RU161982U1 - SCIENTIFIC RESEARCH MODEL FOR FORECASTING OPTIONS FOR CONSTRUCTION OF WINGS OF WING ROCKETS - Google Patents

Abstract

1. A research and development model for predicting the construction of cruise missile attacks, characterized in that it contains an interface for inputting data and modeling results interconnected by digital lines, a model for constructing a network of strategic cruise missile flight routes (SCR) from launch lines to objects shock model, the distribution of TFR from the launch lines to the objects of impact, a model of the distribution of carriers of SKR from the bases of the objects of impact, a model of a temporary program of the structure of the impact, memory block ti modelirovaniya.2 input data and results. The research model according to claim 1, characterized in that the SKR flight route network construction model comprises a block for generating possible flight routes, a block for generating valid routes, a unit for evaluating the feasibility of selected routes installed on a common interface bus and connected by control and switching signals to the interface of the modeling complex and with the memory block of the initial data and simulation results. 3. The research model according to claim 1, characterized in that the TFR distribution model from the start or start boundaries for strike objects contains a digital block for distributing cruise missile streams on graphs mounted on a common interface bus and connected by switching signals to the interface of the modeling complex and the unit memory of initial data and simulation results. 4. The research model according to p. 1, characterized in that the distribution model of the TFR carriers from the bases along the launch lines contains a digital distribution block of the TFR carriers from the bases along the launch lines with the possibility of distribution

Description

The utility model relates to special-purpose digital devices, specifically to research and development models for predicting the options for constructing strikes of airborne space attack equipment for evaluating the performance indicators of airborne defense systems and means.

Known research models / 1-7 / containing a set of models for quantifying the performance indicators of weapons models, connected to the interface of the modeling complex and the memory block of the source data and simulation results.

A disadvantage of the well-known research models is the impossibility of their use for the automated prediction of possible strike options with strategic cruise missiles (TFR) using the aerospace defense system.

Research models for solving such problems in the prior art have not been identified.

The objective of the utility model is to provide the ability to automatically evaluate the parameters of TFR attacks on strategic nuclear forces for the design, creation and testing of systems to combat them.

The technical result of a utility model that provides a solution to the problem is the creation of a research and development model for predicting the options for constructing cruise missile attacks, suitable for the automated estimation of the parameters of air strike attacks on aerospace defense facilities.

The essence of the utility model.

Achieving the claimed technical result and solving the problem is provided by the fact that the research and development model for predicting the construction of cruise missile attacks includes digital input lines connected to each other, an input interface for inputting data and modeling results analysis, a model for constructing a network of SCR flight routes from launch lines to strike targets , a model for the distribution of TFRs from the launch boundaries to the objects of impact, a model for the distribution of carriers of the TFRs from bases along the launch boundaries, a model of temporary first strike of the structure of the program, the memory block of input data and modeling results.

The interface of the modeling complex contains a processor, random access memory, reprogrammable memory with a model management program, an input-output device and a display with a mnemonic control panel. The model for constructing a network of flight routes SKR contains a set of digital blocks for generating possible flight routes, forming valid routes, and evaluating the feasibility of the selected routes. Digital blocks are installed on a common interface bus and are connected via connection switching signals to the interface of the modeling complex and the memory block of the source data and simulation results. The model for the distribution of TFR from the launch lines (launch areas) over strike objects contains a digital block for distributing cruise missile flows over the network, based on the distribution of flows on graphs. The digital distribution unit is mounted on a common interface bus and is connected by switching signals of the module connections and the signal processing sequence to the interface of the modeling complex. The model for the distribution of SCR carriers from the bases along the launch lines contains a digital block for the distribution of carriers and is based on the distribution of the flow over the network, taking into account the probability of successful delivery of carriers to the launch lines (launch areas). The digital unit is installed on a common interface bus and is connected via switching connection signals to the interface of the modeling complex and the memory block of the source data and simulation results. The model of a temporary strike construction program contains a digital block of temporary strike construction, in which the parameters of one of the groups are optimized: flight speeds on the arcs of the route or the spread of launch times at the borders (in the launch areas). The digital unit is installed on a common interface bus and is connected via switching connection signals to the interface of the modeling complex and the memory block of the source data and simulation results.

The proposed implementation of the research model allows us to predict in automated mode the spatio-temporal parameters of the variants of impacts of SKR and their distribution over objects. An additional result of the application of the research model is to obtain more reliable and reasonable quantitative characteristics of the options for constructing TFR hits. The consequence of this is to increase the validity of requirements for the creation of systems and means of combating cruise missiles, the construction of armed forces, the development of forms and methods of their combat use.

The essence of the utility model and the method of its application is illustrated by the drawings presented in FIG. 1-8.

