CN102819665A - Multi-aircraft launching number and timing optimization method on basis of penetration task requirement - Google Patents

Abstract

The invention provides a multi-aircraft launch quantity and timing optimization method based on the requirements of the penetration mission, which solves the problem of the optimal launch quantity and launch timing under the condition of penetration probability. Step 1: Establish a model of the impact of multiple aircraft on the interception system of the intercepting party, and analyze the impact of different numbers of aircraft on the interception capability; Step 2: Establish a time distribution model for aircraft arriving at the interception area; Step 3: Introduce the number of aircraft as a variable into the arrival Time distribution, establish the function table of the number of aircraft, arrival time and penetration probability; Step 4: Solve the distribution parameters of the number of aircraft and aircraft arrival time according to the specified penetration probability; Step 5: Reversely solve the aircraft based on the launch timing constraint library Optimal launch timing: According to the minimum number of aircraft, the take-off time of the aircraft is deduced through the arrival time distribution of the aircraft.

Description

Optimization method of multi-aircraft launch quantity and timing based on penetration mission requirements

technical field

The invention relates to a multi-aircraft launch quantity and timing optimization method based on the penetration task requirements, which can be widely used in the field of launch timing optimization algorithms for aircraft with high requirements for coordinated penetration capabilities and high costs.

Background technique

In the process of multi-aircraft coordinated defense penetration, the number of aircraft affects the coordinated penetration ability of the swarm. At present, the published literature shows that the strategy of saturation attack is often used when deciding the number of aircraft for a specific task at home and abroad. Using the advantage of quantity can certainly improve the coordination ability of multi-aircraft, but blindly adopting saturation attack will inevitably lead to a waste of quantity, especially when the cost of aircraft is high, the optimal solution for multi-aircraft is determined on the premise of meeting the requirements of the penetration mission. The emission quantity and emission timing have important research significance and broad application prospects.

In addition, some literatures consider the issue of the number of aircraft launched under a certain characteristic index, but most of them adopt the basic principles of probability theory when establishing multi-aircraft cooperation models, considering multiple aircraft as independent events and the number of aircraft as independent repeated events This ignores the difference in the degree of coordination between aircraft when the number is different, so the probability model cannot accurately describe the impact of the number on the swarm's cooperative penetration, which in turn affects the collaborative decision-making and control of multiple aircraft.

Contents of the invention

The invention provides a multi-aircraft launch quantity and timing optimization method based on the requirements of the penetration mission, which solves the problem of the optimal launch quantity and launch timing under the condition of penetration probability.

The multi-aircraft launch quantity and timing optimization method based on the requirements of the penetration mission includes the following steps:

Step 1: Establish a model of the impact of multiple aircraft on the interception system of the intercepting party, and analyze the impact of different numbers of aircraft on the interception capability;

The second step: select three typical distributions of Poisson distribution, normal distribution, and average distribution, and consider that the time for multi-aircraft to reach the defense area obeys three typical distributions, and take the parameters of the distribution as variables, and consider the influence of time factors on the distribution parameters, Select typical parameters to describe the distribution of the arrival time, and establish the distribution model of the arrival time of the aircraft in the interception area;

The third step: introduce the number of aircraft as a variable into the arrival time distribution, and establish a function table of the number of aircraft, arrival time, and penetration probability; each table records the corresponding relationship between the number of aircraft and the penetration probability when obeying a certain typical distribution;

Step 4: Calculate the number of aircraft and aircraft arrival time distribution parameters according to the specified penetration probability: According to the specified penetration probability index, calculate the penetration probability expression under the condition of different numbers of aircraft through the function table described in the third step , and then through the comparison of three typical distributions, determine the required minimum number under the condition of satisfying the penetration probability index, and record the distribution form and parameters that the arrival time of the aircraft obeys at this time;

Step 5: Reverse solve the optimal launch timing of the aircraft based on the launch timing constraint library: According to the minimum number of aircraft, reverse the take-off time of the aircraft through the arrival time distribution of the aircraft.

In the process of solving, the take-off time and sequence that satisfy both the index and the take-off sequence constraints are solved by establishing the minimum take-off interval time of the aircraft.

Beneficial effects of the present invention:

The present invention can be widely used in solving the minimum launch quantity of unmanned aircraft, and on the basis of the solution quantity, the optimal launch timing of the aircraft can be obtained according to the distribution of arrival time. The greatly improved requirements for the number of launches in saturation attacks enable the optimal number of launches to meet the requirements of the specified penetration probability, clarify the minimum number required to perform tasks, reduce the cost of launches, and improve combat effectiveness.

