CC BY
17
--------------------□ □----------------------
З використанням розроблених математичних моделей реакції комплексу охоронної сигналізації на появу рухомого об’єкта показана залежність його ефективності від кількості сейсмічних датчиків і схеми їх розміщення на ймовірних маршрутах пересування. В дослідженнях враховано, що ефективність комплексу визначають чутливість сейсмічних датчиків та параметри його систем: ймовірність правильної класифікації рухомих об’єктів та ймовірність правильного приймання радіосигналу
Ключові слова: комплекс охоронної сигналізації, сейсмічні датчики, математична модель комплексу охоронної сигналізації
□----------------------------------□
Используя разработанные математические модели реакции комплекса охранной сигнализации на появление движущегося объекта, показана зависимость его эффективности от количества сейсмических датчиков и схемы их размещения на вероятных маршрутах передвижения. В исследованиях учтено, что эффективность комплекса определяют чувствительность сейсмических датчиков и параметры его систем: вероятность правильной классификации движущихся объектов и вероятность правильного приема радиосигнала
Ключевые слова: комплекс охранной сигнализации, сейсмические датчики, математическая модель комплекса охранной сигнализации --------------------□ □----------------------
УДК 263.09
RESEARCH OF THE DEPENDENCE OF THE GUARD SIGNALING COMPLEX ON THE LOCATION OF SEISMIC SENSORS
B. Yu. Volochiy
Doctor of technical sciences, professor Department of theoretical radio engineering and measuring National university ”lviv polytechnic” Str. Bandera, 12, lviv, ukraine, 79013 E-mail: bvolochiy@ukr.net V. A. Onishchenko Senior research fellow Scientific centre of the land forces Army academy named after hetman sahaidachny Guards str., 32, Lviv, Ukraine, 79012 E-mail: onishchenkovolodymyr@gmail.com
1. Introduction
In the practice of using guard signaling complexes there are the following layouts of the location of seismic sensors (SS) on the possible movement routes of moving objects (MO): four SSs placed in pairs if far and close control zones; two SSS placed on the border in far or close control zones; two SSS placed serially in far and close control zones; one SS placed in far or close control zone.
The effectiveness of GSC depends not only on SS sensitivity but also on the possibilities of the method of MO classification and the way of transmitting over radio channel from autonomous systems of detection, object classification and transmitting radio signals (DOCTRS) to the systems of receiving and displaying information (RDI) of GSC.
In order to research the dependence of the GSC effectiveness on SS location and receive recommended parameters for autonomous systems DOCTRS and RDI it is necessary to develop mathematical models which could allow comparative analysis.
Model of GSC reaction for two SSs located serially in far and close control zones is given in articles [1, 2].
In the given article the authors present a mathematical model of GSC reaction on the MO appearance with SSS placed in pairs in far and close control zones.
Using these models the research has been conducted of the GSC effectiveness for two ways of SSs location. In addition, one model was used to conduct research of GSC
effectiveness with one SS on the route, and the second one -for two SSS placed on the border.
The authors received and analysed dependences of probability of successful carrying out of GSC task on the probability of correct MO classification, probability of correct radio signal receiving and probability of SS reaction on MO. Probability of SS reaction on MO represents its sensitivity, takes into account characteristics of the area (ground, relief), season of the year, and MO parameters.
2. Analysis of researches and publications
Problems as for creation of the guard signaling system are considered in the publications [1 - 9].
The articles [3, 4] describe existing radio electronic guard systems. Radio electronic guard networks are presented among others in which seismic sensors are used (SS). It is determined that seismic electronic magnetic networks are widely used for guarding warehouses with nuclear weapons. They provide detecting a trespasser who walks or crawl slowly. Intelligence signal systems which have SSS in their structure are used for rapid installing of guard systems. Seismic sensors also have guard systems along the perimeter.
The article [5] considers the method of autonomous blocks for creating adaptive algorithms of the detecting of the moving objects (MO). This method allows to model the process of propagation of seismic waves. The research that is
3
© B. Yu. Uoiochiy, U. A. Onishchenko, 2014
being carried aims to examine the peculiarities of formation and propagation of seismic waves on the ground, the influence of the SS characteristics on the formation of signals.
Guard signaling systems have to process seismic signal in order to detect and classify MO in real time. In the article [6] this task is solved by the method of express evaluation of the spectrum characteristics of seismic signals on the base of their extreme filtration. The authors confirm that this method of evaluation of spectrum characteristics is effective, simple and not requiring the expenditure of much labour. Parameters of constituents allow to form diagnostic signs with necessary characteristics, namely, to have physical interpretation, to describe certain characteristics of the signal; to be stable (not to be changed during insignificant change of the signal characteristics); to be computed in real time.
