CN107247879A - Based on the extensive absolutely empty Combat Efficiency Evaluation method for improving Lanchester equation - Google Patents
Based on the extensive absolutely empty Combat Efficiency Evaluation method for improving Lanchester equation Download PDFInfo
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Abstract
The invention discloses a kind of based on the extensive absolutely empty Combat Efficiency Evaluation method for improving Lanchester equation, this method determines initially our the operational aircraft quantity with enemy first, and selects suitable virtual time step-length；Then the average air combat capability index of operational aircraft between ourselves and the enemy is calculated；Then average striking probability is calculated；Then our combat success war is calculated to damage；The absolutely empty fighting efficiency grade of evaluation is damaged finally according to war fighting requirement and our combat success war.The present invention can realize the measures of effectiveness to extensive absolutely empty operation by calculating our war damage and combat success at different virtual moment；This method can be used for prewar to prepare the absolutely empty combat duty measures of effectiveness in stage, provides foundation for force deployment, it can also be used to the real-time assessment in operational implementation stage, foundation is provided for the decision-making of commander.
Description
Technical field
The present invention relates to a kind of absolutely empty Combat Efficiency Evaluation technical field, more particularly to one kind is based on improvement Lanchester side
The extensive absolutely empty Combat Efficiency Evaluation method of journey.
Background technology
Absolutely empty Combat Efficiency Evaluation refers to that operational aircraft completes the capability evaluation of the task of absolutely empty operation, specifically makees
Can the combat success and war damage that war aircraft destroys the aircraft of the opposing party meet combat duty requirement.Absolutely empty Combat Efficiency Evaluation is related to
The performance level of air operation task, is one of important evidence of commanding and decision-making, is army's event horizon, the focus and again of academia's research
Point.
Many is studied to the measures of effectiveness of operational aircraft at present, including analytic hierarchy process (AHP), index method, WSEIAC models etc.
(Zhu Baoluan, Zhu Rongchang, Xiong Xiaofei, assessing of Battle Plane Effectiveness, aircraft industry publishing house, 1993).But to absolutely empty fighting efficiency
Assess and still deploy to study mainly for unit and unit operation, for extensive absolutely empty operation Effectiveness Evaluation Model research compared with
It is few.The efficiency estimation method main method fought for unit and unit for analytic hierarchy process (AHP), (comment by Chen Guoji, absolutely empty fighting efficiency
Estimate the development and exploitation of software systems, Nanjing Aero-Space University, 2014), the value subjectivities of this method various parameters compared with
Greatly, and it is unfavorable for describing real-time dynamic process.
The content of the invention
Goal of the invention：For problem above, the present invention proposes a kind of based on the extensive absolutely empty of improvement Lanchester equation
Combat Efficiency Evaluation method, by virtual time iteration, calculates number of aircraft between ourselves and the enemy and changes with time, fought according to us
Fruit war damage realize it is absolutely empty it is belligerent in my army Combat Efficiency Evaluation.
Technical scheme：To realize the purpose of the present invention, the technical solution adopted in the present invention is：One kind is blue thorough based on improving
The extensive absolutely empty Combat Efficiency Evaluation method of this special formula journey, specifically includes following steps：
Step 1：It is determined that the operational aircraft quantity of initial we and enemy, and select suitable virtual time step-length；
Step 2：Calculate the average air combat capability index of operational aircraft between ourselves and the enemy；
Step 3：Calculate the average striking probability of aircraft between ourselves and the enemy；
Step 4：Calculate our combat success war to damage, if not up to stopping criterion for iteration, returns to step 2；If reaching, iteration is whole
Only condition, then continue step 5；
Step 5：The expection combat success provided according to combat duty and the contrast for calculating obtained combat success, evaluate absolutely empty effect of fighting
Can grade.
The average air combat capability index calculation procedure of both sides' operational aircraft is as follows：
Step 2-1：Mobility is calculated by specific excess power and maximum overload value, formula is：
In formula, nymaxFor maximum overload value, SEP is unit dump power.
Step 2-2：Fire performance is calculated by the range of carry air-to-air missile, one-shoot damage probability, angle of attack sum amount, it is public
Formula is：
Step 2-3：By radar detection ability and visual capacity calculation bullet detectivity, formula is：
Step 2-4：Aircraft survivability is calculated by aircraft size and radar area, formula is：
In formula, RCS is radar area.