In FIG. 1 is a functional diagram of a research model for predicting options for constructing cruise missile attacks; in FIG. 2 is a block diagram of an algorithm for predicting impact construction options; in FIG. 3, FIG. 4 - explanation of the physical nature of the concept of “Voronoi test site” and its use for modeling SKR routes with bending the terrain, respectively; in FIG. 5 - the principle of modeling the launch lines of the TFR and the boundaries of the interception of active means of aerospace defense, in Fig. 6 is a figure explaining the degree of freedom of the spatial position of the TFR at the minimum height of its flight; in Fig. 7 is a drawing explaining possible variations in flight time of the TFR and their components; on Fig 8 is a drawing explaining the geometric meaning of the minimum connecting element; for many segments of the flight time variation of individual TFRs.

Fig. 9 is a drawing explaining the geometric meaning of the minimum connecting element for the case when simultaneous undermining of the SCR BB for impact objects is possible with the simultaneous launch strategy by varying flight speeds along the routes;

Fig. 10 is a functional diagram of a model for constructing a network of SCR flight routes from launch lines to impact objects.

Description in statics.

The research model for predicting the options for constructing cruise missile strikes contains an interface 1 for inputting initial data and analyzing the results of modeling a modeling complex, model 2 for constructing a network of flight paths for ASR from launch lines to strike objects, model 3 for distributing SKR from launch lines for strike objects, model 4 distribution of TFR carriers from bases on impact objects, model 5 of the temporary program of the structure of the impact, block 6 of the source data memory and simulation results interconnected by a digital by communication lines 7. Interface 1 for inputting initial data and analyzing the results of modeling the modeling complex is made on the basis of a personal computer with a window interface of the Windows standard and contains a processor, random access memory (RAM), reprogrammable memory (NIZU), input-output device (VVU) , display with integrated mnemonic control panel. Programs are made with the possibility of alternating output of graphic data or selectively in accordance with the needs of the researcher. The necessary parameters are called up by calling the corresponding interface buttons and mimic diagrams on the display.

и для каждой РЛС заданы ее координаты и высота электрического центра антенны h_k. В модели определяется зона обнаружения отдельной k-ой РЛС:SKR flight route network model 2 (Fig. 10) contains series-connected block 2.1 for forming possible flight routes, block 2.2 for forming valid routes, and block 2.3 for evaluating the feasibility of selected routes. Blocks 2.1-2.3 are made digital, mounted on a common interface bus and connected via control and switching signals to interface 1 of the modeling complex and memory block 6 of the source data and simulation results. When constructing blocks 2.1-2.3, the features associated with the sequence and principles of constructing a network of routes SKR / were taken into account. In accordance with this, in block 2.1, the region of possible flight routes is constructed in digital form, which takes into account the geometry of the radar fields of radar stations of the Federal Intelligence Service (FSR) and command-and-computing points (KVP) groups and the geometry of terrestrial obstacles for TFR. In three-dimensional Euclidean space E ³ , the coordinate system OXYZ is defined. The function Z = Z (x, y) defines in E ³ some supporting surface. The OXY plane is considered as the projective plane for the surface Z = Z (x, y) (map plane), reflecting the state of the relief. The pair (x, y) is considered as the coordinates of an arbitrary point in the projective plane OXY. In the initial data, a group of aerospace defense consisting of a radar,

and for each radar its coordinates and the height of the electrical center of the antenna h _{k are given} . The model determines the detection zone of the individual k-th radar:

S _k = {(x, y, z): R _k (H) ≤ρ (P _k , P), (x, y, z) ∈R},

where (x, y, z) is an arbitrary point of the spatial region R over the defended territory;

, h_k - высота антенны РЛС:R _k (H) is the line of sight of the k-th radar to the target at a height of H (H = Z), i.e.

, h _k - radar antenna height:

ρ (P _k , P) is the distance between the points P _k and P on the OXY plane;

P _k - projection of the standing point of the k-th radar;

P = (x, y) is the projection of the point (x, y, z) ∈R.

представляет собой свободное пространство, не контролируемое ни одной станцией заданного множества K. Запишем условия принадлежности области F для произвольной точки P плоскости OXY. Для чего обозначим

- дальность видимости k-ой РЛСRegion

represents free space not controlled by any station of a given set K. We write down the conditions for the domain F to belong to an arbitrary point P of the OXY plane. Why denote

- visibility range of the k-th radar

at zero target height. Then

At point P, the target is secretive if

дальность видимости цели каждой станцией. Конкретная РЛС и высота СКР над точкой P, при которой она перестает быть скрытной, определяются из условияWith increasing target height above point P, according to (2.1), it increases by

target visibility range by each station. The specific radar and the height of the SCR above the point P, at which it ceases to be secretive, are determined from the condition

From this condition it follows that the maximum height of the secretive flight of the TFR above point P is calculated as

Value

determines the distance of the point P to the detection zone of the nearest radar (with number k), and the range [0, H ^max (P)] determines the choice for the target of the height of the covert flight of the SCR above point P.

Thus, relations (2.2), (2.4) make it possible to calculate the set of points P∈OXY at which secretive flight of the SCR and the range of altitude selection are possible, i.e. points (P, h) ∈τ, h∈ [0, H ^max (P)], where τ is the area of covert flight of the SCR.