The article [7] considers the development of guard systems for the territories and objects of strategic importance. It solves the task of compatible processing of seismic, acoustic and magnetometric signals that come from the sensors. For the complex analysis of the received information it is suggested to use the algorithm the basis of which is method of combinatorial ordered modelling. This method allows to carry out the possibility of self-learning in the process of detection and recognition of MO, and also to reduce the quantity of false alarms from GSC.
In the reference book [8] there is a model with the aid of which you can present the reaction of GSC on the movement of the object through the controlled area. However, the degree of the adequacy of such model does not allow differentially present such peculiarities as detecting by the seismic sensor the appearance of the MO in the controlled zone, successful classification of the MO, correct receiving of the radio signals of RDI (Receiving and Displaying information).
In order to research the effectiveness of GSC in the articles [1, 2] it is suggested to use the mathematical model of the reaction of GSC on the movement of the MO in the distant and close zones of control. Two SSs are installed serially along the route.
In the thesis research [9] the following models are suggested: mathematical models of the analysis of space organizational structure of the object under guard and models of making project decisions during development of technical means complex.
So, in well-known publications about GSC effectiveness, the main attention is given to the development and improvement of the methods of MO classification. There is one more possibility to improve GSC effectiveness - due to the rational placement of seismic sensors.
The aim of the work is to develop a mathematical model of GSC reaction on the appearance of MO with pairwise placement of SSs in far and close control zones in order to conduct research of the dependence of GSC effectiveness on the SS sensitivity, on the effectiveness of the method of MO classification, and on the effectiveness of the radio signal transmitting system.
3. Mathematical model of guard signaling complex on the appearance of moving object
Guard signaling complex detects MO with the aid of SSs of autonomous systems DOCTRS, classification device identifies it, and the transmitter of the autonomous system transmits radio signal to RDI about the type of MO.
Effectiveness of such complex depends on SSs placement of autonomous systems DOCTRS, on their sensitivity, method of MO classification, system of transmitting radio signals. This dependence stipulates necessary degree of adequacy of a mathematical model of GSC reaction on the MO appearance with pairwise placement of SSs in far and close control zones.
The model gives possibility to research optimal structure and technical characteristics of the equipment that will be used under different conditions of its installment [1, 2].
Guard signaling complex is to be installed on probable routes of unauthorized MO movement to stationary object (SO) (Fig. 1). In this research the following variant of installing autonomous systems DOCTRS is examined: in far and close borders there are two by two autonomous systems DOCTRSj and DOCTRS2, DOCTRS3 and DOCTRS4, thus creating appropriate control zones. Zones of SSs sensitivity of each pair border each other. Such variant gives possibility to determine the direction of MO movement.
j SO
N ''
RDI
Close control zone
Far control zone
Autonomous systems of object detecting, classification and radio signal transmitting
Seismic
sensor
Classification
device
Transmitter
Fig. 1. Layout of placement of GSC systems
Technology of modeling discrete continuous stochastic systems [10, 11] was used to create mathematical model. It provides for the formation of the model in the form of graph of state and transitions and compiling system of differential equations of Kolmogorov - Chapman [8].
Method of development of the graph of state and transitions is the development of formalized presentation of the object under research in the form of structural automation model (SAM). This process on the base of SAM is formalized and is carried out with the aid of software module ASNA-1.
Components of SAM are as follows:
1) parameters of the object under research that are included into its mathematical model;
2) state vector of the object under research;
3) basic events (BE);
4) formalized description of the situations in which BES take place (conditions and circumstances taken into attention fot the given BE);
5) formulae of evaluation of the intensity of basic events for each situation in which BE takes place;
6) rules of modification of state vector component.
Parameters of SS reaction of autonomous systems
DOCTRSj 2 3 4 on MO appearance (they are determined with
a glance of soil type, relief, distance of MO from SS, weight and speed of MO):
P1 ( P2 ) - probability that both SSs of autonomous systems DOCTRS1 and DOCTRS2 do not react (react) on the MO appearance in far control zone;
P3 ( P4) - probability that SS of autonomous system DOCTRS1 does not react (reacts) on MO, and SS of autonomous system DOCTRS2 reacts (does not react) on MO when it appears in far control zone;
P13 ( P14 ) - probability that both SSs of autonomous systems DOCTRS3 and DOCTRS4 do not react (react) on the MO appearance in close zone of control;
P15 (P16 )-probabilitythatSSofautonomoussystem DOCTRS3 does not react (reacts) on MO, and SS of autonomous system DOCTRS4 reacts (does not react) on MO, when it appears in close zone of control.
Parameters of classification devices of autonomous systems DOCTRS1, DOCTRS2, DOCTRS3 and DOCTRS4.