Step 2-5：Calculate the air combat capability index of single rack aircraft：
C=[ln B+ln (A1+1)+ln(A2+1)]ε
In formula, C is air combat capability index；B is mobility；A1For fire performance；A2For detectivity；ε for survival can
Power；
Step 2-6：Average air combat capability index is calculated by arithmetic mean method, and formula is：
The average striking probability calculation procedure of aircraft is as follows between ourselves and the enemy：
Step 3-1：My average striking probability is calculated, formula is：
In formula, B is enemy's quantity, γRCorrection factor.
Step 3-2：My intelligence capabilities correction factor：
In formula, we is intelligence capabilities QRSpan [0,1], γQFor correction factor.
Step 3-3：Enemy's interference performance correction factor：
In formula, enemy's interference performance GBSpan [0,1], γGFor correction factor.
Step 3-4：My command ability correction factor：
In formula, we is command ability ZRSpan [0,1], γZFor correction factor.
Step 3-5：Calculate me and integrate average striking probability：
βR=cGcQcZcR
Step 3-6：The calculating process of average striking probability is integrated according to us, enemy is calculated and integrates average striking probability.
Calculating our the improvement Lanchester equation of combat success war damage is：
In formula, αR、αB, R, B represent that we is averaged operational efficiency, the average operational efficiency of enemy, our quantity and enemy respectively
Quantity, βBFor average striking probability of the enemy battle unit to our battle unit, βREnemy is fought for our battle unit single
The equal striking probability of position；The average operational efficiency of our enemy is respectively with the average air combat capability index of our enemyWithWeigh.
Solved using difference method：
Above formula is substituted into improved Lanchester equation, obtain next virtual moment between ourselves and the enemy troops with virtual time
The calculation formula of change：
Rt+1=-αBBtβBRtΔt+Rt
Bt+1=-αRRtβRBtΔt+Bt
If Rt+1And Bt+10 is all higher than, then returns to step 2；If there is one to be less than 0, step 5 is carried out.
The step of assessing absolutely empty fighting efficiency grade is as follows：
Step 5-1：Our expected combat success war damage value is set；
Step 5-2：According to default war damage value, corresponding combat success value is found in obtained change curve is calculated；Contrast
The relative size of the combat success value and default combat success value, determines absolutely empty fighting efficiency grade.
Beneficial effect：The present invention compared with prior art, its remarkable advantage：(1) traditional Lanchester equation is carried out
Improve, when average striking probability takes special parameter, classical Lanchester equation can be deteriorated to, Lanchester equation is improved
Adaptability；(2) the combat success value in the case of being damaged to the war damage value in the case of our different combat successes and different wars is predicted；
(3) contrast damaged with expected combat success war is damaged according to our combat success war and realizes the assessment to extensive absolutely empty fighting efficiency, is solved
The problem of extensive absolutely empty Combat Efficiency Evaluation；(4) the average main performance parameter according to aircraft of air combat capability index in assessing
Calculating is obtained, and average striking probability is calculated according to number of aircraft to be obtained, and is effectively reduced the interference of subjective factor, is improved calculating
As a result confidence level.
Brief description of the drawings
Fig. 1 is based on the extensive absolutely empty Combat Efficiency Evaluation method flow diagram for improving Lanchester equation；
Fig. 2 is the air combat capability index calculation flow chart of single rack aircraft；
Fig. 3 is that I integrates average striking probability and the comprehensive striking probability calculation flow chart of enemy；
Fig. 4 is number of aircraft with virtual time change curve.
Embodiment
Technical scheme is further described with reference to the accompanying drawings and examples.
It is the extensive absolutely empty Combat Efficiency Evaluation method stream based on improvement Lanchester equation of the present invention as shown in Figure 1
Cheng Tu, specifically includes following steps：
Step 1：It is determined that our initial operational aircraft amount R and enemy operational aircraft quantity B, and choose it is suitable it is virtual repeatedly
For time step dt.
Step 2：Calculate the average air combat capability index of operational aircraft between ourselves and the enemy.
Enemy and we couple are calculated according to the mobility of different aircrafts, fire performance, detectivity, survival ability using logarithm method
The air combat capability index of square single rack aircraft；According to the air combat capability index and number of aircraft of single rack aircraft, using arithmetic mean method
Calculate average air combat capability index.
