinal scale
since the distance between the values of the criteria X, and X= does not equal the distance
between the values X2 and Xs. The type of scale in question permits, however, certain
statistical operations, to wit: determination of the frequencies, modes, median, and coef-
ficient of rank correlation.
The d, scale will be represented by the range 0-i; the scale values can be defined as
the ratio of the number of load forms that can be realized to the number of load forms de-
sirable for the class of problems being solved.
The scale of criterion ds can be ordered in the form of the following gradations: 2ql
denotes manual processing of experimental data, =q= recording of experimental data on a data-
storage medium with subsequent processing on a computer, =qs rapid analysis of experimental
data, which can be performed in real time, =q~ secondary processing of experimental data,
and ~qs complex processing, which can be carried out in the cycle of a test series.
The form of processing in question assumes the construction of models, the prediction
of strength properties of the material under investigation in regions of factored space,
which are not encompassed by the experiment, confirmation of the range of applicability of
existing strength theories, etc.
The ordinal ds scale can be ordered in the form of the following values: Sq, denotes
manual control of the experimental apparatus, Sq= automatic stabilization of the parameters
of the loading factors, Sqs automatic program control of certain forms of energy effects,
Sq~ automatic program control of basic forms of energy effects of the testing machines, Sqs
adaptive control of certain parameters of the energy effects, Sq, finite control of certain
forms of energy effects, etc.
The criteria d,, d2, and ds actually determine the possibility of attaining or not at-
taining the goal of the investigations. Criteria of the second and third levels of the
hierarchy characterize the quality of goal attainment for each scale value of the criteria
d,, d2, and ds.
Two scales will be formulated for each criteria *d,-*d~: the first defines the dynamic
range of the loads, and the second the range of variation in the loading rate. Rather well-
1177
developed engineering methods, which are described in many publications, exist for the con-
struction of scales for the criteria Id,-'d~, =dl-2d4, and Sdl-Sd �9 3, therefore, we shall not
dwell on them here.
The scales of these criteria are cardinal, and procedures for findin~ the mathematical
expectancy, standard deviation, coefficient of asymmetry, and mixed moments are applicable
to these scales.
Reflection of Criteria in Estimation Scale. The estimation scale must be obtained using
analytical methods. Solution of this problem is a heuristic procedure, which can be carried
out with consideration of the ASNI goals. For commensurability of the criteria, the values
of the latter must be represented as dimensionless quantities -- estimates indicating the
degree of correspondence between actual values of the criteria and standard values.
The construction of estimation scales requires the acquisition of additional informa-
tion and cannot be performed by formal methods, since there are no objectively correct esti-
mates. This procedure is therefore carried out directly by the processor, or group of
processors, who reflect the actual cardinal or ordinal scales of the criteria in the esti-
mation scale.
Selection of a rational variant of the ATC parameters from a large number of possible
variants reduces to selection of rational estimates from a large number of practicable
estimates:
0 = ~ (Q) = {~O~(tq) , ~qCQ}. (2)
In other words, this is equivalent to assigning a scalar function of the criteria scales,
which is defined in estimate space and which exhibits the following properties: the function
increases monotonically as the quality intensity of the criteria varies. The first de-
rivative of the estimation function, which is called the limiting substitution factor (the
weighting factor of the criterion) between the i-th and j-th criteria at point lqEQ , exists
f o r any lqt, ~q, E di; lq~ =/= ~qi when lql > 2qi , ~ (~qi) > r (2qO, i = 1,-); vtqEdt.
Determination of Weighting Factors for Criteria. All of the criteria under considera-
tion can be structured in the following groups:
D I = { d l , ~ , d s } ; D . z : {ldt, la 2,1aS,IdA};
D , =
The g r o u p s o f c r i t e r i a DI-D~ a r e m u t u a l l y i n d e p e n d e n t by p r e f e r e n c e ( each o f t h e g r o u p s
o f c r i t e r i a i s i n d e p e n d e n t o f i ~ s c o m p l e m e n t ) ; t h i s makes i t p o s s i b l e t o d e t e r m i n e t h e
w e i g h t i n g f a c t o r s o f t h e c r i t e r i a i n e a c h g roup i n d e p e n d e n t l y o f t h e o t h e r g r o u p s . To d e t e r -
mine these factors, let us construct estimation scales, using the method outlined in [2].