As far as SSS of autonomous systems DOCTRS are installed in different soil, results of a correct determination of MO type will differ :
P5 ( P6 ) - probability that classification device of autonomous system DOCTRSj determines MO type incorrectly (correctly);
P7 ( P8 ) - probability that classification device of autonomous system DOCTRS2 determines MO type incorrectly (correctly);
P17 ( P18 ) - probability that classification device of autonomous system DOCTRS3 determines MO type incorrectly (correctly);
P19 ( P20 ) - probability that classification device of autonomous system DOCTRS4 determines MO type incorrectly (correctly).
As far as SSS of autonomous systems DOCTRS are installed on the area under different conditions (distance from RDI, use of different antennas), results of receiving radio signals RDI from autonomous systems DOCTRS might be different:
P9 ( P10 ) - probability that RDI receives (does not receive) a radio signal from DOCTRS1;
P11 ( P12 ) - probability that RDI receives (does not receive) a radio signal from DOCTRS2;
P21 ( P22 ) - probability that RDI receives (does not receive) a radio signal from DOCTRS3;
P23 ( P24 ) - probability that RDI receives (does not receive) a radio signal from DOCTRS4.
State of the object under research is presented by a vector that has 7 component providing necessary degree of model adequacy, namely:
- Component V1 presents the location of MO on the area and can acquire the following values: V1 = 1 - MO beyond the sensitivity zone SS1, SS2, SS3 and SS4; V1 = 2 - MO in far control zone (zones of sensitivity SS11 and SS2 ); V1 = 3 - MO in close control zone (zones of sensitivity SS3 and SS4 ). Initial value V1 = 1.
- Component V2 presents state of autonomous system DOCTRS1 (characterizes interaction of autonomous systems DOCTRS1 with MO). Values of this component: V2 = 0 - autonomous system DOCTRS1 is in good order and ready to work, MO is absent in sensitivity zone SS^ V2 = 1 - autonomous system DOCTRS1 does not react on MO location in sensitivity zone SS1; V2 = 2 - autonomous system DOCTRS1 reacts on MO location in sensitivity zone
SS1, but does not classify it correctly; V2 = 3 - autonomous
system DOCTRS1 reacts on MO location in sensitivity zone SS1 and classifies it correctly. Initial value V2 = 0 .
- Component V3 presents state of autonomous system DOCTRS2 (characterizes the reaction of autonomous system DOCTRS2 on MO). Value of this component: V3 = 0 - autonomous system DOCTRS2 is in good order and ready to work, MO is absent in sensitivity zone SS2; V3 = 1 - autonomous system DOCTRS2 does not react on MO location in sensitivity zone SS2; V3 = 2 - autonomous system DOCTRS2 reacts on MO location in sensitivity zone
SS2, but does not classify it correctly; V3 = 3 - autonomous system DOCTRS2 reacts on MO location in sensitivity zone and classify it correctly. Initial value V3 = 0 .
- Component V4 presents state of autonomous system DOCTRS3. Values of this component: V4 = 0 - autonomous system DOCTRS3 is in good order and ready to work, MO is absent in sensitivity zone SS3; V4 = 1 - autonomous system DOCTRS3 does not react on MO location in sensitivity zone SS3; V4 = 2 - autonomous system DOCTRS3 reacts on MO location in sensitivity zone SS3, but does not classify it correctly; V4 = 3 - autonomous system DOCTRS3 reacts on MO location in sensitivity zone and classifies it correctly. Initial value V4 = 0 .
- Component V5 presents state of autonomous system DOCTRS4. Values of this component: V5 = 0 - autonomous system DOCTRS4 is in good order and ready to work, MO is absent in sensitivity zone SS4; V5 = 1 - autonomous system DOCTRS4 does not react on MO location in sensitivity zone SS4; V5 = 2 - autonomous system DOCTRS4 reacts on MO location in sensitivity zone SS4, but does not classify it correctly; V5 = 3 - autonomous system DOCTRS4 reacts on MO location in sensitivity zone SS4 and classifies it correctly. Initial value V5 = 0 .
- Component V6 presents state of RDI, when MO is in far control zone (sensitivity zones SS1andSS2). Values of component V6: V6 = 0 - RDIS is on in standby condition; V6 = 1 - RDI is activated from radio signal of autonomous system DOCTRS1; V6 = 2 - RDI is not activated from radio signal of autonomous system DOCTRS1; V6 = 3 - RDI is activated from radio signal of autonomous system DOCTRS2; V6 = 4 - RDI is not activated from radio signal of autonomous system DOCTRS2; V6 = 5 - RDI is activated from radio signals of autonomous systems DOCTRS1 and DOCTRS2; V6 = 6 - RDI is not activated from radio signals of autonomous systems DOCTRS1 and DOCTRS2; V6 = 7 - RDI is activated from radio signal of autonomous system DOCTRS1 but is not activated from radio signal of autonomous system DOCTRS2; V6 = 8 - RDI is activated from radio signal of autonomous system DOCTRS2 but is not activated from radio signal of autonomous system DOCTRS1. Initial value V6 = 0 .