In addition, it follows from equality (2.5) that each such point P can be associated with a specific radar (nearest) defining H ^max (P), which allows us to construct a division of the OXY plane into subdomains with respect to the set of all radars. Such a partition of the OXY plane based on the use of (2.5) with respect to the set of points {P _k }, keK is called the Voronoi partition / 8 / (Fig. 3). Voronoi training ground (Fig. 3) for the r-th radar

V _r = {P: ρ (P _r , P) ≤ρ (P _k , P), ∀k∈K}

represents a subarea of points of the OXY plane with a pole at the standing point of the r-th radar (the closest determining the possible range of altitudes for covert flight of the target). Within the Voronoi polygon with increasing distance from the pole according to (2.4), the height range increases due to an increase in H ^max (P). At the border of the Voronoi training ground, the maximum possible range of heights is achieved. The boundary sections of Voronoi polygons are common for adjacent polygons (in Fig. 3 - segment AB). The Voronoi partition defines a dual partition called the Delaunay triangulation, each edge of which connects the poles P _k and P _{r of} adjacent polygons V _k and V _r . In FIG. 3 Delaunay triangulation, with the help of which the maximization of the minimum angle among all angles of all constructed triangles is performed, is depicted by the dash-dot line). Each pair of adjacent poles V _k and V _r (radar numbers k and r) corresponds to an edge of the polygons V _k and V _r and a dividing corridor of free space (if the detection zones of stations do not intersect at H = 0, otherwise such a corridor is torn apart by radar zones) .

Each such edge of Voronoi polygons is a representation of the boundary surface of the corresponding dividing free space corridor, since it allows us to uniquely determine it based on conditions (2.2, 2.3) (see rib AB and the ADEBMN corridor in Fig. 3). The whole set of boundary edges of the Voronoi decomposition polygons is a network S and is the skeletal form of free space F. The network S = [U, D], where U is the set of boundary edges of the Voronoi polygons, D is the set of intersection points of the boundary edges, can be directly represented in the form of the graph G (X, A), where X is the set of vertices of the graph, formed as the set of intersection points of the borders of Voronoi polygons; A is the set of edges of the graph representing the set of fragments of the borders of Voronoi polygons.

The network constructed by this method in block 2.1 takes into account only the geometry of the radar fields of the RTV groups and does not take into account the geometry of obstacles. Obstacles in block 2.1 of model 2 are understood as mountain ranges, the height of which exceeds the maximum possible flight height of the rocket. To build a digital network of SCR flight routes that allows one to take into account such obstacles, these obstacles are set in the source data on the plane of a digital map in the form of figures described by circles with radii that take into account the real configuration of obstacles and are independent of the height of the SCR flight. This representation allows you to build Voronoi polygons for such configurations (Fig. 4)

The ribs AB, ..., SP Voronoi polygons are a fragment of the flight route of the rocket, allowing you to bypass obstacles of a given configuration. In contrast to constructing a network of routes that take into account the geometry of obstacles, the route segments (in Fig. 4, the QW segment) passing between the circles describing the obstacles are not included in the route scheme. Infinitely large costs are attributed to such segments, and the sign of circles belonging to either the geometry of the radar radar fields or the geometry of obstacles is taken into account in the network construction algorithm.

Thus, in block 2.1, constructed taking into account the radar fields and obstacles, a network of possible flight paths for SCR is formed. Block 2.1 on the output of possible flight paths of SKR is connected to block 2.2 of forming a network of permissible routes of SKR.

Block 2.2 is designed to calculate the area of permissible TFR routes, where from the network of possible routes those are selected that, in total length, would not exceed the limiting flight range of the TFR. The principle of constructing a network of permissible SCR flight routes in block 2.2 is to select from the network possible routes of those that, in total length, would not exceed the maximum SCR flight range, provided that their beginnings (launch lines, launch areas) would be outside the boundaries of interception by active means VKO (characteristics of the VKO system are set in the initial data of block 6). Possible boundaries of interception by active means of aerospace defense are modeled as a closed broken line. If, as a result of the check, it turns out that the beginning of the route is inside the contour formed by a broken line describing the interception boundaries, then this route is rejected, otherwise the route must be assessed for feasibility. The points of the beginning of the routes lying beyond the contour are connected and form possible lines of launches of the TFR (Fig. 5) outside the zones of active means of aerospace defense.

The search for routes satisfying the limitation on the limiting range of flight of the SCR in block 2.2 is based on the use of the well-known wave algorithm - Lee / 8 / finding the shortest path on a planar graph. According to the results of modeling acceptable routes, block 2.2 is connected to block 2.3 for assessing the feasibility of valid routes. The estimation algorithm for each section of the TFR route is determined based on its length, the characteristics of the terrain over which it is located and the minimum acceptable from the point of view of secrecy, the height of the TFR flight, the integral value of the probability of not colliding the TFR with the earth's surface. The TFR flight route is realized from those sections where the collision probability is minimal. A feature of this modeling stage is the representation of the terrain over which the SCR flight is permissible in the form of a characteristic σ _p reflecting the degree of its indentation. The characteristic σ _p can be attributed to a site with sizes ranging from 5 × 5 km to 60 × 60 km or more, which is determined by the structure of the terrain. The most appropriate division of the terrain into sections of 5 × 5 km, because this ensures stable characteristics for the terrain of any structure (flat terrain or mountains) and allows you to control the behavior of the rocket using the programmed heights for these terrain sections with the smallest values of the areas of possible deviations from the optimal envelope trajectory. In the absence of information about σ _p for each site with dimensions of 5 × 5 km throughout the territory and adjacent to the border areas, the roughness of the relief can be estimated using a simplified method, namely, the magnitude of the roughness along the selected direction is determined as the fourth part of the maximum difference topography on a section of 30 km, i.e.