The essence of the method is reduced to the following procedures:
find the average estimate of the interval of the criterion scale and consider that
o (~ = 0.5;
f i n d t h e a v e r a g e e s t i m a t e o f t h e i n t e r v a l [ ~ ~d] and assume t h a t
0 (~ = 0.75;
f i n d t h e a v e r a g e e s t i m a t e o f t h e i n t e r v a l [~ ~ and c o n s i d e r t h a t
o (0.25~ = 0.25;
c o n s t r u c t t h e o (d ) = ~ (d ) d i a g r a m .
The o ( d i ) = r f u n c t i o n f o r i = t - - ~ - N c r i t e r i a i s p l o t t e d i n a manner s i m i l a r t o t h e
c a s e d e s c r i b e d .
T h i s method o f p l o t t i n g t h e e s t i m a t i o n s c a l e s y i e l d s a s c a l e o f an o r d e r ( o r d i n a l ) w i t h
s e v e r a l c o n s t r a i n t s b a s e d on t h e d i s t a n c e b e t w e e n e l e m e n t s . These d i s t a n c e s a r e i n s u f f i c i e n t ,
h o w e v e r , t o p r o v i d e f o r an i n t e r v a l s c a l e .
Le t us examine t h e d e t e r m i n a t i o n o f w e i g h t i n g f a c t o r s f o r t h e c r i t e r i a d~, d2, and ds
u s i n g t h e method p r o p o s e d by Kinny and R a i f a [ 2 ] .
Le t us d e s i g n a t e t h e w o r s t v a l u e f o r each o f t h e c r i t e r i a by a i , and b e s t by b i . We
w i l l t h e n have a i ~ X i ~ < b i f o r p o s i t i v e l y o r i e n t e d s c a l e s . Le t N be t h e s e t o f a l l numbers
1178
of the criteria; in our example, N = {i, 2, 3}. Let L be a subset of the set N and ~ be its
complement, i.e., I = N -- L. Let us also designate such values of the criteria that d i =
di{max} i~L and d i = d{mln} for all i~E by d L.
Let us rank the combinations of criteria {a,, Xa, as} and {b,, aa, as}. The quantity
Xa can be varied until there is no difference in the selection between them. Let us desig-
nate X= = qe=. We then have o(a,, q~as) = o(bxaaas), or v2o(d~) = v,. And, since the esti-
mation function o(da) is plotted, the relationship between v, and v= is determined. The
relationship between vs and v2 can be found in a similar manner. Considering the relation-
ship v, + '~2 + ~3 = i, let us determine the values of the weighting factors (solution of a
linear system of equations).
Let us proceed similarly with the criteria that enter into groups Da, Ds, and D4.
The function v, which is determined in the subsets of the set D, possesses conventional
properties of a probabilistic measure [3]: v(L) i~0; v(D) = I for L c- D; ~(SUL) = ~(S) +
v(L) if S and L do not intersect.