- Component V7 presents state of of RDI, when MO is in close control zone (zones of sensitivity SS3 and SS4 ) and may acquire the following values: V7 = 0 - RDI is on and in standby condition; V7 = 1 - RDI is activated from radio signal of autonomous system DOCTRS3; V7 = 2 -RDI is not activated from radio signal of autonomous system DOCTRS3; V7 = 3 - RDI is activated from radio signal of autonomous system DOCTRS4; V7 = 4 - RDI is not activated from radio signal of autonomous system DOCTRS4; V7 = 5 - RDI is activated from radio signals of autonomous systems DOCTRS3 and DOCTRS4; V7 = 6 - RDI is not activated from radio signals of auton-
3
omous systems DOCTRS3 and DOCTRS4; V7 = 7 - RDI is activated from radio signal of autonomous system DOCTRS3 but is not activated from radio signal of autonomous system DOCTRS4; V7 = 8 - RDI is activated from radio signal of autonomous system DOCTRS4 and is not activated from radio signal of autonomous system DOCTRS3. Initial value V7 = 0 .
Basic events (BE) in the object under research are as follows:
- end of MO location beyond far control zone (MO appearance in sensitivity zone of SS1 and SS2 ) (BE1). This BE1 is combined with basic events CBE3 - “End of reaction of SS1 on the MO appearance”, CBE4 - “End of SS2 reaction on MO appearance”, CBE5 - “End of receiving of RDI radio signal from autonomous system DOCTRS2”.
- end of MO location in far control zone (MO appearance in sensitivity zone of SS3 and SS4 ) (BE2). This BE is combined with basic events CBE7 - “End of SS1 reaction on MO appearance”, CBE8 - “End of SS4 reaction on MO appearance”, CBE9 - “End of receiving RDI radio signal from autonomous system DOCTRS4 ”.
The basic event that finishes carrying out corresponding procedure with the duration that tends to zero is called combined basic event (CBE). A tree of modification rules state vector component is built on the determined BEs and serves as a basis for building a model of the object under research in the form of graphs of states and transitions.
During development of the tree of modification rules state vector component the following tasks are solved: formalized description of situations when BEs take place is given; formulae of calculation of basic events intensity (FCBEI) are composed (in these formulae X1, X2 - intensity of MO appearance in far and close control zones respectively); modification rules state vector component (MRSVC) are established. The tree MRSVC is given in Table 1, 2.
Table 1
Tree of modification rules state vector component for BE1
BE1: End of MO location beyond far control zone (MO appearance in sensitivity zone of SS1 and SS2) (CBE3, CBE4, CBE5, CBE6)
Description of situation when BE1takes place: V1=1
FCBEI MRSVC
1 2
VP, V| := 2; V, := 1;V3:= 1
X1 • P2 ' P5 ' P7 ' P9 ' P11 V1 = 2; V2 := 2; V3 := 2;V6:= 5
X •P P ' P P P 2 .5 7 r10 r12 V1 = 2; V2 := 2; V3 := 2;V6:= 6
X •P P P 'P 'P 2 .5 7 9 r12 V1 = 2; V2 := 2; V3 := 2;V6:= 7
X •P P 'P P P 2 .5 7 r10 r11 V1 = 2; V2 := 2; V3 := 2;V6:= 8
1X 2P P P 9P 11P V1 = 2; V2 := 3; V3 := 3;V6:= 5
X •P 'P 'P 'P 'P 7t1 2 r6 8 r10 12 V1 = 2; V2 := 3; V3 := 3;V6:= 6
X •P 'P 'P 'P 'P ^1 r9 rfi rs r9 1 2 V1 = 2; V2 := 3; V3 := 3;V6:= 7
