Agent-based effectiveness evaluation method and impact analysis of airborne laser weapon system in cooperation combat

Likun SHI, Yng PEI, Qiji YUN, Yuxue GE,*

aSchool of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

bBeijing Institute of Astronautical Systems Engineering, Beijing 100076, China

KEYWORDSAgent modelling;Effectiveness evaluation;Hierarchical modularization;Laser weapon;System of system

AbstractThe laser weapons will play a special role in the future high-tech war.To study the impact of airborne laser weapon on the System-of-System (SoS) effectiveness in cooperative combat,this paper proposes an indicator construction method based on the combination of the weapon capability indicator system and the combat simulation.The indicator system of capability is divided into 4 layers by the bottom-to-up generation mechanism of indicators.It can describe the logical relationship between the indicator layers from a qualitative perspective.Together with the 4 layers capability indicator system,a hierarchical framework of airborne laser weapon is established by the agent-based modeling and simulation.Impact analyses show that the SoS effectiveness improves with the increase of the laser weapon output power,the laser launcher diameter,and the photoelectric sensor pixel.But the SoS effectiveness promotion brought by the photoelectric sensor pixel is limited.The results can be used for the development of tactical airborne laser weapon.

1.Introduction

As a new conceptual weapon, the airborne laser weapon is promising for future cooperative combat because of its high power density and precision strike.It will be as powerful as 100 kW around 2025 and can be implemented into active defense against the medium-range air-to-air missile or the target at sea.1However, the laser beam is very sensitive to the atmosphere and the installment of laser weapon changes the aircraft performance.2Therefore, the study of the impact of airborne laser weapon on cooperative combat is essential for the System-of-System (SoS) effectiveness evaluation of future war.

The laser beam burns the strike point on the target if its accumulated energy is high enough.In a single confrontation,the combat effectiveness of the airborne laser weapon can be evaluated by the energy on the target and the dwell time to damage the target.3It depends strongly on the aiming accuracy,the laser intensity,and the target material.4To overcome these disadvantages, the airborne laser weapon can be applied to cooperative combat.

The effectiveness evaluation of the airborne laser weapon in cooperative combat needs an indicator system construction, which can be established by the capability structure of the weapon system.Huang et al.introduced a multivariate statistical indicator method to analyze the combat capability of a system.5Based on the network, Li et al.proposed an operational capability indicator of a weapon SoS architecture6.

A much clearer architecture of the indicator system can be constructed by function decomposition.Zhong et al.divided the MAV/UAV cooperative indicator system into three hierarchical levels: the mission level, the task-cluster level, and the task level.7A series of simulations have been used to verify the effectiveness results of the proposed algorithm.Yin et al.proposed a task-oriented cooperative combat evaluation method based on a comprehensive indicator model with Analytic Hierarchy Process (AHP), using the weight model to study among different levels.In these studies, the indicators on the upper levels are aggregated from the lower levels.8Hence, the practical meaning of upper levels is missing.

The network indicator system can reflect the actual performance of the system by simplifying the combat behavior and the cooperation of the entities into nodes and edges.Fan et al.proposed an indicator system to analyze the characteristic parameters of the abstract network model and conducted qualitative and quantitative research on the synergistic effect.9Liu and Li used the improved Availability, Dependability, and Capacity (ADC) indicator method to evaluate the operational effectiveness.10Wang et al.proposed a weight method that allows users to set the relationship and the weight value of indicators according to subjective preferences.11However, the simplification of node and edge makes the performance description of the weapon equipment insufficient.Since sea warfare is a typical Complex Adaptive System (CAS), in which a wide variety of combat systems are closely connected and interacted, an inadequate model of operation may decrease the accuracy of the effectiveness evaluation.

The Agent-Based Modeling and Simulation (ABMS) is suitable for describing the bottom-to-up emergence of individual microscopic behavior,which is a common characteristic of a CAS.And it has been widely used in warfare evaluation.Ilachinski developed a multi-agent-based simulation tool to predict terrorist behavior in self-organized CASs.12Massei and Tremori built an interoperable ABMS for the asymmetric urban warfare system.13Peng et al.combined the ABMS method and the system dynamics to establish a damage degree model and combat personnel model with the medical support and the war rescue system.14

To study the SoS effectiveness evaluation of cooperative combat at sea with the airborne laser weapon, this paper will propose an indicator construction method based on the weapon capability and the ABMS combat simulation.In Section 2, the cooperative combat mode with the airborne laser weapon is briefly presented.The combat effectiveness evaluation indicator system based on the weapon capability and the hierarchical framework of ABMS is illustrated in Sections 3 and 4.Simulation results are shown and analyzed in Section 5.

