Liu Hang,Xu Ming,Chen Nanyu,Zhu Chengmin,Wu Zhe

(1.School of Aeronautical Science and Engineering,Beijing University of Aeronautics and Astronautics,Beijing,100191,P.R.China;2.Beijing In stitude of Aeronautical Materials,Beijing,100095,P.R.China;3.Naval Equipment Department,Beijing,100841,P.R.China;4.School of Astronautics,Beijing University of Aeronautics and Astronautics,Beijing,100191,P.R.China)

INTRODUCTION

Modern warfare is often undertaken with high-technology. Based on C4ISR system,modern navy can fulfill the task of area-airdefense(group defense)and self-defense(point defense)through a four-layer air-defense system on ship,including long-,medium-and shortrange missiles and end artilleries. The improvement of fleets’air-defense capabilities inevitably leads to the development of highper for mance aircrafts and air-to-ship missiles.Thus,the difficulty and complexity of anti-ship warfare will be further upgraded.

In the old deterministic models derived directly from deterministic theory, the effectiveness is defined as the multiplication of the probabilities of accomplishing tasks at the stages of aircraft acquiring, identifying, aiming,launching,guiding,and killing targets,etc.The probabilities are calculated merely under several basic conditions such as technical reliability,enemy anti-aircraft fire and electronic countermeasure. And it is assumed that the effectiveness of all air-to-surface missiles is same in the deterministic models. Therefore, the evaluation of operational effectiveness is simplified as the consumption of unitary missiles destroying typical targets[1].

However,because of the complexity of the process in real confrontations,the probabilities of task accomplishments at all stages are determined by many other random factors or technical parameters,e.g.relative equipments,tactics,operational environment and two-side confrontation effects.In addition,the cumulative damage should be considered in the case of intensive penetration and saturation attacks.Meanwhile,the correlation between the missiles is prominent when considering the cumulative damage.Moreover,in the deterministic models the assumption that the missiles have the same effectiveness is obviously unreasonable if different types of air-to-ship missiles are used[1].

However,task effectiveness evaluation on anti-ship attack of fighter aircrafts involves multidisciplinary knowledge,such as combat,aircraft,fighting ship,missile,radar,radio,etc. Few papers related to anti-ship attack effectiveness have been published.And most of them discussed defining evaluation criteria and in dices,building deterministic probability models, allocating targets and decision-making, establishing the framework of support environment,evaluating the operational effectiveness of anti-ship missiles[2-9],etc.These scattered evaluation can not actually meet the needs of advanced fighter aircraft conceptual design.

Therefore, random factors and technical parameters, significantly related to combat effectiveness,should be involved.These random factors and technical parameters include operational environment, tactics, search in gaiming,electronic war and so on,and they are regressed by using the simulation models of effectiveness integration.To reasonably assess the aircraft effectiveness of anti-ship combat,a new analysis method including both deterministic models and simulation models is developed.Deterministic models reflect the determined circumstances of operational mission and aircraft trajectory. Simulation models describe the complex process of opposing sides.

1 CONFRONTATION PROCESS AND SIMULATION

As the quantity of carrier-based fighters is limited and the ships in the fleet are relatively dispersed,fighter aircrafts often attack several ships in the way of small-formation raid from multi-directions(Fig.1).The process of attack can be divided into five stages[10]: (1)Fly over the target area to search,find and identify the target on the sea,and make a decision to attack,(2)Finish aiming preparation,(3)Aim and launch air-to-ship missiles, (4) Guide the missiles,(5)Withdraw.In this process,aircrafts can use anti-radiation missiles and various radio interference equipments to destroy enemy airdefense systems and even organize a special offensive team loading anti-radiation missiles to suppress enemy air-defense radars.

Fig.1 Confrontation process between fighters and airdefense weapons on ship

The confrontation process of air-defensemissile systems on ship[10]includes:(1)Searching and predicting the flight path of incoming aircrafts,(2)Launching and guiding anti-aircraft missiles,(3)Camouflaging themselves,shutting down radar,hopping frequently and taking other protective measures after aircrafts launching an tiradiation missiles, (4) Inflicting damage to aircraft team. Generally, the confrontation process of air-defense-missile systems on ship is not transparent to the aircraft team.Coordinate boundaries of each stage cannot be pre-definecl in the confrontation process according to the stage division of fighters attack.So the effectiveness of killing an aircraft team must be simulated in real time by mathematical models for working effectiveness of ship radar and optical systems,electronic warfare equipments,command and control systems,launchers and anti-aircraft missiles[1,11].