σ _p ≈ 0.25 (H _{p max} -H _{p min} ).

Based on this, the entire area where the TFR flight routes are built is divided into 30 × 30 km squares. Such a partition allows, with practical accuracy, to represent the radar detection zones on the plane in the form of circles, the minimum radii of which at large values of a _p and, accordingly, safe flight heights from 100 to 250 m, are 42-50 km and several times exceed the size of the assessment sites . This provides an account of possible changes in the programmed flight altitude of the TFR within the zone. Flying SCR over the flat terrain (slightly crossed) can be carried out at altitudes of 15-30 m. Moreover, the radii of the detection zones of the SCR are also minimal and do not exceed 24 km. Considering that the characteristics of such a relief within the zone are almost constant and do not depend on the size of the site, the size of the assessment site for flat terrain can be any, including 30 × 30 km.

By averaging the values of the roughness obtained on the sides of the square, one can characterize the terrain taking into account the average values of the correlation radii of typical reliefs, assigning to each square the value of σ _p . Based on a comparison of the minimum possible height of the SCR flight over the terrain characterized by the values of σ _p and the flight altitude at which the SCR should fly based on the condition of “not detecting” its radar, for each section of the route at its most “narrow” point the value of H (P) (Fig. 6), reflecting the degree of freedom of the spatial position of the TFR. The higher the value of H (P) at the critical points of the route, the more feasible the route (less likely the collision of rockets with the ground in the “narrow” places of the route, the greater the throughput of the route, and accordingly it is more preferable when choosing the target distribution.

определяется вероятностями нестолкновения на каждом из участков маршрута. Для участков маршрута размером 30×30 км P_нст может быть получена по формуле:When solving the target distribution problem for each SCR route, the integral probability value of the missile not colliding with the earth's surface is calculated in order to obtain the numerical values of missile losses on the routes. This is the integral value of the probability of collision.

determined by the probability of collision on each of the sections of the route. For route sections measuring 30 × 30 km, P _nst can be obtained by the formula:

where t is the flight time of the Kyrgyz Republic on a segment of 30 km;

λ is the average frequency of collisions;

,

,

where σ _ΔН is the standard deviation (RMS) of the height keeping error;

- среднеквадратическое отклонение скорости изменения ошибок выдерживания высоты;

- standard deviation of the rate of change of errors in maintaining the height;

H _pr - software flight altitude of the rocket.

The output of block 2 according to the realizable results of the SKR route is connected to the input of model 3 of the distribution of SKR from the launch lines (launch areas) for impact objects.

Model 3 is made in the form of a digital block distribution of flows of cruise missiles over the network in graphs. The digital unit is installed on a common interface bus and is connected via connection switching signals to the interface 7 of the modeling complex and the memory unit 6 of the source data and simulation results. In the digital block of model 3, the problem of distributing the TFR from the launch boundaries to the objects of impact is solved, as the problem of the minimum cost flow in a network with amplifications. According to / 8-9 /, a network with amplifications is understood to mean a network of permissible SCR flight routes to impact objects, assuming that the number of missiles in a stream passing through an arc can decrease due to losses from FFP systems and collisions with the earth's surface. It is believed that if f (υ, u) missiles enter any arc (υ, u) at the vertex υ, then k (υ, u) f (υ, u) missiles come out of this arc at the vertex, where υ, u - values characterizing the location of the vertices of the arc in the plane. Each flow unit (each SCR) passing along the arc (υ, u) is multiplied by the value k (υ, u). In the general case, this value is the arc gain (υ, u). For the problem under consideration, 0 <k (υ, u) <1, where k (υ, u) is a coefficient that takes into account the attenuation of the flow in the arc (υ, u) due to the existence of probabilities of a rocket collision with the ground, failure of the missile flight control system and destruction missiles by means of the aerospace defense system.

Thus, we can write that

- вероятность нестолкновения ракеты с поверхностью Земли на отрезке (υ,u);Where

- the probability of a rocket not colliding with the Earth’s surface in the interval (υ, u);

- вероятность исправной работы системы управления полетом ракеты на отрезке (υ,u);

- the probability of proper operation of the missile flight control system on the segment (υ, u);

- вероятность того, что крылатая ракета не будет сбита средствами ПКО на отрезке (υ,u) маршрута полета.

- the likelihood that the cruise missile will not be shot down by means of FFP on the segment (υ, u) of the flight route.

Then k (υ, u) is the probability of rocket delivery from the point υ to the point u on the segment (arc) (υ, u).