X •P 'P 'P 'P 'P 7W 2 r6 8 r10 r11 V1 = 2; V2 := 3; V3 := 3;V6:= 8
X •P 'P P 'P 'P 7t1 2 r5 8 r9 r11 V1 = 2; V2 := 2; V3 := 3;V6:= 5
X •P 'P 'P 'P 'P 7t1 2 r5 8 r10 12 V1 = 2; V2 := 2; V3 := 3;V6:= 6
X •P 'P P 'P 'P 7t1 2 r5 8 r9 12 V1 = 2; V2 := 2; V3 := 3;V6:= 7
X •P 'P 'P 'P 'P 1 2 5 8 10 11 V1 = 2; V2 := 2; V3 := 3;V6:= 8
1X 2P 6P 7P 9P 11P V1 = 2; V2 := 3; V3 := 2;V6:= 5
Continuation of Table 1
1 2
X •P P 'P 'P P r2 r6 7 r10 12 V1:= 2; V2 := 3;V3:= 2;V6:= 6
2P 6P 9P to PP V1:= 2; V2 := 3;V3:= 2;V6:= 7
X •P 'P 'P 'P 'P 7^1 2 r6 7 r10 r11 V1:= 2; V2 := 3;V3:= 2;V6:= 8
X •P P P A1 r3 7 r11 V1:= 2; V2 := 1;V3:= 2;V6:= 3
X •P P P 7t1 r3 7 12 V1 := 2; V2 := 1;V3:= 2;V6:= 4
X •P P P 7t1 r3 8 r11 V1:= 2; V2 := 1;V3:= 3;V6:= 3
X •P P P 7t1 r3 8 12 V1:= 2; V2 := 1;V3:= 3;V6:= 4
X P P P • 7H 4 5 9 V1:= 2; V2 := 2;V3:= 1;V6:= 1
X1 • P4 ' P5 ' P10 V1:= 2; V2 := 2;V3:= 1;V6:= 2
X1 • P4 P6 ' P9 9 V1:= 2; V2 := 3;V3:= 1;V6:= 1
X1 • P4 ' P6 P10 V1:= 2; V2 := 3;V3:= 1;V6:= 2
Table 2
Tree of modification rules state vector component for BE2
BE2: End of MO location beyond far control zone (MO appearance in sensitivity zone of SS3 and SS4) (CBE7, CBE8, CBE9, CBE10)
Description of situation when BE2 takes place: Vj=2
FCBEI MRSVC
X P 2 r13 V1 := 3; V4 := 1;V,:= 1
X P ' P ' P ' P P 2 14 17 19 21 23 V1:= 3; V4 := 2;V5:= 2;V7:= 5
X P ' P ' P ' P P 2 14 17 19 22 24 V1:= 3; V4 := 2;V5:= 2;V7:= 6
X P ' P ' P ' P P 2 14 17 19 21 24 V1:= 3; V4 := 2;V5:= 2;V7:= 7
X P ' P ' P ' P P 2 14 17 19 22 23 V1:= 3; V4 := 2;V5:= 2;V7:= 8
X P P ' P ' P ' P 2 14 18 20 21 23 V1:= 3; V4 := 3;V5:= 3;V7:= 5
X P P ' P ' P P 2 r14 18 20 22 r24 V1:= 3; V4 := 3;V5:= 3;V7:= 6
X P P ' P ' P ' P 2 14 18 20 21 24 V1:= 3; V4 := 3;V5:= 3;V7:= 7
X P P ' P ' P P 2 r14 18 20 22 23 V1:= 3; V4 := 3;V5:= 3;V7:= 8
X P P ' P ' P ' P 2 r14 17 20 21 23 V1:= 3; V4 := 2;V5:= 3;V7:= 5
X P P ' P ' P P 2 14 17 20 22 24 V1:= 3; V4 := 2;V5:= 3;V7:= 6
X P P ' P ' P ' P 2 14 17 20 21 24 V1:= 3; V4 := 2;V5:= 3;V7:= 7
X P P ' P ' P P 2 r14 17 20 22 23 V1:= 3; V4 := 2;V5:= 3;V7:= 8
X P ' P ' P ' P P 2 r14 18 19 21 23 V1:= 3; V4 := 3;V5:= 2;V7:= 5
X P ' P ' P ' P P 2 14 18 19 22 24 V1:= 3; V4 := 3;V5:= 2;V7:= 6
X P ' P ' P ' P P 2 14 18 19 21 24 V1:= 3; V4 := 3;V5:= 2;V7:= 7
X P ' P ' P ' P P 2 r14 18 19 22 23 V1:= 3; V4 := 3;V5:= 2;V7:= 8
X ' P ' P ' P 2 r15 19 23 V1:= 3; V4 := 1;V5:= 2;V7:= 3
X ' P ' P ' P 2 15 19 24 V1 := 3; V4 := 1;V5:= 2;V7:= 4
X ' P ' P ' P 2 r15 20 23 V1:= 3; V4 := 1;V5:= 3;V7:= 3
X ' P ' P ' P 2 r15 20 24 V1 := 3; V4 := 1;V,:= 3;V7:= 4
X ' P P P 2 r16 17 21 V1:= 3; V4 := 2;V5:= 1;V7:= 1
X ' P P P 2 r16 17 22 V1:= 3; V4 := 2;V5:= 1;V7:= 2
X ' P P P 2 r16 18 21 V1 := 3; V4 := 3;Vq:= 1;V7:= 1
X ' P P P 2 r16 18 22 V1:= 3; V4 := 2;V5:= 1;V7:= 2
E
Developing of SAM finishes with its verification. The essence of verification method is in finding discrepancies in comparing test model of the object under research in the form of graph of states and transitions with the graph of states and transitions which forms software module ASNA-1 on the basis of SAM, and elimination of errors that are the cause of discrepancies. Development of test model is carried out by method of single-step analysis of states for actual BEs [12] and it is given in Table 3.