From the above analysis on characteristics of operational process,it can be concluded that the simulations of operations between the opposing sides should be performed on a unified time step.Specifically,the tasks of the offensive and the defensive are simulated in turn at each stage.All the events which can lead to the changes in the survival and destruction situations of both sides are simulated, including aircraft searching,finding, identifying, intercepting, tracking,aiming, firing, guiding toward and killing targets, air-defense-system finding, locating,tracking, intercepting, targeting, shooting,guiding toward and killing targets,etc.,as well as radar warning and protecting themselves,an tiradiati on missiles’suppression,noise,imitation,and chaff jamming,and sea waves,weather conditions and other events. The simulation models[10-12]are used for random events that affect the mission effectiveness,and the deterministic models[10]for the determined cases such as technical reliability and trajectory.Through the two kinds of models,the probabilities of fulfilling tasks influenced by all events are multiplied at each stage of battle process.

2 TASK EFFECTIVENESS INDICES

The operational mission of the fighter team is to break through three-layer defense systems,namely long-, mid-and short-range missile systems of the fleet,destroy outer area-airdefense ships,and strike the most valuable ship at the center of the fleet.The main task of airdefense systems on ship is to kill targets in the air, protect the ships against destruction.Therefore,for air-to-ship missions, the most reasonable index of effectiveness is the number of required fighters to eliminate ship targets into a specified amount,as well as the number of aircraft losses. The index can be discomposed into two basic in dices. One is the survival probability of fighter team,and the other is the specified damage effect on the fleet.

3 ALGORITHM FOR TASK EFFECTIVENESSINDICES

Ref.[12]presented the simulation models of electronic warfare and work effectiveness of airborne systems and Ref.[11]elaborated the effectiveness simulation models of marine radar systems affecting the probabilities of mission fulfillment at the stages of operational process.The probability model of airborne radar system finding targets[12]is briefly introduced due to limited space.

In a rectangular area of Mx×Mz,there are N moving targets at the speed of V t in a terrain background.If the detection range is longer than R,which is the near boundary of attack zone,the probability of finding targets can be calculated as

where[]denotes rounding the number down to the nearest integer.

where P1 denotes the probability of finding a typical stationary target outside the rangeof D1 in background S O1, and the radar cross section(RCS)of the target is equal to e1,P2 the probability of finding a typical stationary target outside the range of D2 in background SO2,and the RCSof the target is equal to e2,ΔR the range resolution of radar,λradar wavelength,A an the horizontal dimension of antenna,Tkthe time of forming the image in synthetic aperture radar(SAR)mode,e the RCS of target unit,S O the RCSof background per unit area.P1,e1,D1,SO1,P2,e2,D2,SO2and Tkare all related to the type of radar.

The study on the index algorithm for task effectiveness of fighter formation attacking the fleet collectively protected by multi-layer air defense missile systems is exerted. In the operational mode of air-to-ship,it is generally thought that flight performance and handling characteristics of modern fighter can meet the requirements of implementing the tactics.Consequently,fligh t performance and handling characteristics are not concerned in task effectiveness in dices.

3.1 Survival probability of f ighter team

The survival probability of a single fighter is P s,which can becalculated as the probability of a fighter destroying anti-aircraft weapons

where P d,i is the probability of destroying the aircrafts at the i th shot,m the total number of intercepts of air-defense systems.However,there are greater differences among the survival probabilities of individual aircrafts in a team,so Eq.(9)is not suitable for calculating the survival probability of an aircraft team.

Define the survival state vector of a team of N aircrafts as

where P0, P1,…, PN are the survival probabilities of the No.0,1,…,N aircrafts,respectively.Therefore,the survival probability of an aircraft team can be expressed as

The initial state vector of the survival of a team with N aircrafts is given as S(0)=[0,0,…,0,1]T.Hence,after k shots,the survival state vector of the formation is

Usually,the probabilities of killing aircrafts vary with different types of weapons.The killing probability is designated as P d(k+1)at the(k+ 1)th shot of an air-defense weapon.After the shot of every anti-aircraft weapon,only two kinds of results occur:shooting down a plane,or not.Hence,after the launch of k anti-aircraft weapons,the probability of i survival aircrafts in the team is Pi(k). After the launch of the(k+1)th anti-aircraft missiles,the number of aircrafts is reduced to i-1 by the probability of Pd(k+1)and i by the probability of 1-Pd(k+1).Thus,after the launch of k+ 1 anti-aircraft missiles,the survival state vector of the team is

3.2 Specified eff ect of damageon fleet targets

Practically,designated damage effect on a single ship is often described as that the ship can be destroyed by m hits of anti-ship missiles with the probability of P d.

The probability of a single missile hitting a ship can becalculated as

where P E is the probability of a missile hitting on the shooting range,P f the probability of missing caused by various factors(e.g.the interruption of aircraft guidance).If k anti-ship missiles are launched,the probability of a ship hit by exactly j missiles is

For the formation composed by N aircrafts and each aircraft loading L air-to-ship missiles,the probability of more than m missiles hitting the ship is

where Pi is the probability of the survival of i aircrafts,P h,j(iL)the probability of j hits after launching iL anti-ship missiles.If the minimum of iL shots with m successful hits can becaculated by Eq.(15)with the trial and error method,a solution for the problem of specified damage effect can be worked out.

