The paper proposes a method for solving the problem, which was formulated. The solution to this problem is based on comparing the characteristics of the functioning of the system under study. Characteristics compares with similar characteristics of a reference on a variety of criteria. This solution can be used when testing systems of various types, purposes and arbitrary level of complexity. This method of presenting the assessment results makes it possible to quickly navigate the totality of the data obtained. And also to carry out a quick search for unsatisfactory functioning elements of the system under study. This technique can be used to select the optimal mode of functioning of the system, to select from a certain class of functional elements to build an optimal system and to consistently modernize the system under study by improving the unsatisfactory functioning elements identified during the assessment process, etc.
The study of the functioning laws for complex
dynamic systems of various types (technical,
economic, and social) has attracted the attention
of researchers for a long time [
Among the eternal problems that arise in this case, the following problems can be singled out as especially important: the choice of optimal modes of operation for such systems, the choice of an optimally functioning system from a certain class of equivalent systems, the quality assessment of complex dynamic systems functioning.
The paper proposes a method for solving the problem, which was formulated. It is based on comparing the characteristics of the system's functioning under study with similar characteristics of a certain reference system according to a number of criteria.
Obviously, only a versatile, multi-criteria and multi-level assessment will be sufficiently objective. At the same time, its manual acquisition for complex dynamical systems is impossible in practically admissible periods of time. This is impossible even for any particular case due to the large volumes of processed information. One or a little territorial analysis will give only one-sided assessments, while important features of the laws of the systems functioning that are being investigated are often ignored. Therefore, a problem arises related to the development of methods for optimal processing of this information in order to quickly obtain the required estimates.
( ) = [ ( )] =1, ∈ [0, ], where T is the time during which the test study was carried out.
We assume that each characteristic
( ) = [ ( )] =1, = 1, 2, 3 …,
represents a vector of constant values or a vector
– a function that describes individual aspects of
the system
functioning
under study (initial,
intermediate and final state, phase vector, control
vector, etc.) [
Let us assume that the system can operate in modes , = 1, 2, … 3, … , . The characteristics of the functioning laws for an information security system (ISS) can be obtained both as a result of experimental research and by means of mathematical modelling of the dynamics of its functioning.
Let us assume that five criteria are used to assess the functioning quality of the system that is being investigated , = 1, 2, 3 … , . It is necessary to determine the limits of change of indices and t values. If there is no special need for this, it is omitted. We denote reference values of the component ( ) when the system operates in the k-th mode according to the ( ) as the area of p-th evaluation criterion.
Equivalent systems are understood as systems of the same type and purpose, the law of functioning of which is described by a set of characteristics А( ). We denote by -class of equivalent dynamical systems, which includes N elements.
An example of a complex dynamic system is an information security system. Let's simulate the dynamics of the functioning of a ISS, which is a system with many links.
The functioning of the ISS can be described by
dynamic, energetic
and a
number of
other
characteristics [
Among the evaluation criteria, one can point out the deviation from
work information tolerances, the protection, the effectiveness effectiveness absorption, etc. The areas of their variation are used as the areas of reference values of the characteristic components.
The
class
equivalent systems in this case can be a reference
system that functions under optimal conditions. In
general, the amount of information that needs to
be
analysed
for a
sufficiently
substantiated
objective assessment of the functioning quality of
an ISS can clearly exceed that available for
nonof
of
of
automated processing [
Let us assume that the investigated dynamic system (ISS) is a new (N + 1)-th element of the class. It is necessary to formulate the problem based on a numerical analysis of the characteristics of the system ( ) = [ ( )] =1. It is necessary to form a sequence of qualitative local estimates for the behavior of the components of these characteristics ( ) = [ ( )] , =1, =1.
This must be done according to a set of criteria , = 1, 2, 3 … , 5, for a given set of operating modes , = 1, 2, … 3, … , .
Based on the resulting set of local estimates, it is necessary to form a sequence of weighted averaged estimates of varying degrees of generality.
These assessments
make it possible to analyse the features of the behaviour of both individual characteristics of the system and the quality of its functioning as a whole.
Consider a solution technique for the formulated problem. Let us assume that the system under study is assessed according to the pth criterion when it is operating in the -th mode. To solve the formed problem, we introduce an auxiliary function
( ) = 0, ∀ ( ) ∈ ( ); ( ) = ( ) −
( ), ∀ ( ) > ( ) = ( ) − ( ), ∀ ( ) < > <
Let us introduce the numerical parameters of the local assessment for the i-th component and the j-th characteristic of the system according to the p-th criterion in the k-th mode of operation by the relations ( , , ) = || || [0, ] = max[ ( )], ( , , ) = || || 2[0, ] =
= [∫ ( ( ))2 ]2.
