=Paper=
{{Paper
|id=Vol-1903/paper3
|storemode=property
|title=Control of component alterations according with the target efficiency of data processing and control system
|pdfUrl=https://ceur-ws.org/Vol-1903/paper3.pdf
|volume=Vol-1903
|authors=Vladimir E. Gvozdev,Murat B. Guzairov,Daniya V. Blinova,Aliya S. Davlieva
}}
==Control of component alterations according with the target efficiency of data processing and control system ==
https://ceur-ws.org/Vol-1903/paper3.pdf
Control of component alterations according with the target efficiency of
data processing and control system
V.E. Gvozdev1, M.B. Guzairov1, D.V. Blinova1, A.S. Davlieva1
1
Ufa State Aviation Technical University, Karl Marx street, 12, Ufa, Russia
Abstract
In this article we describe the solution to make an estimate of allowed alternations in model components parameters that make up a data
processing and control system. They reflect properties of physical and information components of the aforementioned system. This solution is
derived according to the limitations of possible changes in integral property that describes the system behavior in different modes of operation.
The proposed solution makes it possible to solve not only the direct problem - making a conclusion whether the vulnerability of the data
processing system is negligible with respect to alternations in parameters of this systems components but the inverse as well, finding tolerable
levels in alterations in systems components parameters from an acceptable level of uncertainty of targeted efficiency. The proposed solution
follows known demands: inner properties of the system must be so that customer demands are fulfilled.
Keywords: data processing and control system; system vulnerability; target system efficiency; parameter alternations; uncertainty in systems
components
1. Introduction
Nowadays information environment is a key factor in the life of our society, which leads to critical importance of managing
the functional vulnerabilities of data processing and control systems. (DPCS) [1]. Concept of "security" is tightly coupled with
the concept of "reliability" [2]. Reliability estimate is done by comparison of actual functional properties of the system and base
functional properties defined in the development specification. These base functional properties in turn are the reflection of
wishes and demands of the users onto the functional properties of DPCS. One of the properties of "general reliability" is
survivability, the property of the system to continue functioning under influence of external and internal malicious factors, such
factors include alternations in parameters of components of the system [3,4]. The opposite to survivability is vulnerability - a
parameter that describes the possibility of the system being damaged by external and internal causes of different nature. These
can be functional, economical, management, physical and so on. One of the distinct properties of modern DPCS is that they have
infinitely many internal states. This is caused by infinite combinations of input data as well as other external factors that can
cause errors of different nature. The cause of these defects are flaws of different types made on certain stages of software
lifecycle [5-8]. The latter promotes development of vulnerability research techniques of DPCS by analysis of external behavior
of the system [9-11]. This work presents a technique to study the influence of alterations in systems parameters, running in
different modes; on it’s vulnerability in cases when the external behavior of the system is defined by the target efficiency
property.
2. Target efficiency as indirect property of functional vulnerability
Functional vulnerability is the factor that negatively effects consumer qualities and consumption of resources needed to
maintain DPCS.
Target efficiency shows the degree of match between actual functions of the system and it’s target functions [2]. Due to this
fact target efficiency can be viewed as integral quality property of DPCS, used in different modes. This quality property shows
the correlation between the expected by users behavior and external behavior of the given system. Decline in the target
efficiency is an indirect property of deviation of the system from state S k and base state S 0 , in other words it is an indirect
vulnerability criteria. Random nature of the target allows the usage of statistical methods to research the target efficiency [3].
In [3] robustness of the system is defined as follows: "...conditional probability of end system state S k will not deviate from
base state S 0 more than a given value 0 when event happens". The same reference contains formal relations between functional
vulnerability and robustness.
v f 1 Rob , (1)
where Rob 1 P[ Sk S0 0 ] . Here is an attribute of unwanted event.
Based on the given definition of robustness relations between robustness and functional vulnerability it is possible to state
that there exists a direct dependency between robustness and target efficiency. Existence of such dependency lets us postulate
the following: functional vulnerability of the system v f is contained in tolerable limits 0
(v f )
, if the probability of deviation of
target efficiency property Э does not rise over a base value 0
(v f )
:
(Э ) (v )
P[ Э Э( 0) 0 ] v f 0 f . (2)
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Alteration of systems components parameters is the inherent property of any DPCS. Statistical uncertainty as a probability of
state parameters being in tolerable intervals comprise the metric property of such alteration. On the other hand change in the
parameters is the cause of statistical uncertainty of target efficiency property:
v f f1 ( Н D ) , (3)
H Э f2 (Н D ) , (4)
Here H Э is the metric uncertainty characteristic of the target efficiency;
f1 () – a direct functional relationship, making a relationship v f between the metric characteristics of the uncertainty Н D
and the state parameters vector components D .
f 2 () – a direct functional relationship that makes a relationship H Э between the metric characteristics of uncertainty Н D .
