The article considers the issue of assessing the combat potential of a strike unmanned aerial vehicle. An analysis of existing methods for assessing the combat potential of manned aircraft and found that they often use methods of expert assessment, which require a significant number of experienced experts and are quite time consuming. The scientific and methodical apparatus for calculations is given: probabilities of unmanned aerial vehicle damage for one departure and for a certain number of departures; mathematical expectation (average number) of combat sorties; mathematical expectation (average value) of the number of single targets hit in one combat flight by an unmanned aerial vehicle; the maximum value of the mathematical expectation (average value) of the relative number of single targets hit in one combat flight by an unmanned aerial vehicle; mathematical expectation of the number of single targets hit by an unmanned aerial vehicle; maximum mathematical value expectations of the number of single targets hit by an unmanned aerial vehicle for the entire period of life; the coefficient of combat potential of the unmanned aerial vehicle; the average combat potential of an unmanned aerial vehicle. The construction of a mathematical model of combat potentials of strike unmanned aerial vehicles based on a block-hierarchical approach is carried out. In this approach, the mathematical model of the modeling object is not represented as a function of many variables, but as a hierarchy of models of much smaller dimension. The basis for building a hierarchy of models is the physical content of the modeling object and the patterns it reflects.
1. Introduction
In the field of unmanned aerial vehicles, there
is a transition from the single use of unmanned
aerial vehicles (UAVs) to the group (mass) use in
cooperation with manned aircraft. In addition to
reconnaissance tasks and individual tasks of
combat support of manned aircraft, strike tasks of
UAVs are becoming increasingly important [
The problem is that the methods of estimating
of the CP of UAVs, which are similar to the
methods of estimating of the CP of manned
aircraft, have not found appropriate distribution.
The known methods of estimating of the combat
potential of the manned aircraft are based mainly
on the methods of expert assessments [
Analysis of the recent researches and publications
In [
Initially, the СP of armaments samples were
determined either empirically, based on statistics
obtained from past wars (armed conflicts) [
In the 80s years of the last century the methods
of mathematical modeling of hostilities [
The construction of mathematical models of aircraft CP, which take into account a fairly complete list of aircraft characteristics and conditions of their use, proved to be quite a problematic task. An alternative solution of this problem remains the methods of expert assessments.
The purpose of the article is to determine the approach to construction of a mathematical model for calculating the combat potential of a strike UAV without the involvement of expert or other “fuzzy” information. 2. Presentation of the main material
The difficulty of constructing analytical
mathematical models for calculating the CP of
aircraft functionally related to the characteristics
of aircraft, their weapons and parameters of
combat conditions, can be attributed to the
nonintegrability of the vast majority of systems of
differential equations [
The concept of “combat potential of a sample
of weapons”, judging by its various definitions
[
Combat potential of a sample of weapons is an
integral indicator that characterizes the maximum
set of tasks performed by the sample weapons and
military equipment (WME) for the intended
purpose in the implementation of the limit tactical
and technical characteristics (TTC) for the typical
operating time in typical design conditions [
The number of combat sorties that a UAV can perform before its defeat is a random variable. When performing n combat sorties UAV will be struck with a probability of :
1 1 (2)
Mathematical expectation (the average number) of combat sorties is determined by the ratio of this probability to the probability of defeat in one combat sortie:
1 1
For multiple UAVs n>>1 і n and is reduced to the inverse probability :
1
The mathematical expectation (average value) of the number of single targets hit in one UAV combat flight is determined by the number of successful target attacks during the combat flight. It is limited by the number of means of destruction in combat charge. It is assumed that the ammunition of the aircraft consists of the same type of means of destruction, and launches on one target is carried out by only one means of destruction. This simplification is not fundamental and allows you to reduce the recording of basic expressions in the article. Expression for mathematical expectation (average value) of the relative number of single targets hit in one UAV combat flight:
The combat potential of a sample of weapons
is an integral indicator that characterizes the
maximum amount of combat tasks that can
perform a sample of weapons for its functional
purpose in the given (calculated) conditions of use
during its existence [
In the definition [
As shown in [
It is the indicator “combat potential of the sample of weapons”, which combines the indicators of “firepower” and “survivability” should be used in conceptual research on the formation of basic requirements for UAVs on a complex criterion of “combat potential – cost”.
The model of combat operations of reusable UAVs can be thought of as a series of repetitive combat sorties in each of which it hits a number of targets. Each subsequent flight can be performed provided that the previous ones were performed.