By the air combat capability index arithmetic mean of our all operational aircrafts, our average air combat capability index is calculatedBy the air combat capability index arithmetic mean of all operational aircrafts of enemy, calculate the average air combat capability of enemy and refer to
Number
It is the air combat capability index calculation flow chart of single rack aircraft as shown in Figure 2, first according to aircraft type, obtains unit
Dump power, maximum overload value, the range of the absolutely empty bullet of carry, one-shoot damage probability, angle of attack, quantity, airborne radar are most wantonly searched for
Rope radius, azimuth, aircraft size, radar area；Then mobility is calculated according to specific excess power, maximum overload value
Can, fire performance is calculated according to the range of the absolutely empty bullet of carry, one-shoot damage probability, angle of attack, quantity, it is maximum according to airborne radar
Search radius, azimuthal angle calculation detectivity, survival ability is calculated according to aircraft size, radar area；Finally according to machine
Dynamic performance, fire performance, detectivity and survival ability calculate air combat capability index Ci。
Specifically, the average air combat capability index of both sides' operational aircraft is calculated in accordance with the following steps：
Step 2-1：Mobility is calculated by specific excess power and maximum overload value, calculation formula is：
In formula, nymaxFor maximum overload value, SEP is unit dump power.
Step 2-2：Fire performance is calculated by the range of carry air-to-air missile, one-shoot damage probability, angle of attack sum amount, it is single
Hair air-to-air missile fire performance calculation formula be：
Step 2-3：By radar detection ability and visual capacity calculation bullet detectivity, calculation formula is as follows：
Step 2-4：Aircraft survivability is calculated by aircraft size, radar area, calculation formula is as follows：
In formula, RCS is radar area.
Step 2-5：Above-mentioned four kinds of abilities are substituted into following formula, the air combat capability index of single rack aircraft is obtained.
C=[ln B+ln (A1+1)+ln(A2+1)]ε
In formula, C is air combat capability index；B is mobility；A1For fire performance；A2For detectivity；ε for survival can
Power.
Step 2-6：Average air combat capability index is calculated by arithmetic mean method, and formula is：
Step 3：Calculate the average striking probability of aircraft between ourselves and the enemy.
If Fig. 3 is that I integrates average striking probability and the comprehensive striking probability calculation flow chart of enemy, me is calculated first and is averagely beaten
Hit probability cR, then it is modified according to my intelligence capabilities, enemy's interference performance, my command ability, obtains me and integrate average strike
Probability βR.Then the average striking probability c of enemy is calculatedB, repaiied finally according to enemy's intelligence capabilities, my interference performance, enemy's command ability
Just, the comprehensive average striking probability β of enemy is obtainedB。
The specific calculation procedure of the average striking probability of aircraft is as follows between ourselves and the enemy：
Step 3-1：My average striking probability is calculated, calculation formula is as follows：
In formula, B is enemy's quantity, γRCorrection factor.For the sake of simplicity, it is considered that γRIt can be attacked simultaneously with our weapon
Number of targets n it is relevant, for absolutely empty belligerent, γRTake 0.
Step 3-2：My intelligence capabilities correction factor：
In formula, we is intelligence capabilities QRSpan [0,1], is determined, γ by scoringQFor correction factor, 1 is typically taken.
Step 3-3：Enemy's interference performance correction factor：
In formula, enemy's interference performance GBSpan [0,1], is determined, γ by scoringGFor correction factor, 1 is typically taken.
Step 3-4：My command ability correction factor：
In formula, we is command ability ZRSpan [0,1], is determined, γ by scoringZFor correction factor, 1 is typically taken.
Step 3-5：I integrates average striking probability：
βR=cGcQcZcR
Step 3-6：Average striking probability β is integrated according to usRCalculating process, calculate enemy and integrate average striking probability
βB。
Step 4：Our combat success war is calculated to damage.
The form for calculating the improvement Lanchester equation that the war of our combat success is damaged is：
In formula, αR、αB, R, B represent that we is averaged operational efficiency, the average operational efficiency of enemy, our quantity and enemy respectively
Quantity, βBRepresent average striking probability of the enemy battle unit to our battle unit, βROur battle unit is represented to enemy
The equal striking probability of square battle unit.
The average air combat capability index of we and enemyWithUs is weighed with the two parameters flat with enemy
Equal operational efficiency.
Equation is solved using difference method, and time discrete uses single order forward difference method, while the time in formula
For virtual time, specific formula is as follows：
Above formula is substituted into improved Lanchester equation, obtain next virtual moment between ourselves and the enemy troops with virtual time
The calculation formula of change：
Rt+1=-αBBtβBRtΔt+Rt
Bt+1=-αRRtβRBtΔt+Bt
If Rt+1And Bt+10 is all higher than, then returns to step 2, if there is one to be less than 0, step 5 is carried out.