The character f 2 () is defined by the structure of the system.
From (3) and (4) it can be concluded that, from the limitations on the statistical uncertainty of the system's target efficiency,
there is a limitation on the value of the statistical uncertainty of the system state parameters. In other words, if the limitations on
the variability (the uncertainty characteristic) of the average target efficiency’s index are kept, then it can be argued that the
vulnerability of the system is within the permissible limits.
3. Task statement and assumptions
The initial data of the problem are:
(A) Description of the system states set Si (i 1; N ) , with each state matching the characteristics of the target efficiency Эi ;
(B) The same characteristics of the statistical uncertainty of the target efficiency for each states H i (Э ) ;
(C) A system model that characterizes the relationships ij between the states i and j (i, j 1; N , i j ) ;
(D) A rule that allows us to estimate the average proportion of the time pi (i 1; N ) the system is in the i-th state;
(E) Uncertainty characteristics of relations Н ij ( ) ;
(F) The rule for estimating the average target efficiency Э as a function of Эi and p i :
Э ( Эi , pi ) ; (5)
(G) The rule for estimating the statistical uncertainty characteristics of the average target efficiency H Э based on
Hi (Э), Hij ( ) :
H Э f 2 ( H i ( Э), H ij ( )) (6)
Note that in (5) components H i ( Э), H ij ( ) are the components of the state parameters vector (see (H)).
(Э )
(H) Limitations on the variability H Э of the uncertainty characteristic of the average target efficiency 0 .
It is required: to estimate the limits on the possible values of uncertainty characteristics H i ( Э), H ij ( ) based on the
limitation on the values H Э of the uncertainty characteristic of the average target efficiency.
Assumptions:
(A) The apparatus of Markov processes is used as a basis for modeling the state of DPCS [12];
(B) Intervals Эi [Эi( l ) , Эi( u ) ] ; ij [(ijl ) , (iju ) ] are used as characteristics of the statistical uncertainty of the target
efficiency H i (Э ) and relationships H ij ( ) accordingly. The index "l" corresponds to the lower limit of the interval;
index "in" - the upper;
(C) Linear convolution is used as an estimate of the target efficiency
Э i 1 рi Эi ,
N
(7)
which is the average value of the target efficiency;
(D) Probability is a uncertainty characteristic of the target efficiency
H Э P[а ( н ) Э а ( в ) ] , (8)
where, а (l ) , а (u ) are determined by (Fig. 1):
(Э )
P[0 Э а ( н ) ] P[а ( в ) Э ] 0 / 2 . (9)
Fig. 1. The graphical illustration to the problem of estimating confines on the of uncertainty characteristics values of the target efficiency.
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In Fig. 1 Э(0) corresponds to the basic values {Эi }, {ij } .
4. Solution for the task1
The basis solution for the task is the construction of the dependence (6), which connects the statistical characteristics of the
uncertainty of the average target efficiency of the system with the statistical characteristics of the uncertainty of the components
of the system model. The basis for constructing the dependence (6) is a statistical experiment, the scheme of which is shown in
Fig.2.
Specifying a model (graph) linking the states of the system (nodes) and transitions (edges)
between states
Specifying the statistical uncertainty characteristics of nodes and edges as lower and upper
limits {Эi(l ) , Эi(u ) } ; {ij , ij } , i , j 1; N , i j
(l ) (u )
( )
Generation arrays of random numbers corresponding to H i( ) (Э ) , H i , j ( ) , 1; and
( )
calculation on their basis an array of random values of average target efficiency H Э ,
1;
( )
On the base of the H i( ) ( Э) H i , j ( ) , H Э( ) was formulated the dependence
H Э f 2 ( H i ( Э ), Н ij ( ))
(Э )
Setting a limitations 0 on the variability of the statistical uncertainty index the average
target efficiency, determining the limits Э(l ) , Э(u ) , the range of possible values Э
Estimation based on the dependence H Э f 2 ( H i ( Э ), H ij ( )) and {Э
(l )
, Э(u ) } limitations
on the values {Эi , Эi } , {ij , ij }
(l ) (u ) (l ) (u )
Fig. 2. Scheme of statistical experiment.
In the experiment as the uncertainty characteristic of the average target efficiency H Э was the distribution density f (Э ) of
the average target efficiency Э . As the uncertainty characteristics of system components H i ( Э ), H ij ( ) were interval limits of
possible values {Эi(l ) , Эi(u ) } , {(ijl ) , (iju ) } . These limits were determined by the rules:
Эi(l ),(u ) Эi( ) (1 Э ) ; ij
(l ),(u )
(ij) (1 ) ,
where the sign "–" corresponds to the lower limit of the interval of possible values of the graph component characteristic; the
"+" sign corresponds to the upper limit;
the index " " corresponds to the basic values of the characteristic.