Detailed ways

Assuming that there are a total of N aircraft capable of performing the defense penetration mission, the probability of each aircraft performing the defense penetration mission alone is P, and the penetration probability index requirement is P _e . When the probability is greater than P _e , determine the minimum launch number N _l of aircraft required, and calculate the launch time and sequence of N _l aircraft, according to the influence of time factors, space factors, quantity factors, and threat level factors on the coordinated penetration of multiple aircraft ,set up

a) The influence ρ _t of the time factor on the detection, identification, tracking/orbit measurement, and interception of the defender's system;

ρ _{t_ji} =f ₁ (t _i ,t _j ), where t _i is the moment when the i-th aircraft arrives at a certain key defense point.

b) The impact of space factors on the detection, identification, tracking/orbit measurement, and interception of the defender's system ρ _p

ρ _{p_ji} = f ₂ (y _i , y _j ), where y _i is the spatial position of the i-th aircraft.

c) The influence of quantity factors on the detection, identification, tracking/orbit measurement, and interception of the defender's system ρ _N

ρ _{N_ji} = f ₃ (N), where N is the number of aircraft.

d) The influence of threat level factors on the detection, identification, tracking/orbit measurement, and interception of the defender's system ρd

ρ _{d_ji} = f ₄ (d _i , v _i , d _j , v _j ), where d _i is the distance between the i-th aircraft and the enemy target at a certain threat judgment time, and v _i is the distance at a certain threat judgment time The speed of the i-th aircraft.

Therefore, in the case of cluster cooperative defense penetration, the penetration probability P _{new_i} of the i-th aircraft is:

$P_{\mathrm{enw}\_i}=P_i+\underset{j=1,j\≠i}{\overset{N}{\mathrm{\Σ}}}({\mathrm{\ρ}}_{t\_\mathrm{the\; ji}}\&Center\; Dot;{\mathrm{\ρ}}_{p\_\mathrm{the\; ji}}\·{\mathrm{\ρ}}_{N-\mathrm{the\; ji}}\·{\mathrm{\ρ}}_{d\_\mathrm{the\; ji}})\·(1-P_i),$ P _{new_i} also describes the interception capability of the defender in the case of multi-aircraft coordinated penetration.

In this embodiment, the time when the aircraft arrives at the interception area is taken as an example according to the Poisson distribution, and the probability distribution function of the Poisson distribution is When the distribution parameters are different, the number of aircraft arriving at the interception area at the same time is different. The difference in the number of aircraft at the same time affects the overall penetration probability of multiple aircraft, so the multi-aircraft penetration system can be described as the following penetration probability model:

P _swarm ＝g(λ,k,P _{new_i} (k)), where λ is a parameter of a typical distribution, assuming that m typical distribution parameters are taken in total, k is the number of required aircraft, and P _{new_i} is In the case of defense, the penetration probability of the i-th aircraft is a function of the number of aircraft k.

On the basis of the established penetration probability model, the number of aircraft and the parameters of the typical distribution are used as two independent variables to determine the overall penetration probability expression of the aircraft under different variables, and establish a probability two-dimensional variable table, as shown in the following table Shown:

Table 1 The probability table of multi-aircraft cooperative penetration when the arrival time obeys the Poisson distribution

According to the above method, the functional relationship expressions of the overall penetration probability of the aircraft with respect to the number of aircraft and the typical distribution parameters are established when the arrival time of the aircraft to the interception area obeys the normal distribution and the average distribution, and the influence of different typical distributions on the penetration probability is analyzed. According to the given penetration probability index, the minimum number of aircraft required to meet the requirements of the index is found in the three typical distribution penetration probability two-dimensional tables. Assuming k=k _a , the penetration probability function g _a,b when λ=λ _b meets the requirements of the index, record the number of aircraft k _a at this time, the form of the typical distribution and the parameter λ _b .

Select k _a launch points from the N aircraft launch points, and the flight time of each aircraft is determined after the launch point is determined. Let the flight time of each aircraft be t _fi , i=1,2,..., k _a , this can use the launch timing constraint library to calculate the optimal launch timing of each aircraft, the time distribution of aircraft arriving at the interception area satisfies F(λ _b ), and the launch time of each aircraft is t _li , i=1,2 ,...,k _a , the following mathematical problems can be established: $\left\{\begin{array}{c}{t}_{\mathrm{li}}+t_{\mathrm{the\; fi}}\∈f\left({\mathrm{\λ}}_b\right)\\ t_{\mathrm{li}}\∈\mathrm{\Φ}\end{array}\right.,$ Among them, Φ is the launch timing constraint library introduced in the patent of a ballistic aircraft cooperative attack launch timing optimization algorithm based on the time constraint library. The launch timing constraint library can solve the problem of collision avoidance during flight, and then solve the optimal launch time t _li . At the same time, the starting point determines the flight time of the aircraft, and due to the arbitrariness of the starting point selection, the solved take-off time may not be unique. At this time, specific indicators can be established, such as the minimum time between aircraft take-offs, which can be established as follows