Step 5：The result calculated according to above-mentioned steps, draws number of aircraft with virtual time change curve, such as Fig. 4.
We fight damage=our initial aircraft quantity-difference it is virtual when our aircraft volume residual for inscribing；Our combat success
=enemy initial aircraft quantity-difference inscribes enemy's aircraft volume residual when virtual.
N is damaged according to default war0 war is damagedCorresponding n is found in figureCombat success.Pass through the default combat success n of contrast0 combat successWith nCombat success, advised greatly
The efficiency of the absolutely empty operation of mould.
The step of assessing absolutely empty fighting efficiency grade is as follows：
Step 5-1：Our expected combat success war is set to damage；
Step 5-2：According to default war damage value, corresponding combat success value is found in obtained change curve is calculated, is contrasted
The relative size of the combat success value and default combat success value, determines absolutely empty fighting efficiency grade；Control methods is as follows：
Efficiency is good
Efficiency is general
Efficiency is poor
It is very inefficient
In formula, c is efficiency Classification Index, typically can use 20%.
In order to more preferably illustrate, it is now assumed that we sends, 100 frame aircrafts and 100 framves of enemy are belligerent, and we requires to damage for war
Less than 40 framves, combat success is more than 50 framves.When can find us from Fig. 4 and losing 40 frame, enemy loses 55 framves, that is, predict I
Fang Zhanguo is 55 framves.
Illustrate under the mission requirements, the operation effect for the aircraft that we sends is general, can meet mission requirements.
The present invention can be realized and absolutely empty fought to extensive by calculating our war damage and combat success at different virtual moment
Measures of effectiveness.This method can be used for prewar to prepare the absolutely empty combat duty measures of effectiveness in stage, and foundation is provided for force deployment,
The real-time assessment in operational implementation stage is can also be used for, foundation is provided for the decision-making of commander.
Claims (6)
1. it is a kind of based on the extensive absolutely empty Combat Efficiency Evaluation method for improving Lanchester equation, it is characterised in that：Specific bag
Include following steps：
Step 1：It is determined that the operational aircraft quantity of initial we and enemy, and select suitable virtual time step-length；
Step 2：Calculate the average air combat capability index of operational aircraft between ourselves and the enemy；
Step 3：Calculate the average striking probability of aircraft between ourselves and the enemy；
Step 4：Calculate our combat success war to damage, if not up to stopping criterion for iteration, returns to step 2；If reaching iteration ends bar
Part, then continue step 5；
Step 5：The expection combat success provided according to combat duty and the contrast for calculating obtained combat success, evaluate absolutely empty fighting efficiency etc.
Level.
2. the extensive absolutely empty Combat Efficiency Evaluation method according to claim 1 based on improvement Lanchester equation, its
It is characterised by：The average air combat capability index calculation procedure of both sides' operational aircraft is as follows：
Step 2-1：Mobility is calculated by specific excess power and maximum overload value, formula is：
<mrow>
<mi>B</mi>
<mo>=</mo>
<msub>
<mi>n</mi>
<mrow>
<mi>y</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
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<mrow>
<mi>S</mi>
<mi>E</mi>
<mi>P</mi>
</mrow>
<mn>30</mn>
</mfrac>
</mrow>
In formula, nymaxFor maximum overload value, SEP is unit dump power；
Step 2-2：Fire performance, formula are calculated by the range of carry air-to-air missile, one-shoot damage probability, angle of attack sum amount
For：
Step 2-3：By radar detection ability and visual capacity calculation bullet detectivity, formula is：
Step 2-4：Aircraft survivability is calculated by aircraft size and radar area, formula is：
In formula, RCS is radar area；
Step 2-5：Calculate the air combat capability index of single rack aircraft：
C=[lnB+ln (A1+1)+ln(A2+1)]ε
In formula, C is air combat capability index；B is mobility；A1For fire performance；A2For detectivity；ε abilities for survival；
Step 2-6：Average air combat capability index is calculated by arithmetic mean method, and formula is：
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<mi>n</mi>
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</mrow>
3. the extensive absolutely empty Combat Efficiency Evaluation method according to claim 2 based on improvement Lanchester equation, its
It is characterised by：The average striking probability calculation procedure of aircraft is as follows between ourselves and the enemy：
Step 3-1：My average striking probability is calculated, formula is：
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In formula, B is enemy's quantity, γRCorrection factor；
Step 3-2：My intelligence capabilities correction factor：
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<mi>c</mi>
<mi>Q</mi>
</msub>
<mo>=</mo>
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<mi>&gamma;</mi>
<mi>Q</mi>
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In formula, we is intelligence capabilities QRSpan [0,1], γQFor correction factor；
Step 3-3：Enemy's interference performance correction factor：
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<mi>c</mi>
<mi>G</mi>
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<mo>=</mo>
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<mo>(</mo>
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<mi>&gamma;</mi>
<mi>G</mi>
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In formula, enemy's interference performance GBSpan [0,1], γGFor correction factor；
Step 3-4：My command ability correction factor：
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<msub>
<mi>c</mi>
<mi>Z</mi>
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<mo>=</mo>
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In formula, we is command ability ZRSpan [0,1], γZFor correction factor；
Step 3-5：Calculate me and integrate average striking probability：
βR=cGcQcZcR
Step 3-6：The calculating process of average striking probability is integrated according to us, enemy is calculated and integrates average striking probability.