Suppose that in the process of performing a
combat sortie UAV is exposed to fire from the
enemy with an intensity of λ, which leads to its
defeat in one sortie with probability
[
1 (1) conditional probability of the sample damage under one exposure; duration of the combat flight (3) (4) (5) ∙ ∙ where – – – the number of single potential targets of the j-type, hit in the kcombat flight of the UAV by means of the i-type; mathematical expectation of the number of single targets of the jtype, struck in the k-combat flight of the UAV by means of the i-type; the probability of fulfilling the conditions preceding the launch (reset, etc.) of the means of defeat of the i-type on the target of the j-type: detection and recognition of the target by external means, long-range guidance, target detection by own means of UAVs, target attack. Depending on the problem to be solved and the method of using the UAV, the composition of the stages of preparation for the launch of the means of destruction may differ from the above. For example, in the case of an autonomous method of UAV application, the stages of external targeting may be absent, and target detection and recognition may be carried out by its own means; – the probability of defeat by one means of defeat of the i-type of the j-type target; – the number of means of defeat of the i-type AV used in the kcombat flight;
The maximum value of the mathematical expectation (average value) of the relative number of single targets hit in one combat flight of UAVs is determined by the expression: ∙ ∙ where – the total number of means of defeat of the i-type aircraft, used in the kcombat flight.
For the entire period of the UAV's life, ie during n combat sorties, the mathematical expectation of the number of single targets hit by the UAV:
The maximum value of the mathematical expectation of the number of single targets hit during the entire life of the UAV, ie during n combat sorties by definition is the UAV CP as to destruction by i-type means of the j-type targets: or where = = ∙ ∙ – ∙ ∙ ∙ ∙
∙ the average value of the number of means of aircraft destruction (combat kits) of i-type on departures; (6) (7) (8) – the average number of single potential targets of the j-type, affected by means of the i-type on departures.
If the CP of UAV is already known, which can be taken as a reference, it is more convenient to use the CP coefficient instead of the CP. It is determined by the ratio of the CP of UAV to the reference CP of UAV. It is assumed that UAVs are used in similar conditions. In this case, expression (9) is simplified because the variables are reduced: ∙ ∙ ∙ (10)
The CP coefficient has a clear physical meaning. It is reduced to the product of the ratios of the indicators of effectiveness of the destruction means, the number of means in the ammunition and the inverse ratio of survivability.
Model (10) can be applied during researches at the initial stages of UAV creation (external design) when searching for a design compromise between the combat potential and the cost of UAVs.
To optimize (select) the options of technical and design solutions of UAVs, it is necessary to use the dependences of the generalized indicators , , , of the TTC of UAVs. Such dependences should be considered as components of mathematical models of CP.
in (10) is an element of the matrix, where the types of means by which the UAV will hit the enemy's targets are indicated in the lines, and the types of targets - in the columns.
The matrix (10) is similar to the matrix of efficiency of application of different models of weapons in different conditions. The use of the data contained in the matrix (10) depends on the objectives of research and the method of decisionmaking based on them.
For example, in comparing of different UAVs, several different approaches can be used to select the best option.
The simplest approach is to collapse the matrix (9) (10) into a scalar quantity. Then the average CP of UAV is determined: ∙ 1 ∙ ∙ ∙ (11) where N – the number of types of UAVs
destruction; M – number of types of targets. weight factor that determines the relative frequency (probability) of use of weapons of the i-type,
1 ; ∑ – weighting factor that determines the relative part (probability) of the targets of the j-type that will be affected, ∑ 1 .
Weight multipliers , are determined by
the typical composition of enemy targets and
weapons of strike UAVs [
With a more detailed approach, it is possible to
make comparisons when folding the matrix (10)
into a vector or without folding. In this case, the
problem is reduced to a comparison of a set of
criteria [
When folded into a vector-line, it is assumed that the entire weapon is used only for targets of the j-type:
Obviously,
reaches its maximum value when using ammunition to hit targets of the same type with maximum efficiency. 3. Conclusions
To select options for technical and design solutions of unmanned aerial vehicles, it is necessary to use the dependences of generalized indicators: the probability of fulfilling the conditions preceding the launch (reset) of a certain type of destruction means for the determined target, ie detection and recognition of targets by external means, long-range guidance, target detection by own means of a UAV, target attack; the probability of defeat by one means of defeat of a certain type of a certain type of a target; the probability of a UAV damage in one flight; the average value of the number of means of destruction of unmanned aerial vehicles (combat kits) of a certain type by departures from the tactical and technical characteristics of the unmanned aerial vehicle. Such dependences 1
∙ 1 ∙ ∙ ∙ should be considered as components of mathematical models of CP.
The considered methodical approach to development of mathematical model of combat potential of strike UAVs allows to build mathematical models for conducting researches of military and economic efficiency of strike unmanned aerial vehicles without involvement of expert or other “fuzzy” information. 4. References