It must be emphasized that in model 3 the problem of finding the optimal cost method for “sending” the flow of missiles through the network from the source (launch line or launch area) to the drain (strike object) for a given number of cruise missiles in the source is considered. At the same time, we note that if V units of missiles are sent from the source to the network, the number of missiles arriving at the objects, impact due to losses in arcs, does not necessarily coincide with V. Therefore, there may be a situation where the available resource of missiles at the bases, due to losses on route sections, it is not enough to solve the assigned combat mission. In this case, the level of its implementation is determined by the given resource of missiles at the borders (in the launch areas). We set the maximum c (υ, u) and minimum e (υ, u) the number of units of the missile stream that can enter the arc (υ, u), as well as the cost a (υ, u) of passing through the arc of each missile entering it ( for the selected arc, these values will be considered equal).

The cost a (υ, u) of a rocket passing through an arc (υ, u) in model 3 is understood to mean the reciprocal of the maximum value Hmax (P) of the quantity H (P), which characterizes the degree of freedom of the spatial position of the rocket. The physical meaning of the quantity H (P) is shown in FIG. Obviously, the value of H (P) will determine the range [Hmin (P), Hmax (P)] of the heights of the covert flight of the SCR above point P. The value of Hmax (P) can be calculated by formula (2.4).

The maximum value c (υ, u) of the number of missiles that can enter the arc is calculated by the formula (3.2):

where M (Hmin) is the width of the corridor of missile passage between radar detection zones when rockets move at the lowest possible altitudes between these zones, taking into account the terrain m (cm / m):

α is the limit value of the intervals between missiles along the front, m

The minimum value of e (υ, u) is taken equal to unity. The solution to the problem of the minimum cost flow in a network with amplifications can be written as follows. To find:

provided that

Expression (3.3) determines the total cost of the stream. Equation (3.4) shows that the net flux from the vertex S must be equal to V, and the net flux from any other vertex, not counting the vertex t, must be equal to 0. Relation (3.5) shows that the flux in each arc should be in the interval between the lower and upper bandwidth limits. Thus, the recorded optimization problem allows us to find the flows of minimum cost for a given number of missiles at the launch lines (in the launch areas), which is implemented in this model 3. Model 3 output based on the results of optimization of the TFR stream with the input of model 4 of the distribution of TFR carriers from the bases start-up boundaries.

Model 4 is made in the form of a digital optimization unit installed on the interface bus and connected via control and switching signals to the interface 1 of the modeling complex and the memory unit 6 of the source data and simulation results.

The optimization problem of the distribution of SCR carriers from the bases at the launch boundaries in model 4 is presented in the following form.

Given:

I - many launch lines (launch areas);

S - many bases on which the same carriers with cruise missiles are deployed;

, s∈S;xsi - the number of TFRs assigned from the S base to the i-th line,

, s∈S;

Csi - the cost of delivering TFR from the S base to the i-th line;

- признак допустимости доставки с базы S на рубеж I;

- a sign of admissibility of delivery from base S to line I;

As is the number of SCR on the S base;

Bi is the required number of TFRs at the i boundary.

To find:

provided

The sign λsi of the admissibility of delivery by SKR carriers from the S base to the i boundary is formed as follows. For the boundary i with coordinates φ, α and the required number of TFRs at this boundary, the nearest base with coordinates φ ', α' is selected. For this base, the sign λsi = I is formed. If the available number of SCR on the selected base is less than that required at the start of the launch, then the next base closest to this boundary is selected and the attribute λsi = I is also assigned to it.

Expression (4.1) determines the total cost of the stream. Equation (4.2) shows that the required number of TFRs at the i-th line should not exceed their total number at the bases.

Equation (4.3) shows that the number of missiles distributed from the S base should not exceed the resource of missiles at the S base. The flow cost in this task is understood as the probability of successful delivery of TFR to the launch lines (to the launch areas).

The probability of successful delivery from the S base with the coordinates φ ', α' to the i boundary with the coordinates φ, α of the ASR carriers can be defined as the product of the probabilities of successfully overcoming the forward echelon of the FFP (long-range aircraft interception systems (ACS), anti-aircraft missile complexes (SAM) DD) and successful exit (with the required spatial and temporal accuracy) to a given launch line (to the launch area).

According to the results of the optimal distribution of TFR over impact objects, model 4 is connected to model 5 of the temporary construction of the impact.

Model 5 contains a digital optimization unit, in which the parameters of one of the groups are optimized: flight speeds on the arcs of the route or the spread of launch times at the borders (in the launch areas). The digital optimization block of model 5 is installed on the interface bus and connected via control and switching signals to interface 1 of the modeling complex and memory block 6 of the source data and simulation results.

The task of temporary strike planning, solved by model 5, is to provide a time-coordinated (at an interval not exceeding a predetermined) blasting of ASF warheads over impact targets. This is the main temporary requirement affecting the effectiveness of the response of the defending side. The simultaneous defeat of a group of objects can be carried out with an appropriate choice of the time of launch of carriers to the launch lines, the choice of temporary programs for the movement of missiles on flight routes. The time at which launch vehicles reach launch lines depends on the time programs of rocket movement on each of the sections of the selected routes, as well as on the requirements for “simultaneity” or “stretching” of launches along the lines. The latter requirement can be formulated by a specialist researcher based on the intent of the strike and his chosen hypothesis about the tactics of overcoming the forward echelon of FFP.