4. the extensive absolutely empty Combat Efficiency Evaluation method according to claim 3 based on improvement Lanchester equation, its
It is characterised by：Calculating our the improvement Lanchester equation of combat success war damage is：
<mrow>
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<mrow>
<mi>d</mi>
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<mi>B</mi>
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<mi>R&beta;</mi>
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<mi>B</mi>
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In formula, αR、αB, R, B represent that we is averaged operational efficiency, the average operational efficiency of enemy, our quantity and enemy's number respectively
Amount, βBFor average striking probability of the enemy battle unit to our battle unit, βRIt is our battle unit to enemy battle unit
Equal striking probability；The average operational efficiency of our enemy is respectively with the average air combat capability index of our enemyWithWeigh；
Solved using difference method：
<mrow>
<mfrac>
<mrow>
<msub>
<mi>dR</mi>
<mi>t</mi>
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Above formula is substituted into improved Lanchester equation, obtaining next virtual moment, troops change with virtual time between ourselves and the enemy
Calculation formula：
Rt+1=-αBBtβBRtΔt+Rt
Bt+1=-αRRtβRBtΔt+Bt
If Rt+1And Bt+10 is all higher than, then returns to step 2；If there is one to be less than 0, step 5 is carried out.
5. the extensive absolutely empty Combat Efficiency Evaluation method according to claim 4 based on improvement Lanchester equation, its
It is characterised by：The step of assessing absolutely empty fighting efficiency grade is as follows：
Step 5-1：Our expected combat success war damage value is set；
Step 5-2：According to default war damage value, corresponding combat success value is found in obtained change curve is calculated；Contrast the war
Fruit value and the relative size of default combat success value, determine absolutely empty fighting efficiency grade.
6. the extensive absolutely empty Combat Efficiency Evaluation method according to claim 5 based on improvement Lanchester equation, its
It is characterised by：
Control methods in the step 5-2 is as follows：
In formula, c is efficiency Classification Index.
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| CN109241591A (en) * | 2018-08-21 | 2019-01-18 | 哈尔滨工业大学 | Anti-ship Missile Operational Effectiveness assessment and aid decision-making method |
| CN110083971A (en) * | 2019-05-08 | 2019-08-02 | 南京航空航天大学 | A kind of explosion type unmanned plane cluster fight force deployment method based on deduction of fighting |
| CN112258062A (en) * | 2020-10-28 | 2021-01-22 | 中国人民解放军战略支援部队航天工程大学 | System contribution degree determination method and device |
| CN113408137A (en) * | 2021-06-29 | 2021-09-17 | 中国舰船研究设计中心 | System combat effectiveness analysis method based on task completion degree and loss ratio |
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| 王威: ""基于改进型兰彻斯特方程的舰艇推演评估研究"", 《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》 * |
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| CN112258062A (en) * | 2020-10-28 | 2021-01-22 | 中国人民解放军战略支援部队航天工程大学 | System contribution degree determination method and device |
| CN113408137A (en) * | 2021-06-29 | 2021-09-17 | 中国舰船研究设计中心 | System combat effectiveness analysis method based on task completion degree and loss ratio |
| CN113408137B (en) * | 2021-06-29 | 2022-06-10 | 中国舰船研究设计中心 | System combat effectiveness analysis method based on task completion degree and loss ratio |
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