Table 3
Test model of reaction of guard signaling complex on MO appearance
№ State and BE that are examined State vector № of sta- te Transition from state to state In- ten- sity of BE
V1 V2 V3 V 4 V 5 V6 V7
1 IS 1 0 0 0 0 0 0 1 - -
2 1BE1 2 1 1 0 0 0 0 2 1—2 *1
3 2BE2 3 1 1 1 1 0 0 3 2—3 %2
4 2BE2 3 1 1 2 2 0 5 4 2—4 %2
5 2BE2 3 1 1 2 2 0 6 5 2—5 %2
6 2BE2 3 1 1 2 2 0 7 6 2—6 %2
7 2BE2 3 1 1 2 2 0 8 7 2—7 %2
8 2BE2 3 1 1 3 3 0 5 8 2—8 %2
9 2BE2 3 1 1 3 3 0 6 9 2—9 %2
10 2BE2 3 1 1 3 3 0 7 10 2—^10 %2
11 2BE2 3 1 1 3 3 0 8 11 2—^11 %2
12 2BE2 3 1 1 2 3 0 5 12 2—12
13 2BE2 3 1 1 2 3 0 6 13 2—13 %2
14 2BE2 3 1 1 2 3 0 7 14 2—14 %2
15 2BE2 3 1 1 2 3 0 8 15 2—15 %2
16 2BE2 3 1 1 3 2 0 5 16 2—16 %2
17 2BE2 3 1 1 3 2 0 6 17 2—17 %2
18 2BE2 3 1 1 3 2 0 7 18 2—18 %2
19 2BE2 3 1 1 3 2 0 8 19 2—19 %2
20 2BE2 3 1 1 1 2 0 3 20 2—20 %2
21 2BE2 3 1 1 1 2 0 4 21 2—21 %2
22 2BE2 3 1 1 1 3 0 3 22 2—22 %2
23 2BE2 3 1 1 1 3 0 4 23 2—23 %2
24 2BE2 3 1 1 2 1 0 1 24 2—24
25 2BE2 3 1 1 2 1 0 2 25 2—25
26 2BE2 3 1 1 3 1 0 1 26 2—26
27 2BE2 3 1 1 3 1 0 2 27 2—27
28 1BE1 2 2 2 0 0 5 0 28 1—28 X1
29 28BE2 3 2 2 1 1 5 0 29 28—29 %2
30 28BE2 3 2 2 2 2 5 5 20 28—30 %2
649 626BE2 3 3 1 2 1 2 2 649 626— —649 %2
650 626BE2 3 3 1 3 1 2 1 650 626— —650 %2
651 626BE2 3 3 1 3 1 2 2 651 626— —651 %2
Generated graph has 651 states and 676 transitions. On the base of this graph a mathematical model of GSC reaction on the MO appearance has been made, with pairwise placement of SSs in far and close control zones in the form of system of differential equations of Kolmogorov - Chapman.
dQ1(t)
dt
- = -^(tXP! + (P2(P5 + P6)(P9 + P10 ) +
+P 3XP7 + P8)(Pn +P12) +P4(P5 +P6)(P 9 +P10)), dQ2(t)_
dt
- = ^1Q1(t)P1 -X 2Q2(t)(P13 +
+(P14(P21 + P22)(P17 +P18) + P15)(P23 +P24 )(P19 + P20) + +P16(P21 + P22 )(P17 + P18)),
dQs(t).
dt
-=X ' Q2 (t) ' P13 ,
= X2 ' Q626(t) ' P16 ' P17 ' P22 , = X2 ' Q626(t)' P16 ' P18 ' P21 , = X2 ' Q626(t)' P16 ' P18 ' P22 ,
dQ649(t) dt
dQ650(t) dt
dQ651(t) dt
where dQ1(t)...dQ651(t) - probabilities of location of the object under research in states from one to six hundred fifty one.
4. Results of comparative analysis of GSC effectiveness
Suggested mathematical model of GSC reaction on MO appearance with pairwise SSS placement in far and close control zones, and also model of GSC reaction given in [1, 2] have the necessary level of adequacy and allow receiving reliable results concerning effectiveness of its work.
