Кластерна модель комп’ютерної візуалізації мережі сенсорів

Abstract

З використанням методу Делоне розроблено кластерну модель комп’ютерної візуалізації бездротової мережі сенсорів, на яких можливим є здійснення атак із подальшим їх підсиленням чи послабленням сигналу. Така модель дозволяє сформувати в конфігураційному двовимірному евклідовому просторі комп’ютера геометричну структуру у формі шестикутника, яка складається із обвідки внутрішнього шестикутника правильними трикутниками, вершинами яких є сигнальні точки, а сторонами – функціональні зв’язки між сигнальними точками.

Using Delaunay method and methods of the fracture structure plotting the claster model of the computer visualization of the wireless sensor net has been developed. Such model allows constructing geometric hexagonal structure on the configuration 2D Euclid space, which consists of the regular triangle outlines, of the internal hexagonal, the vertex of which are points and the sides are the functional connection between signal points. She claster, built up in such a way, consists of 18 signal points, which are connected between each other by 36 functional connections of the same length. Signal points in the claster are connected with other points by not less than three functional connections. It allows obtaining information from each of them and visualizes the sensor operation failure. To provide visual computer interpretation of the possible attacks on the sensor, the images of which in the configuration space are signal points from different classes of their fracture, the properties of four-point com-plex are used, the possibility to find the square of its volume in particular, using Keli-Menger determinant, the elements of which are the squares of the six distances between four-point of simplex. This index for simplexes, which are expressed by the flat geometric shapes, will equal 0. Four-point triangle pyramid shaped simplex will be found by the Keli-Menger determinant, which is different from zero. Attacks on sensors cause the claster symmetry failure, which results in creation of the four-point sim-plexes in the form of three geometric shapes: simplexes, which are not connected directly which the functional connections, which define the level of the attack on the sensor in the configuration space being of the plate rhomb shape; simplexes, which have two functional connections, which change their length during the attack on the sensor, transforming into the quadrangle, the shape of which can be presented by neither a rhomb nor a quadrangle; simplexes with three functional connections, the change of length of which is caused by the attack on the sensor and are transformed into the triangle pyramid. Thus, the attack on the sensor causes: firstly geometric shape of the main part of the simplex, which fill the claster and their edges are not changed functional connections, is unchanged; secondly, transformation of two sensors with two changed functional connections into quadrangle figure of 2D configuration space; thirdly, local deflection of the configuration space to the 3D with the epicenter in the signal point, which is treated as the attacked sensor resulted from the transformation from one to three simplexes into the 3D triangle pyramid. Under such deflection of the configuration space the high of the triangle pyramid, beside the accepted in-to computer the noise signal parameters and the sensor, will define the attacked signal parameters as well. That is why local deflection of the configuration space makes it possible to find the attacked sensor, and the analytical definition of the high – to valuate the attack value on the sensor.