CN102819665B - Multi-aircraft based on prominent anti-mission requirements launches quantity and timing optimization method - 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 saturation attack strategy is often used when deciding the number of aircraft for a specific mission 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 use the basic principles of probability theory when establishing a multi-aircraft collaborative model, 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;

Step 2: Select three typical distributions: Poisson distribution, normal distribution, and average distribution. It is believed that the arrival time of multiple aircrafts in the interception area obeys three typical distributions. The parameters of the distribution are used as variables, and the influence of time factors on the distribution parameters is considered. 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 minimum number of required aircraft under the condition of meeting 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 of the 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 launch timing constraints are solved by establishing the minimum take-off interval of the aircraft.

Beneficial effects of the present invention:

The present invention can be widely used in solving the minimum launch quantity of unmanned aerial vehicle, and on the basis of the solution quantity, the optimal launch timing of the aerial vehicle 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 interceptor 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 interception point.

b) The impact of space factors on the detection, identification, tracking/orbit measurement, and interception of the interceptor 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 impact of quantity factors on the detection, identification, tracking/orbit measurement and interception of the interceptor system ρ _N

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

d) The influence of threat degree factors on the detection, identification, tracking/orbit measurement and interception of the interceptor system ρ _d

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 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: $P_{\mathrm{new}\_i}=P_i+\underset{j=1,j\≠i}{\overset{N}{\mathrm{\Σ}}}({\mathrm{\ρ}}_{t\_\mathrm{the\; ji}}\&Center\; Dot;{\mathrm{\ρ}}_{p\_\mathrm{the\; ji}}\&Center\; Dot;{\mathrm{\ρ}}_{N\_\mathrm{the\; ji}}\&Center\; Dot;{\mathrm{\ρ}}_{d\_\mathrm{the\; ji}})\&Center\; Dot;(1-P_i),$ P _{new_i} also describes the interception capability of the interceptor in the case of multi-aircraft coordinated penetration from the side. Among them, P _i is the probability that the i-th aircraft performs the penetration mission alone; the value range of i can be inferred to be 1-N.

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. However, 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 the parameter of the typical distribution, assume that a total of m typical distribution parameters are taken, k is the number of required aircraft, P _{new_i} is the penetration probability of the i-th aircraft in the case of multi-aircraft cooperative penetration, which is the aircraft function of quantity 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: $\mathrm{the\; s}.t.\left\{\begin{array}{c}{t}_{\mathrm{the\; fi}}\&Element;\mathrm{\&Phi;}\\ 0\&le;f_{\mathrm{the\; fi}}\&le;t_{\max }\\ t_{\mathrm{li}}+t_{\mathrm{the\; fi}}\&Element;f\left({\mathrm{\&lambda;}}_b\right)\end{array}\right.,$ 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 launch quantity and timing optimization method required by the penetration task, it is characterized in that, comprising 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; Step 2: Select three typical distributions: Poisson distribution, normal distribution, and average distribution. It is believed that the arrival time of multiple aircrafts in the interception area obeys three typical distributions. The parameters of the distribution are used as variables, and the influence of time factors on the distribution parameters is considered. 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 minimum number of required aircraft under the condition of meeting 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. 2. as claimed in claim 1 based on the multi-aircraft launch quantity and timing optimization method required by the penetration task, it is characterized in that, wherein the 5th step is in the process of solving, by establishing the aircraft take-off interval minimum to solve simultaneously satisfying The index and launch timing constraints the timing and sequence of takeoffs. 3. as claimed in claim 1 or 2, based on the multi-aircraft launch quantity and timing optimization method required by the penetration task, it is characterized in that, in the first step, the multi-aircraft is analyzed according to time factor, space factor, quantity factor, threat degree factor The impact of coordinated penetration Establish the impact model of multi-aircraft on the intercepting party's interception system; a) The influence ρ _t of the time factor on the detection, identification, tracking and orbit measurement, and interception of the interceptor 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 interception point; b) The impact of space factors on the detection, identification, tracking and orbit measurement, and interception of the interceptor system ρ _p ρ _{p_ji} = f ₂ (y _i , y _j ), where, y _i is the space position of the i-th aircraft; c) The impact of quantity factors on the detection, identification, tracking and orbit measurement, and interception of the interceptor 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 and orbit measurement, and interception of the interceptor system ρ _d 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 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: $P_{\mathrm{new}\_i}=P_i+\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{\&rho;}}_{t\_\mathrm{the\; ji}}\&CenterDot;{\mathrm{\&rho;}}_{p\_\mathrm{the\; ji}}\&CenterDot;{\mathrm{\&rho;}}_{N\_\mathrm{the\; ji}}\&Center\; Dot;{\mathrm{\&rho;}}_{d\_\mathrm{the\; ji}})\&Center\; Dot;(1-P_j),$ P _{new_i} also describes the interception capability of the intercepting party in the case of multi-aircraft cooperative defense penetration from the side; among them, P _i is the probability that the i-th aircraft performs the defense penetration task alone; the value range of i is 1～N; j Indicates the jth aircraft, and the value of j ranges from 1 to N.