Thus, the search for ~ is related to the problem of establishing the appropriate prob-
ability distribution in finite random space. Considering what has been stated, the weight-
ing factors of the criteria of the second and third levels of the hierarchy are defined as
the conditional measures
= , , ; ( ,o , ) /d , , ,,, , , v , = , , : -
= 8v~ (s%)Id3 . . . . . 'vs = 8v 3 ('oOld8
* " (Xo I ,)Idt, M1 . . . . ~ I - 2 = f 1VI--I = 91--I --
[ = t~_2 (lol_2)/dx, 1dr
I . . . . . . . . . . . . . . . . . ( 3 )
/3va-, = ~ t (s% ,)Ida,~d3, ~v =
- - - - " ' " ' 3 - - 4
= s~_ 4 ( 3%_4) Ids , 3ds,
where v* is an unconditional measure, or
11%, 1 = lu - - - , 1 , , = I ? ; . ? I
]
3 - - 8 , * �9 3 - - 3 *. , ~ 1 - %i'%3,-. . ~ V 3 - - V 3 %3
and, respectively,
I V I _ I = I ~ T _ I " I ' V I ' V I , ... , IV4_ , 2 = I 'V4_2.'V 4.'V I
3V3--1=3%';--[" 3V3"V3, . . . , 3V3--4 = 3~--4 "3Va"V3" ( 4 )
Considering what has been stated, the overall ATC estimate can be represented as an ad-
ditive package of estimates of criteria with allowance for their weight :
N
0 = ~ rio i (di) -+ max. (5)
i = I
Formal p r o o f o f the p o s s i b i l i t y o f (5) i s g iven i n [4, 5 ] .
In c e r t a i n cases, the a n a l y t i c a l l y complete s o l u t i o n can be o b t a i n e d by f i n d i n g the ex -
tremum o f r e l a t i o n s h i p (5) us ing the appara tus o f i n d e f i n i t e Lagrang ian m u l t i p l i e r s . In
t h i s case, we can speak o f the s y n t h e s i s o f op t ima l ATC parameters ,
Le t us r e p r e s e n t r e l a t i o n s h i p (5) i n the form
N
0 ---- ~ v~oi ( d . d2 . . . . . d,v). (6)
/ = l
As a result of differentiation, we obtain the following system of differential equations
in partial derivatives:
1179
O0 N O0 i (dt , d~ . . . . . dN)
---- ~ v i =-- O;
Od I ~ Od l
i=1
O0 ,v do i (d i , d2 . . . . . d^,)
- - -~ ~" v i ~ = 0 ;
Od z -- Od 2
(7)
dO ~" 0o i (di, d2 . . . . . d N)
~d~, = ~ v~ od^, = O.
i = l
n 2 ~ - l!
If o i are functions of all d i (i = I,N), we have 2 partial derivatives.
It is obvious that if n 2 +______n__ n = n~--n__ equations are introduced for the relation between
2 2
dl, ..., dN, a system of n~--n equations with n~--~ unknowns can be constructed using
2 2
Lagrangian multipliers.
The result of solution of the given system of equations will be o i = ~i(dt, ..., d N) in
explicit form. Using D. Sylvester's criteria, it is possible to establish the conditional
extremum of relationship (6), which actually defines the possible limit of ATC refinement
under available constraints.
CONCLUSION
An increase in the complexity of solvable problems must be related, in final account,
to the potentials of ATC; this, in turn, leads to the need for a more detailed investigation
of both the parameters of the problem and also the corresponding characteristics of the pro-
Jected ATC. This requires solutions in a multicriterial statement, i.e., modeling of the
optimal selection in indicators.
In plotting estimates of the criteria under consideration, the possibility of their
mutual compensation is proposed. Although not rigid, the assumption in question is, in our
opinion, however, completely acceptable in practical situations.
Further progress in engineering is impossible without the creation of new automated
testing complexes, the requirements for which are growing more and more; this governs the
need for the development of methods free from erroneous design solutions. In the evolution
of our study, we considered the creation of a package of applied programs and dialogue pro-
cedures that can be used in automated systems invoked to assist developers in searches for
optimal solutions.
LITERATURE CITED
i. ,\A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Certain Problems [in Russian],
Nauka, Moscow (1979).
2. R.L. Kinny and C. Raifa, Adoption of Solutions with Many Criteria: Preference and
Substitution [Russian translation], Radio i Svyaz', Moscow (1981).
3. E.S. Wetzel, Theory of Probabilities [Russian translation], Nauka, Moscow (1969).
4. G. Debreu, "Topological methods in cardinal utility theory," in: Mathematical Methods
in the Social Sciences, Stanford, California (1959), pp. 89-124.
5. P.C. Fishburn, Utility Theory for Decision Making, Wiley, New York (1970).
1180
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