Note that the interval uncertainty characteristics estimates in accordance with the principle of maximization of entropy [13,
14] can be associated a law of random variable distribution.
Fig. 3 shows the model (states graph) of the system [15, 16]. Table 1 shows the base values of average target efficiencies
(Эi(b ) , i 1;4) . The base values of the transitions intensities ((ijb) , i, j 1;4, i j ) were taken to be the same and equaled ten.
During the study, Э , took a different value ( Э [0;1], [0;1]) . Fig. 4 shows estimates of the distribution densities
f (Э ) , corresponding to different Э , for different uncertainty distribution by the graph components:
(A) The statistical uncertainty corresponds to the graph nodes, the nominal values of the transitions intensities correspond
to the edges;
1
In the development of the program for conducting a statistical experiment and processing the results of the experiment, the undergraduate student of the
Department of Technical Cybernetics of the Ufa State Aviation Technical University Teslenko V.V. actively participated.
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(B) The statistical uncertainty corresponds to the graph edges, the nominal values of the average target efficiency
correspond to the nodes;
(C) The statistical uncertainty corresponds to both the edges and the nodes of the graph.
S3
λ23 λ43
λ32 λ13 λ34
λ24
S2 S4
λ42
λ12 λ31 λ14
λ21 λ41
S1
Fig. 3. States graph of the system.
Table 1. Characteristics of graph nodes.
System state S S2 S3 S4
1
Base value of average target
efficiency 10 20 30 40
At estimating f (Э ) value was taken 10 4 . To determine the number of grouping intervals in the histograms construction,
the Sturges rule was used:
n int(1 3.3 lg )
a) b)
c)
Fig. 4. Estimates of the distribution densities by: a) Э 0, 0.2 ; b) Э 0.2, 0 ; c) Э 0.2, 0.2 .
The constructed estimates f (Э ) became the basis for constructing H Э , for various combinations of characteristics the
(Э )
statistical uncertainty of the graph components. Fig. 5 shows the resulting dependencies, corresponding to different values 0
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a) b)
c) d)
Fig. 5. Uncertainty characteristics dependences of average target efficiency on uncertainty characteristics of graph components.
The resulting dependences H Э allow us to solve a direct problem: an estimation of uncertainty characteristics of target
average efficiency H Э on the information basis on model components parameters variability; and the inverse problem: an
estimation limitations on the parameters variability of graph’s nodes and edges based on the limitations on the characteristics of
the target average efficiency.
(Э )
An example of solving a direct problem. Given: 0 ; Э . It is believed that the variability of transitions intensities is
absent. It is required to estimate the expected uncertainty H Э . The scheme for solving the problem is shown in Fig. 6.
Fig. 6. An example of solving a direct problem.
An example of solving an inverse problem.
(Э )
Given: H Э ; 0 ; . It is required to estimate the possible value Э . Fig. 7 shows an example of solving an inverse
problem with the selected value . Thus, the proposed technique allows us to formalize the procedure for making conclusions
about the vulnerability of the data processing and control system based on the analysis the characteristics of the external
behavior of the system.
5. Conclusion
Nowadays DPCS play more and more of a substantial role as a vital component in systems that control complex objects. This
promotes posing the problem of developing theoretical basis and development tools for managing the functional security of
DPCS. One of the key tasks in solving such a problem is analyzing vulnerabilities of DPCS. They are affected by internal
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properties (construction, component properties) and by external environment in which the system is operated. The allowed level
of the vulnerability is determined by whether the deviation of the systems behavior from the base behavior is affecting the
quality of control of a complex object.
Fig. 7. An example of solving an inverse problem.
In this article a solution is given to estimate the possible deviation in components parameters of the model OF DPCS (such
parameters reflect physical and information properties of the system). This solution is based of the limitations on alternation of
the integral factor that shows the behavior of the system in different modes of operation, this behavior is the target efficiency of
the system. Proposed solution follows known demands: inner properties of the system must be so that customer demands are
fulfilled (Kano’s model). The described solution makes it possible to solve not only the direct problem - making a conclusion
whether the vulnerability of the data processing system is negligible with respect to alternations in parameters of this systems
components but the inverse as well, finding tolerable levels in alterations in systems components parameters from an acceptable
level of uncertainty of targeted efficiency’s index.
Acknowledgements
This work was supported by RFBR grant No. 17-07-00351 "Methodological basics of dependability assurance of
transmission systems telemetry information with use of intelligent data analysis technologies".
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