Effectiveness of GSC work is studied with different requirements to the method of MO classification and to the system of radio signal transmitting under the condition of given SS sensitivity with a glance of ground, relief of the area, distance of MO from SS, MO weight and speed. GSC effectiveness is evaluated by probability of detection and correct MO classification due to the signal of even one SS (Ps,f).
In order to conduct researches the authors set actual for practical realization ranges of changes of probability values for correct MO classification ( Pcc ) and probability of correct radio signal receiving RDI (Pcr ) from 0.6 to
0.99.Probability values of SS reaction on MO appearance are given with a glance of the fact that SSS are installed on soft ground.
Fig. 2 - 5 show dependences of GSC effectiveness on probability of correct MO classification and on probability of correct radio signal receiving for four layouts of SSS placement on possible routes of moving object movement. It is accepted in the researches that the value of probability of successful fulfilment of the GSC task has to be not less than 0.95.
3
Fig. 5. Dependence of GSC effectiveness (Psf) on Pcc and PCr during placement of one SS in far or close control zones
5. Conclusion
The received results showed that in order to ensure probability of successful fulfilment of seismic sensor task on the soft ground not less than 0.95, it is necessary to place four seismic sensors pairwise in far and close control zones. And requirements to the method of seismic sensor classification and to the system of radio signal transmitting can be not high. To ensure high requirements it is possible to place two SSs - one in far control zone and one in close control zone. Suggested models are assumed as a basis of the methods which gives possibility to determine parameters of seismic sensor classification device and system of transmitting radio signals with given seismic sensor sensitivity under the worst conditions of their use. And vice versa, it is possible to determine seismic sensor sensitivity with given parameters of classification device and system of transmitting radio signals.
Mentioned results show what requirements it is necessary to lay down to the classification method and the way of signal transmitting in order to keep given effectiveness of guard signaling complex ( Psf = 0.95 ), if necessary, to reduce number of seismic sensors on probable route of moving object movement from four to two.
In further researches concerning creating perspective guard signaling complex, one should pay attention to the improvement of the method of moving object classification on the basis of signals from seismic sensors.
References
1. Volochiy B. Yu. Interaction Model between Reconnaissance Signaling Complex and Detected Object under Different Operative-Tactical Situation [Text] / B. Yu. Volochiy, V. A. Onyshchenko // “Military Technical Review,” Ukrainian Army Academy, c. Lviv: UAA. -2013. - № 8(1). - P. 50-57.
2. Volochiy, B. Yu. Mathematical Model of Detection Process of Moving Objects with Stationary Object Guard Signaling Complex [Text] / B.Yu. Volochiy, V. A. Onyshchenko Edited by Yurkova N.K// International “Reliability and Quality.” Vol. 1. Russia, c. Penza, PGU publishing office, 2013. - P. 156-159.
3. Mosalev, V. “Electronic Guard Systems of the US Army. Prospects for Development”, “Foreign Military Review” [Text] / V. Mosalev // M.: Publishing house “Red Star.” - 2001. - № 3. - P. 26-29. - № 4. - P. 23-26.
4. Khoroshev, D. “Reconnaissance-Signal Guard Systems and Warning Assets of the US Army” [Text] / D. Khoroshev // M.: Publishing house “Red Star”, “Foreign Military Review.” - 2011. - № 4. - P. 45-53.
5. Golovanov, O.A. “Decomposition Approach in Modelling Seismoacoustic Waves Dissemination in the Earth Surfice” [Text] / O. A. Golovanov,
A. A. Kichkidov, N.V Prokina, S. A. Tarasov // “Sensors and Systems: Methods, Assets and Technologies to Receive and Process Measuring Information” (Sensors and Systems - 2012): International scientific and technical conference with the elements of science school for young scientists (c. Penza, 22-26 October 2012) / Edited by Lomteva E.A., Dmitrienko A. G.: The PGU publishing office, 2012. - P. 149-153.
Fig. 2. Dependence of GSC effectiveness (Psf) on Pcc and P^ during placement of four SSs in pairs in far and close control zones
Py.B
0,960,95'-
0,92-----
0,880,84-----
0,8 -0,76-^;
0,72-^
0,680,640,6
0,6
Fig. 3. Dependence of GSC effectiveness (Psf) on Pcc and P^ during placement of two SSs on the border in far and close control zones
1 Py-B
Pn.n=0,99 Pn.n=0,9 Pn.n=0,8
Pn.n=0,7
Pn.n—0,6
Pn.K
Fig. 4. Dependence of GSC effectiveness (Psf) on Pcc and P^ during placement of two SSs serially in far and close control zones
6. Myasnikova, N. V. “Express Analysis of Seismosignals” [Text] / N. V. Myasnikova, M.P. Beresten, V.A. Dudkin // “The News of High Edu-
cation Schools. Povolgsky Region. Technical Sciences.” - 2001. - № 7. - P. 144-151.