2.Cooperative combat analysis of laser weapon

2.1.Cooperative combat mode with laser weapon

The mission goal of a laser weapon in this paper is to improve the active defense capabilities of the combat aircraft against the aircraft carrier battle group.

The cooperation of airborne laser weapon mainly includes three stages: target detection, target allocation, and cooperative strike.The combat aircraft with a laser weapon first scans the airspace through airborne radar, infrared sensors, or photoelectric sensors.When the aircraft detects an enemy target at the best launch position, it will immediately launch a laser beam while conducting a damage assessment.Otherwise,it will send the target track and situation information to the command center.In this situation, the command center can build the superiority function of every friendly aircraft against the target.Then, it will allocate the target to the aircraft with the highest superiority function.Thereafter, the aircraft that has been commanded to strike the target will fly towards the target, strike the target by laser beam and conduct a damage assessment.

2.2.Typical cooperative sea warfare scenario

The typical cooperative sea warfare scenario is shown in Fig.1.The offensive and defensive combatants are in red and blue respectively.The red side has the aircraft, the carrying antiship missiles, and the airborne laser weapon.The blue side is composed of the aircraft carrier, the frigate, the aircraft, and missiles.The mission is performed through a data link.

3.Construction method of indicator system

This section presents a construction method of the indicator system by combining the capability-based and the simulation-based indicator system construction methods so that the new indicator system is adapted to missions with laser weapon on the offensive side.

Based on a traditional hierarchical description method,15the indicator system is divided into 4 layers.As shown in Fig.2, they are the SoS effectiveness layer, the SoS capability layer, the system capability layer, and the platform performance layer.

Fig.1 Cooperative combat scenario.

Fig.2 Capability description of laser weapon cooperation on offensive side.

3.1.Platform performance layer

The platform performance layer describes the equipment performance by using 7 parameters that attribute to the laser weapon, the aircraft, and the formation.The indicators of the laser weapon are the output power P, the diameter of the laser launcher D, and the pixels of the photoelectric sensor Pix.The aircraft indicators are the Mach number Ma,altitude H, and the radar cross section RCS.The indicator of the aircraft formation distance RBcan reflect the coordination capability of the combat aircraft.RBis the distance between friendly aircraft,and it determines the distance of each aircraft to the target and the angle between the airborne laser and the target, thereby influencing target allocation and the delivered power density of the airborne laser.

3.2.System capability layer

The system capability layer describes the survivability and the defense capability of the combat aircraft system.There are 2 indicators in this layer: the number of the killed missiles m and the average dwell time Tdur.The aircraft performance affects the scope and the stay time of detection range,thereby affecting the number of killed missiles.The performance of the laser weapon and the formation affect the average dwell time.

The total number of killed missiles is defined as

where mA-Ais the killed number of air-to-air missiles fired by aircraft on the blue side, and mS-Ais the killed number of ship-to-air missiles fired by frigates on the blue side.

It takes time for each aircraft to destroy a target with the laser weapon for the first time, which is defined as the average dwell time.It is expressed as

where nredis the number of red aircraft, tifireis the time when the red combat aircraft first fires a laser weapon against an incoming missile, and tidestroyis the time when the red combat aircraft first destroys an incoming missile.

3.3.SoS capability layer

The SoS capability layer includes two indicators,which are the aircraft survival rate and the enemy casualty rate.

The survival rate of the aircraft refers to the ratio of mission completed and survived aircraft to the total number of aircraft.It is expressed as

where nred_surviveis the number of surviving combat aircraft of the red side, and Sris the survival rate of the red aircraft.

The enemy casualty rate is defined as the ratio of the blue casualty targets to all of the blue targets,including the aircraft and the aircraft carrier.The aircraft has the survival state and the destroyed state.The enemy casualty rate is defined as

where Kais the importance of the blue aircraft, na_killis the number of destroyed blue aircraft,nais the number of the blue aircraft, and Kcis the importance of the blue aircraft carrier.The damage level of the blue aircraft carrier ηcis the ratio of the number of anti-ship missiles that hit the aircraft carrier to the number of anti-ship missiles required to damage the aircraft carrier, and Ckis the casualty rate of the blue side.

3.4.SoS effectiveness layer

The SoS effectiveness is a direct manifestation of the combat effectiveness of the weapon and the equipment system being a function of the loss ratio on both sides of the combat.The SoS effectiveness E can be calculated according to battle damage rate,16which is expressed as

where Kris the importance of the red side combat aircraft.

Combined with the simulation, the platform performance layer indicators are inputs of cooperative combat.The indicators on the SoS layers can be obtained in the simulation.Therefore,this indicator system can clarify not only the calculation relationship between the indicators, but also the generation mechanism of the upper-layer indicators, and describe the logical relationship between the indicator layers from a qualitative perspective.