The specified effect of damage on fleet targets refers to designated individual effect of damage on each warship by each small formation of aircrafts attacking.

4 SIMULATION FLOWCHART OF OPERATIONAL PROCESS

In simulation process,the measures taken by fighters and the ship fleet are determined by the relationships between fighters, anti-ship missiles,ships,air-defense systems on each time step.Survival probability of a fighter team and specified effect of damage on the targets at the moment are calculated with the algorithm discussed above.Because of limited space and lack of decrypting parameters, subsystem models[10-11]of movements, radars, optical equipments, missiles, electronic warfares of aircrafts and ships are briefly introduced.Detailed simulation flowchart of operational process is shown in Fig.2.

Fig.2 Simulation flowchart of operational process

5 SIMULATION EXAMPLE

As shown in Fig.3,the defensive S1-S4 are area-defense ships,and S5 is the most valuable point-defense ship.The first off sensive formation launches anti-radiation missiles to suppress enemy marine radar systems. After that,the second formation launches air-to-ship missiles to ships S1-S4, respectively, for clearing airdefense barrier.The third formation attacks S5.It should be noted that although the defense of S1-S4 has been partly broken, the third formation still has a low probability to be attacked by S1-S4area-air-defense systems when attacking S5.

Fig.3 Formation of fighters attacking group-defense fleet

As shown in Fig.2,initial input is required including the characteristic paremeters of weather,time,sea conditions,targets of ship,air-defense missiles, the flight technology of fighters,airborne radars and ship radars,optical systems, radar warning devices, anti-ship missiles, anti-radiation missiles, targeting guidance systems[10-11]. According to the operational program of the offensive and the defensive, task effectiveness indices of the example is simulated with the presented algorithm. The simulation results show the survival probability of the fighter team is 0.83,and S1-S5 ships can be destroyed through 3,3,2, 2, 8 hits by anti-ship missiles with the probability of 0.8 of attaining designated damage effect.Therefore,at least four anti-radar fighters and 13 attacking fighters (four air-to-ship missiles loaded per aircraft),namely a total of 17 fighters,are needed to fulfill the task.And three aircrafts are lost in this mission.

6 CONCLUSION

Based on the features of anti-ship process,a new simulation method is developed with the consideration of somefacors and in dices of combat skills,including operational environment,aircraft tactics, searching-aiming, electronic countermeasures, and aircraft-missile relationships.Self-and collective defenses using the long-, mid-and short-range ship-to-air missiles are also introduced in the simulation method. The effectiveness in dices algorithm derived from Markovian stochastic theory is given by combining the advantages of deterministic models with the simulation models. The algorithm can improve the computing efficiency

and better reflect the complexity of real confrontation.Therefore, the method for effectiveness evalution can be applied to aircraft design and the tactical research on choosing attacking program.

[1] Guseinov A B.The effectiveness of cruise missile[M].Moscow:Moscow Aviation Institute Press,2003.

[2] Xu Haojun,Wei Xianzhi.Operational effectiveness of aero-complex[M].Beijing: National Defense Industry Press,2006.

[3] Qu Yepin,Liao Ying.Study on anti-ship capability for naval aircraft[J].Aerospace Shanghai,2004(5):30-33,60.(in Chinese)

[4] Sun Weiqi,Hou Zhiqiang,Wang Wenshuang,et al.Airto-ground attack effectiveness model based on markov course [J]. Journal of Naval Aeronautical and Astronautical University,2009,24(1):20-22.

[5] Ma Qidong, Fang Ligong.Operational effectiveness model of medium-long-rang ship-to-air missile based on task[J].Fire Control& Command Control,2010,35(7):77-79,83.

[6] Ai Jianliang,Qian Guohong.Combat efficiency analysis model of attacker during the final stage[J].Fire Control&Command Control,2000,25(2):19-22.

[7] Liu Yong,Galati D G,Simman M A.A game theoretic of approach to team dynamics and tactics in mixed initiative control of automa-teams[C]∥43rd IEEE Conference on Decision and Control.Atlantis,Bahamas:IEEE,2004,4:3811-3816.

[8] Tai Ching-Chu,Szu H.An artificial neural network for naval theater ballistic missile defense program[C]∥International Conference on Neural Networks.Huston,USA:IEEE,1997,1:53-55.

[9] Liu Chisheng,Song Guibao,Li Hongliang.Study on the structure model of the probability of damage to aircraf t carrier by anti-ship missile[J]. Journal of Naval Aeronautical Engineering Institute,2004,19(6):661-666.

[10]China Aviation Industry Development Research Center.The manual of the effectiveness evaluation theory of aircraft completing combat mission for the case of the target resisting[M].Beijing:ADR,2000.

[11]ADR. The software of the effectiveness evaluation theory of aircraft completing combat mission for thecase of the target resisting[M].Beijing:ADR,2000.

[12]Wei Jinzhong. Research on the cost efficiency of uninhabited combat aerial system based on simulation[D].Beijing: Beijing University of Aeronautics and Astronautics,2008.