7. Kotelnikov, A. V “Processing of Information Received from the Sensors of Object Detecting System Using the Grating Method” [Text] /
A. V Kotelnikov, V. B. Lebedev // “Sensors and Systems: Methods, Assets and Technologies to Receive and Process Measuring Information” (Sensors and Systems - 2012): International scientific and technical conference with the elements of science school for young scientists (c. Penza, 22-26 October 2012) / Edited by Lomteva E.A., Dmitrienko A.G.: c. Penza, The PGU publishing office, 2012. - P. 157-161.
8. Abchuk, V. A. “Handbook on Researching Military Operations” [Text] / V. A. Abchuk, F. A. Matveichuk, L. P. Tomashevsky // M.: Publis-
hing agency of Defense Ministry of USSR, 1979. - 368 p.
9. Zaffel, Ali Muhammad. “Subsystem of Supporting Project Decisions on Creating Security Systems at Nonproduction Inductry Objects.”
[Text] / Ali Muhammad Zaffel // Author’s referat on the degree of candidate of technical sciences, speciality code 05.13.12 - automatization systems of project works, c. Kharkiv, The Kharkin State University of Radio Electronic, 2001. - 20 p.
10. Volochiy, B. Yu. Technology modeling algorithms behavior of information systems [Text] / B. Yu. Volochiy // Lviv: Lviv Polytechnic National University edition, 2004. - 220 p.
11. Bobalo, Yu. Mathematical models and methods of analysis of radioelectronic, electromechanic and software systems [Text] / Yu. Bobalo,
B. Volochiy, O. Lozynskyy, B. Mandziy, L. Ozirkovskyy, D. Fedasyuk, S. Shcherbovskykh, V Yakovyna // Lviv: Lviv Polytechnic National University edition, 2013. - 300 p.
12 Volochiy, B. Yu. System engineering projecting of telecommunication networks. Practical work: textbook [Text] / B. Yu. Volochiy
L. D. Ozirkovskyi // Lviv: Lviv Politechnika Publishing House,
-------------------□ □----------------------
Представлено систему моделювання на основі К-значного диференційного числення, яка дозволяє отримати більш якісне і точне моделювання в порівнянні з двійковим моделювання за рахунок обліку при моделюванні крутизни фронтів, К-значного квантування рівня сигналів по амплітуді та обліку електромагнітної сумісності. Моделювання в системі виконується за рахунок спільного розв’язання звичайних К-значних диференціальних рівнянь і К-значних диференціальних рівнянь із запізненням
Ключові слова: система моделювання, К-значне диференційне числення, електромагнітна сумісність, квантування сигналів
□ □
Представлена система моделирования на основе К-значного дифференциального исчисления, которая позволяет получить более качественное и точное моделирование по сравнению с двоичным моделированием, за счет учета при моделировании крутизны фронтов, К-значного квантования уровня сигналов по амплитуде и учета электромагнитной совместимости. Моделирование в системе выполняется за счет совместного решения обыкновенных К-значных дифференциальных уравнений и К-значных дифференциальных уравнений с запаздыванием
Ключевые слова: система моделирования, К-значное дифференциальное исчисление, электромагнитная совместимость, квантование сигналов
-------------------□ □----------------------
1. Введение
Сложность современных элементов и устройств вычислительной техники требует для их разработ-
Еш.................................................
2012. - 128 p.
УДК 004.94
СИСТЕМА ОБРАБОТКИ СИГНАЛОВ ЦИФРОВЫХ УСТРОЙСТВ НА ОСНОВЕ ^ЗНАЧНОГО ДИФФЕРЕНЦИАЛЬНОГО ИСЧИСЛЕНИЯ
В. Д. Дм итриен ко
Доктор технических наук, профессор* Е-mail: valdmitrienko@gmail.com
С. Ю. Леонов Кандидат технических наук, доцент* Е-і^іі: serleomail @gmail.com *Кафедра вычислительной техники и программирования Национальный технический университет “Харьковский политехнический институт” ул. Фрунзе, 21, г. Харьков, Украина, 61002 Т. В. Гладких Кандидат технических наук ТОА “Украина”
пр. Гагарина, 43/2, г. Харьков, Украина, 61001 Е-mail: gladtv@gmail.com
ки создания новых методов и средств, позволяющих учитывать при их проектировании особенности применяемых технологий. Одним из возможных путей решения этой задачи является разработка новых не-
© В. Д. Дмитрием-», С. Ю. ileoi-юв, Т. В. Гладнин, 2014