4.Hierarchical ABMS framework

The hierarchical ABMS of the combat simulation system is presented in Fig.3.The combat unit, the command center,and the system components constitute the simulation framework.The combat unit is an entity to simulate with the aircraft agent, the missile agent, and the ship agent.It has the subagent on both red and blue sides.The basic system component sub-module is used to support the combat unit, and the command center module generates the task to command the combat unit to change state.The following will introduce the basic system component and related states in the simulation framework.

Fig.3 A hierarchical ABMS framework for cooperative combat effectiveness with airborne laser weapon in sea warfare.

4.1.Basic components modeling

4.1.1.Dynamics model of aircraft

In the flight-path coordinate system, the origin locates at the centroid of the aircraft, the x axis is along the direction of the aircraft speed, the z axis is perpendicular to the x axis and points downward, and the y axis is perpendicular to the xz plane and points to the right.The dynamics of the aircraft is described by the 3-Degree-of-Freedom(DOF)centroid kinematic equation in the flight-path coordinate system, and is defined as17

where v is the speed of the aircraft and ˙v is the acceleration of v,χ is the track azimuth angle and ˙χ is the angular acceleration of χ,γ is the climb angle and ˙γ is the angular acceleration of γ.The movement of level flight,accelerating,and turning maneuvers can be realized by controlling the overload of the aircraft agent (nx, ny, nz).

4.1.2.Detection model of radar

The unit average constant false alarm algorithm can be used to calculate the detection probability of radar.18The radar detection model is

where NCAis the number of samples in the reference window,aCAis the false alarm processing constant, SNR is the signalto-noise ratio of the radar system,Pdis the detection probability, and Pfais the false alarm.

4.1.3.Guidance model of missile

The missile adopts the proportional guidance law, which is to make the rotation angular velocity of the missile be proportional to the rotation angular velocity of the target sight vector.19The missile overload control command equation under totally proportional guidance is defined as

with Rrbeing the relative distance between the missile and the target, Vrthe relative speed of the missile to the target, NGthe proportional guidance coefficient, Vmthe velocity vector of the missile, ω the rotational angular velocity of the target sight vector, and ac the acceleration command.

4.1.4.Detection model of photoelectric sensors

The detection probability of the photoelectric sensor to the target can be calculated by the Johnson criterion.20According to the projection size of the target image on the sensor, the photoelectric sensor perception of the target can be divided into the level of detection, identification, and recognition.Then it is defined as

where θ is the field of view, Pix is the pixel pitch, GSD is the ground sampling distance of the sensor, the subscripts of h and v stand for the horizontal and vertical direction respectively,wtgand htgare the width and height of the target respectively, r is the distance from the lens to the target, δlookis the angle of lens installation, dcis the feature size of the target,Ncycis the number of cycles across the target, and Ncyc,50is the 50 % success probability of performing a detection task in three stages: detection, recognition, and identification.Its value is 0.75, 3.0, and 6.0 for three stages respectively.

4.1.5.Laser beam model

The model of the laser includes the transmission model of the laser beam and the related damage model.

The atmosphere can twist the laser beam during the transmission and weaken the spot power on the target.This paper describes the influence of the atmosphere on laser transmission as the increase of the spot area and the attenuation of the laser energy.The equivalent spot power density is expressed as21

where P is the output power, τais the atmospheric transmission coefficient, and NDis the thermal blooming distortion parameter.ad,aj,and atare the beam radius expansion caused by the diffraction, the beam jitter, and the turbulence respectively.These parameters can be calculated according to the methods in Refs.22–25.

The laser beam can destroy the target surface by heat.The shell of the missile is usually made of metal materials such as titanium and steel.Assuming that the inner wall of the missile shell is in ideal contact with the warhead charge, the temperature of the warhead charge is equal to the temperature of the inner wall of the missile shell.When the temperature of the warhead charge is high enough, an explosion will occur.The temperature of the shell is calculated by25.

where T0is the initial temperature of the shell surface,θdis the angle between the outer normal direction of the irradiation spot and the laser vector, S is the unit area, kris the surface reflectivity of the shell material, tsand teare the time when the laser reaches the target and the time away from the target respectively,and cm,qm,and hmare the heat capacity,density,and thickness of the surface shell respectively.

4.2.State modeling

After completing the construction of the basic component model, it is necessary to define the combat behavior of the two combatants so that their interaction can drive the operation of the simulation.The combat behavior is illustrated by the state machine modeling.The state machine changes the state and parameters of the agent according to the interaction conditions with other agents or the external environment,thereby changing the behavior.