Based on this, the investigated modeling issues in optimization model 5 can be formulated as follows:

A. Is there such a variant of a massive strike that provides simultaneous launch of TFR from all selected lines (launch areas) and simultaneous undermining of their warheads at strike targets?

B) What can be achieved the maximum (minimum) spread of start times so that the spread of fall times does not exceed a given value?

We consider the target distribution plan to be fixed, and the variable speed of the TFR on the arcs of the route and the launch times as variable parameters.

In order to set a temporal plan for constructing a strike, it is necessary for each i-th SKR (SKR group) to indicate flight speeds on the route M-υi (m), m∈M is the area of permissible routes included in the target distribution plan; start start times ti (c),

Then the temporal plan of impact P is:

.P = {υi (M), ti (c)},

.

Let Δ (c) = Δ (c) (P) be the spread in the time of launch of the SCR in impact P, equal to the time interval from the moment of the start of the first SCR to the moment of the start of the last and determined by the difference in the time the carriers reach the launch line (to the start areas) .

Then

For each SCR group, you can find, setting their flight speed on each arc n of the route M, the total flight time until the BB is undermined:

,

,

.

,

,

.

The moment of undermining the BB of the i-th KR is:

ti (n) = ti (s) + ti (gender),

.Similarly, the spread of the times of undermining the BB of the SCR in the shock can be written as: Δ (p) = Δ (p) (P),

.

Based on the introduced notation, one can formulate the posed questions in the form of the following optimization submodels of model 5:

Model A. Maximizing the spread of the start times Δ (s) for a given restriction Δ0 on the spread of the undermining times and the given plan of the CR

Model B. Minimization of the dispersion of launch times Δ (s) for a given restriction Δ0 on the spread of detonation times and a given plan of CR

, либо, во втором случае,

, то это значит, что существует план удара, обеспечивающий одновременный пуск СКР и одновременный подрыв их боевых блоков у объектов удара.If in these models A, B with Δ0 = 0,

, or, in the second case,

, then this means that there is a strike plan that provides the simultaneous launch of TFR and the simultaneous undermining of their warheads at the targets of the strike.

Each of these submodels, in turn, can be represented as two nested submodels in which the parameters of only one of the groups are optimized: flight speeds on the arcs of the route - υi (m) or launch strategies t (c). For this, we transform (5.1), (5.2) as follows:

Where:

ΩS - the set of valid strike plans with a given target distribution S, differing from each other in temporary programs for the movement of SCR along the routes and the launch strategy;

ΩSυ is the set of valid strike plans with a given target distribution S, temporary travel programs on routes that differ in launch strategy.

Consider the internal submodels in (5.3) and (5.4):

The content of these submodels is as follows. It is necessary to find the maximum (minimum) scatter of the times of SCR starts in impact, provided that the target distribution and time programs for the movement of SCR on the routes are set, maximization (minimization) is carried out by choosing the start times t (c).

Denote by Δ (sex) the spread of flight times of the SCR in impact P

.

.

As can be seen from the definition of flight time, the magnitude of the dispersion of flight times depends on the time programs of missile movement on the routes included in the target distribution plan and does not depend on the launch strategy of the TFR. Then the general solution of extremal problems (5.5), (5.6) can be written as:

,

,

.

.

Both of these tasks can be reduced to two tasks, respectively:

, при которых обеспечивается соответствующая полетная дальность. Предположим, что полет СКР реализуем для любой скорости в этом диапазоне.If the target distribution is specified, for each TFR (group of TFRs) the coordinates of the launch points and coordinates of the targets are determined, then for all TFRs the permissible limits of the change of flight speeds υi∈ [υimin, υimax] can be determined,

at which the corresponding flight range is provided. Suppose that the flight of the SCR is realized for any speed in this range.

, ti(пол) является немонотонной убывающей функцией от

. На основании зависимости

и диапазона υi∈[υimin,υimax] может быть найден диапазон изменения полетного времени [τi(1),τi(2)],Flight time ti (floor) at fixed launch and detonation points is a continuous function of speed

, ti (gender) is a nonmonotonic decreasing function of

. Based on addiction

and the range υi∈ [υimin, υimax] can be found the range of changes in flight time [τi (1), τi (2)],

;

;

.

.

, задача (5.7) сводится к:We call the segment of the number line [τi (1), τi (2)] = Ti the segment of the i-CKP flight time variant. Since for each value of τ∈Ti, the flight speed υi can be selected for i-CKP (SKR group), at which

, problem (5.7) reduces to:

,

,

and problem (5.8) to:

,

,

Then, with a fixed target distribution, the maximum spread of flight times can be written as:

and the minimum spread of flight times is written as

Рассмотрим сегмент

. Для всех сегментов Ti

. Выберем для каждой СКР (группы СКР) такую скорость полета

, чтобы

. Поскольку все ti(пол) при таком способе выбора

лежат в D, то

.where: Ti = [τi (1), τi (2)] is the segment of variation of flight time i SCR,

Let's consider a segment

. For all Ti segments

. For each TFR (TFR group), we choose this flight speed

to

. Since all ti (gender) with this method of choice

lie in D then

.