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; the\; fi</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; li</span>}}<span\; class="notranslate">\; |</span>$

Optimization: $\mathrm{the\; s}.t.\left\{\begin{array}{c}{t}_{\mathrm{the\; fi}}\&Element;\mathrm{\&Phi;}\\ 0\&le;t_{\mathrm{the\; fi}}\&le;t_{\max }\\ t_{\mathrm{li}}+t_{\mathrm{the\; fi}}\&Element;f\left({\mathrm{\&lambda;}}_b\right)\end{array}\right.,$ On this basis, the t _sj meeting the performance index is obtained through an optimization algorithm, and then the take-off time and order of each aircraft are obtained.

Claims (3)

1. based on the multi-aircraft emission quantity and the timing optimization method of prominent anti-mission requirements, it is characterized in that, may further comprise the steps:

The first step: set up the influence model of multi-aircraft, analyze of the influence of number of vehicles difference to interdiction capability to the side's of interception intercepting system;

Second step: choose Poisson distribution, normal distribution, be evenly distributed three kinds of exemplary distribution; Think that multi-aircraft arrives three kinds of exemplary distribution of time obedience in defence zone; With the parameter that distributes as variable; The consideration time factor is chosen the distribution that canonical parameter is described time of arrival to effects of distribution parameters, sets up aircraft and arrives interception distributed model zone time;

The 3rd step: number of vehicles is introduced distribution time of arrival as variable, set up the function table of number of vehicles, time of arrival and penetraton probability; Writing down the corresponding relation of number of vehicles and penetraton probability when obeying certain exemplary distribution in each table;

The 4th step: find the solution number of vehicles and the aircraft distributed constant time of advent based on the penetraton probability of appointment: based on the penetraton probability index of appointment; Through the penetraton probability expression formula under the function table calculating aircraft varying number condition described in the 3rd step; And then the comparison through three kinds of exemplary distribution; Confirm to satisfy the required minimum number under the penetraton probability index condition, and the distribution form and the parameter of the record aircraft this moment obedience time of advent;

The 5th step: launch sequential based on the anti-aircraft optimum that solves in emission temporal constraint storehouse:, distribute the anti-departure time that solves aircraft through aircraft according to minimum number of vehicles time of arrival.

2. multi-aircraft emission quantity and timing optimization method based on prominent anti-mission requirements as claimed in claim 1; It is characterized in that; Wherein the 5th step solved the departure time and the order that satisfies this index and the temporal constraint that takes off simultaneously through setting up aircraft takeoff minimum interval time in the process of finding the solution.

3. multi-aircraft emission quantity and timing optimization method based on prominent anti-mission requirements as claimed in claim 1 or 2; It is characterized in that, based on time factor, space factor, quantity factor, threaten degree factor multi-aircraft is worked in coordination with prominent anti-influence in the first step and set up the influence model of multi-aircraft the side's of interception intercepting system;

A) ρ that influences that surveys rail, interception is surveyed, discerns, followed the tracks of to time factor to the defence method, system _t

ρ _{T_ji}=f ₁(t _i, t _j), wherein, t _iIt is the moment that i aircraft arrives a certain crucial defence stand;

B) ρ that influences that surveys rail, interception is surveyed, discerns, followed the tracks of to space factor to the defence method, system _p

ρ _{P_ji}=f ₂(y _i, y _j), wherein, y _iIt is the locus of i aircraft;

C) ρ that influences that surveys rail, interception is surveyed, discerns, followed the tracks of to quantity factor to the defence method, system _N

ρ _{N_ji}=f ₃(N), wherein, N is a number of vehicles;

D) ρ that influences that surveys rail, interception is surveyed, discerns, followed the tracks of to the threaten degree factor to the defence method, system _d

ρ _{D_ji}=f ₄(d _i, v _i, d _j, v _j), wherein, d _iFor moment i aircraft and enemy's distance to be struck target, v are judged in a certain threat _iFor the speed of i aircraft is constantly judged in a certain threat;

Therefore work in coordination with under the prominent anti-situation penetraton probability P of i aircraft at cluster _{New_i}For:

$P_{\mathrm{Enw}\_i}=P_i+\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{\&rho;}}_{t\_\mathrm{Ji}}\&CenterDot;{\mathrm{\&rho;}}_{p\_\mathrm{Ji}}\&CenterDot;{\mathrm{\&rho;}}_{N-\mathrm{Ji}}\&CenterDot;{\mathrm{\&rho;}}_{d\_\mathrm{Ji}})\&CenterDot;(1-P_i),$ P _{New_i}The interdiction capability of defence side under the collaborative prominent situation of preventing of multi-aircraft has been described simultaneously from the side.