0 1 2, ∀ ( , , ) { [ ( , , ) − ( , , ) − [ ( , , ) + ( , , )]/4, ( , , ) − ( , , )]/4 }, we consider this assessment is satisfactory; = 3, ∀ ( , , ) > ( , , ) − [ ( , , )]/4, we ( , , ) − consider this for which ( , , ) = ( , , ) = 0 ∀ , , , will be considered a reference system.
Obviously, direct analysis of the entire totality of the numerical parameters of local assessment is a complex problem. This analysis is complicated by the analysis of behaviour for the functioning of the system and functional dependences of ( ), in the form
of graphs, in order to obtain generalized estimates of the functioning of the system under study, which is a dynamic system. The reason for this complexity is in the amount of parameters, which is equal to 5 = 2 and is large enough.
Suppose that for the characteristic [ ( )] =1 of systems for class certain values ( , , ) = min ( , , ), ( , , ) = max ( , , ); ( , , ) = min ( , , ), ( , , ) = max ( , , ).
We introduce for each function ( ) under study (N+1)-th for the dynamic system the illogical arrays of local qualitative estimates: = 1, ∀ ( , , ) < ( , , ) + [ ( , , )]/4, assessment is unsatisfactory; ( , , ) − we consider this rating is good.
Similarly, arrays are introduced for estimation ( ) and accurate. primary assessment parameters.
Obviously, graduation of estimates depending on the needs can be narrowed or expanded. Note that when the class
is expanding (Introduce (N+1)-th element), the change in value ( ) in order to "unreliable recognition" limits of ( , , ) is inappropriate, unlike ( , , ). Naturally, the wider class , the score will be more objective, high-quality We formally form on the basis of a set of local qualitative assessments of varying degrees of generality until the final conclusion on the quality of the functioning of the studied dynamic system. Such a construction will be carried out in two directions, which can be changed vertical and horizontal, which corresponds to a method for further evaluation that facilitates their perception and qualitative analysis.
The assessment in the vertical direction makes it possible to analyse the behaviour of individual characteristics or the system as a whole according to the corresponding parameter, criterion or mode, namely:
Step 1. For the separate type of estimated parameter for a set of components of each characteristics for a digital evaluation criterion , , , ,
= ∑ =1
= ∑ =1 / ∑ / ∑ =1
, =1 , =1 where { }
– are weight coefficients that determine the significance of the component of the system characteristics. Here and then the values of weight coefficients are determined by the experts exploring the dynamic systems under consideration in accordance with the specifics of the latter or the objectives of the study itself. The assessment of the values , similarly to the valuation by values. ( ). ,
, ( , ) are made
Step 2. For the separate evaluation criterion for the set of estimated parameters , , = ( , , + , , )/( + ), determine parameters. where , – are weighing coefficients that the importance of evaluation
Step 3. For the certain mode, the functioning of the assessment criteria
, = ∑ / ∑ =1 , ,,
/ ∑ =1 ;
Step 2. For used estimated parameters for the aggregate criteria for estimating relative each component characteristics , = ( , , + ,
, )/( + );
Step 3. For the separate mode of functioning by set of components. Characteristics
, = ∑ =1 ,, / ∑ =1 .
The statement 1. ≡ = V .
Obviously, the following statement is right Note that the assessments of the last level characterize the behaviour of individual characteristics of the system in terms of the set of parameters in specified modes and functioning.
The graphic results of the first stage of the assessment are shown in Figure 1.
The values of ) correspond to the ( elements of the table that are at the intersection of the rows and the columns C(L), the rest are estimates of the 1-3rd generality.
C L ∙ ∙ C L ∙ ∙ C L ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ determine the significance of the characteristic of – are weighting factors that
In the horizontal direction, the assessment is carried out according to the set of modes for each characteristic of
the protection system, i.e. investigated dynamic
= ∑ =1
, / ∑ =1 , where { } =1 determine the significance of the modes of functioning of the system.
– are weighting factors that The following statement is obvious.
The statement 2.
∑ =1 , / ∑ =1 ∑ =1 = .
= ∑ =1 /
The VH value makes it possible to make a final
conclusion about the quality of the functioning of
the investigated protection system (dynamic) as a
whole. The graphically generalized results of the
estimates obtained at the second stage are shown
in Figure 2. The elements of the table, which are
at the intersection of rows and columns Rq,
correspond to the values
, the rest are
estimates of the 4th level of generalization and the
final conclusion about the quality of the system.
of operation of the system [
This article proposes the methodology for a versatile, multi-criteria and multi-level assessment of the functioning quality for the information security system. This system is dynamic. The technique can be used for testing systems of various types, purposes, and arbitrary levels of complexity.
The proposed method of presenting the results of the assessment makes it possible to quickly navigate in the totality of the data obtained, as well as to quickly search for unsatisfactory functioning elements of the system under study.
In addition, this technique can be used to select the optimal mode for the system operating, select from a certain class of functional elements to build an optimal system and consistently modernize the system under study by improving the unsatisfactory functioning elements identified during the assessment process, etc.