Тогда D является минимальным по длине сегментом, имеющим непустое пересечение со всеми Ti. Если считать условно, что для множества сегментов, имеющих непустое пересечение, длина минимального связующего сегмента равна 0, то при фиксированном целераспределении минимальный разброс полетных времен в ударе равен длине минимального связующего сегмента для множества сегментов вариации полетных времен отдельных СКР.We call segment D the connecting segment for the set of flight time variation {Ti} segments, since

Then D is a minimal segment with a nonempty intersection with all Ti. If we assume conditionally that for a set of segments having a nonempty intersection, the length of the minimum connecting segment is 0, then with a fixed distribution, the minimum spread of flight times in impact is equal to the length of the minimum connecting segment for many segments of the variation of flight times of individual SKR.

A geometric interpretation of the above is presented in FIG. 7, 8, where:

T1, T2, T3, T4 - segments of the variation of flight time on the flight paths of the SKR to the object of impact;

ti, ti ′, ti ″, ti ′ ″ - segments flight time options on route sections.

As can be seen from the figure shown in FIG. 8,

.

.

.Therefore, the minimum connecting segment

.

, либо

.Obviously, any decrease in D leads to either

either

.

Then the flight times of the TFR should have the meanings

, т.е.

,

, i.e.

,

, т.е.

,

, i.e.

,

, т.е.

,

, i.e.

,

, т.е.

.

, i.e.

.

. Таким образом, правило определения минимального разброса полетных времен можно записать так:Only in this case is the minimum spread of flight times equal to

. Thus, the rule for determining the minimum spread of flight times can be written as follows:

.

.

,

. Для обеспечения одновременности подрыва ББ СКР необходимо изменить стратегию пусков, т.е. выполнить условие:

. Это условие может быть выполнено в случае растяжки времени пусков СКР на интервале

за счет разновременного выхода носителей СКР на рубежи пусков (в районы старта) либо организации последовательного пуска СКР при одновременном выходе носителей. Отсюда следует, что минимальный интервал растяжки пусков при условии одновременного подрыва ББ СКР равен минимальному следующему элементу D. Очевидно, что при менее жестком ограничении на интервал подрыва ББ, интервал разброса времен пуска СКР уменьшается. На фиг. 9 показан случай, когда возможен одновременный подрыв ББ СКР у объектов удара при стратегии одновременного пуска за счет варьирования скоростями полета на маршрутах.From FIG. 8 it follows that with the strategy of simultaneous launch (TF = 0) of TFR along routes (1) - (4), simultaneous undermining of combat units (BB) of TFR can be carried out by varying flight speeds for the following route numbers: 1-2, 2-3, 3-4. The simultaneous undermining of the SCR BB at impact targets with the selected launch strategies on all four routes is impossible due to the fact that:

,

. To ensure simultaneous detonation of the BB TFR, it is necessary to change the launch strategy, i.e. to fulfill the condition:

. This condition can be fulfilled in the case of stretching the time of the start of the SCR on the interval

due to the simultaneous release of TFR carriers to the launch lines (to the launch areas) or the organization of the sequential launch of TFR with the simultaneous release of carriers. It follows that the minimum interval of launch stretching under the condition of simultaneous undermining of the BB of the SCR is equal to the minimum of the next element D. Obviously, with a less stringent restriction on the interval of undermining the BB, the interval of the spread of the SCR start times is reduced. In FIG. Figure 9 shows the case when simultaneous undermining of the SCR BB by impact objects is possible with a simultaneous launch strategy by varying flight speeds along routes.

, а полетные времена СКР должны иметь значения:For this case, the minimum connecting segment D

, and flight times TFR should have the following values:

, т.е.

,

, i.e.

,

, т.е.

,

, i.e.

,

, т.е.

,

, i.e.

,

, т.е.

.

, i.e.

.

As you can see, all flight times are in the same range of flight times, which allows you to choose such flight speeds υ1 (floor), υ2 (floor), υ3 (floor), υ4 (floor) SKR on routes that provide simultaneous approach of SKR to hit objects on all four routes. Based on the simulation results, model 5 is connected to interface 1, and according to the source data and formalization programs, with block 6 of the source data memory.

Memory block 6 contains digital data sets: on strike objects and their characteristics, tactical and technical characteristics of cruise missiles and their carriers, carrier-based areas, boundaries of the strike forecast area and temporal requirements for a strike, characteristics of a FSS system, characteristics of the terrain at the borders impact prediction region and is connected by control and switching signals to interface 1 of the modeling complex and models 2-5. Description in dynamics.

The research model for predicting the options for constructing cruise missile attacks works as follows. In accordance with the operation algorithm (Fig. 2), first, on the control panel (on the display mimic) of the input data input interface 1 and analysis of the results of modeling the research model, the scientific research task is selected through the control module in the form of an impact target, solved problems, and impact requirements , involved forces and means, the order of their combat use. For the selected research task, in the block 6 of the data set memory, the initial data is selected to simulate the selected variant of constructing an SCR shock. The selected source data is automatically loaded into random access memory (RAM) of interface 1. After loading the initial data for modeling into RAM, the researcher includes the corresponding program for managing models 2-5 located in removable memory of interface 1. At the same time, interface processor 1 generates a specified research program model management teams 2-5.

Let among the many possible tasks, as the research task, we chose the task of delivering a strike by cruise missiles at three positional areas of the Strategic Missile Forces with PGRK. In this case, the following initial data are loaded into the RAM of interface 1: data sets: on strike objects and their characteristics, tactical and technical characteristics of cruise missiles and their carriers, carrier-based areas, boundaries of the strike forecast area and temporal requirements for a strike, characteristics of an ASD system, terrain characteristics within the boundaries of the region of impact prediction.

After the initial data are loaded, model 2 of building a network of flight paths for the TFR from launch lines to impact targets is automatically turned on. In model 2, a network of possible SKR flight routes is constructed, a network of valid flight routes, and the feasibility of the selected routes is evaluated. Further, on the basis of the route network constructed in model 2, in models 3 and 4, cruise missiles are distributed from launch lines to strike targets and cruise missile carriers are distributed from bases (basing areas) along launch lines (launch areas). At the same time, the number of cruise missiles and their carriers at the launch lines is calculated for the performance of combat missions. Based on the results of solving distribution problems in model 5 of the temporary strike structure program, the times of the launch of cruise missile carriers to the launch lines, the times of undermining of warheads of missiles at the targets of the strike are calculated.

After the calculations and analysis of the spatio-temporal characteristics of the impact are completed, the researcher selects the next task of scientific research and the process of predicting the options for constructing TFR impacts within the framework of 2–5 models is repeated.

The utility model is developed at the physical layout level of a complex of models 2-5 on FPGA cells with interface 1 based on a personal computer. The utility software of the utility model is developed at the level of individual pieces of software of models 2-5 in the language "C ++" of IBM PC.

Sources of information taken into account when compiling the description:

1. A device for solving the problem of evaluating the effectiveness of missile and artillery weapons. RU 29598, 05.20.2003.

2. A device for solving the problem of evaluating the effectiveness indicators of control of missile and artillery weapons. RU 24886 08/27/2002.

3. A device for solving the problem of evaluating the performance indicators of multi-parameter control of missile and artillery weapons. RU 30205, 06.20.2003.

4. Target selection device for air defense units. RU 106401, 07/10/2011.

5. A research model for evaluating the performance of electronic systems. RU 126168, 03.20.2013.

6. A comprehensive model for assessing the effectiveness of global strategic stability based on a balance of strategic offensive and defensive weapons. RU 2009141308, 2010.02.10.

7. Akimova I.Ya. Application of Voronoi diagrams in combinatorial problems. M. Publishing House of the Academy of Sciences of the USSR Technical Cybernetics No. 2, 1984

8. Barnes D., Jensen P. Stream Programming. M. Publishing House "Radio and Communications", 1994

9. Meinike E. Optimization algorithms on networks and graphs. M. Mir Publishing House, 2011

Claims (5)

1. A research and development model for predicting the construction of cruise missile attacks, characterized in that it contains an interface for inputting data and modeling results interconnected by digital lines, a model for constructing a network of strategic cruise missile flight routes (SCR) from launch lines to objects shock model, the distribution of TFR from the launch lines to the objects of impact, a model of the distribution of carriers of SKR from the bases of the objects of impact, a model of a temporary program of the structure of the impact, memory block five original data and simulation results. 2. The research model according to claim 1, characterized in that the SKR flight route network construction model comprises a block for generating possible flight routes, a block for generating valid routes, a unit for evaluating the feasibility of selected routes installed on a common interface bus and connected by control signals and switching with the interface of the modeling complex and with the memory block of the initial data and simulation results. 3. The research model according to claim 1, characterized in that the TFR distribution model from the start or start boundaries for strike objects contains a digital graph distribution block of cruise missile streams mounted on a common interface bus and connected by switching signals to the interface of the modeling complex and a block of memory of the source data and simulation results. 4. The research model according to claim 1, characterized in that the model for the distribution of TFR carriers from the bases at the launch lines contains a digital distribution block of TFR carriers from the bases at the launch lines with the possibility of distributing the TFR stream over the network, taking into account the probability of successful delivery of carriers to the boundaries start-up or to start areas, installed on a common interface bus and connected via control and switching signals to the interface of the modeling complex and the memory block of the initial data and simulation results. 5. The research model according to claim 1, characterized in that the model of the temporary strike construction program comprises a digital unit with the possibility of optimizing the parameters of the SCR flight speeds on the arcs of the route or the scatter parameters of the SCR launch times at the lines or in the launch areas, the digital block being installed on a common interface bus and connected by switching signals to the interface of the modeling complex and the memory block of the source data and simulation results.

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