4.2.1.Red aircraft state

The state machine of the red combat aircraft is shown in Fig.4.It starts from the standby state and turns to the penetration state after receiving the departure command.The agent uses photoelectric sensors to search threat warnings in the airspace ahead.After locking the target, a cooperative target assignment with the friendly aircraft will be carried out to decide which aircraft should launch the laser weapon and strike the target.If the blue aircraft carrier is found, the agent will launch an anti-ship missile and return when the missile enters the terminal guidance phase.Otherwise, if the agent is killed, it will be removed from the simulation.

4.2.2.Blue aircraft state

The state machine of the blue combat aircraft is shown in Fig.5.The agent flies along the patrol route with the radar on.It starts from the standby state and turns to the encounter state when targets have been found.When the target is found,the agent will conduct a threat assessment to assign the target to the most suitable aircraft.When the target enters the firing range,the agent will launch the missile and follow the target to guide the missile.When the missile enters the terminal guidance state or the aircraft loses the target, the agent will return to the patrol state.Otherwise, if the agent is killed, it will be removed from the simulation.

Fig.4 State machine of red aircraft agent.

Fig.5 State machine of blue aircraft agent.

4.2.3.Command center state

The aircraft carrier performs as the command center on each side.It can coordinate the state information of the combat unit and the detected target,conduct a threat assessment,and allocate targets.The state of the command center is shown in Fig.6.There are six modules in the command center.The functions are described below:

(1) Local situation processing.The combat unit calls the radar module to generate the trajectory of the target.

(2) Uploading information.The aircraft generates its tactical status and the target information and uploads them.

(3)Uplink preprocessing.This modular is to extract the target trajectory from the uplink message while completing the trajectory association.The information of one target collected by different aircraft agents will be correlated to generate a set of local trajectories.At the same time,it extracts tactical status from the uplink message to generate a list of free agents.

(4)Global situation processing.This module fuses the measurement information of the same target from different aircraft agents to generate a global trajectory and sorts the trajectories to obtain a threat list.

Fig.6 State machine of command center agent.

For the combat aircraft on both the red and blue sides,the threat regarding the distance26can be represented as

where k1and k2are constants representing the threat level.They are taken as k1= 10, k2= 1.On the red side, Lris the relative distance between the red combat aircraft and the threat.On the blue side, Lris the relative distance between the blue aircraft carrier and the red aircraft.Lr0is the reference safety distance.

(5) Task processing.This step allocates tasks according to the order of the threat list.It calculates the superiority of task resources for each threat and selects the aircraft agent with the highest superiority to execute the task.Finally, a one-to-one task list of resources and threats is generated.

For the red combat aircraft, the superiority of its airborne laser weapon against a target is estimated by the dwell time as

where tkillis the dwell time to kill the target.

For the blue combat aircraft, its superiority is defined as

where Lbris the relative distance between the blue combat aircraft and the red combat aircraft.

(6)Downloading information.This module is to download the task list to all aircraft agents.

5.Results and discussion of cooperative combat

Based on the proposed indicator system and the effectiveness simulation framework,this simulation utilizes Java to perform the code.The ABMS code is briefly shown in Fig.7,compiling the performance and the basic behavior of the agent to a field and a method in the class.According to the hierarchical modeling method,the main class includes all agents.The state models are embedded in the state instruction.

5.1.Simulation setting

The simulated cooperative sea combat scenario is shown in Fig.8.The red side is composed of 1 aircraft carrier and 9 aircraft with airborne laser weapon, moving towards the blue side.The blue side is composed of 1 aircraft carrier,5 frigates,and 6F/A-18E fighters with missiles.The frigates are 80 km in front of the aircraft carrier, and 6F/A-18E fighters are patrolling 240 km in front of the aircraft carrier battle group.The importance of the blue aircraft and the aircraft carrier are Ka= 1 and Kc= 90, respectively.The importance of the red combat aircraft is Kr= 2.To damage the aircraft carrier,30 anti-ship missiles are required.

The simulation parameters are shown in Table 1.Each simulation point, which includes 500 experiments, is produced by holding other indicators in their intermediate values.

5.2.Impact analysis of laser weapon on SoS effectiveness

The corresponding survival rate and the enemy casualty rate are shown in Fig.9 and Fig.10 respectively.The results of the combat effectiveness regarding the airborne laser weapon performance are shown in Fig.11.

When the output power P increases from 150 kW to 300 kW, the increment of Sr, Ck, and E are 61.36%, 52.94%,and 200% respectively.When the diameter of the laser launcher D increases from 40 cm to 70 cm, the increment of Sr, Ck, and E are 165.38%, 120.59%, and 400% respectively.Therefore, P and D can cause a large increment in combat effectiveness.In contrast, the magnitude of the combat effectiveness caused by D is greater than that of P.

Fig.7 ABMS simulation code structure for cooperative combat effectiveness with airborne laser weapon in sea warfare.

Fig.8 Cooperative combat scenario with offensive and defensive sides in red and blue.

From Figs.9-11, we learn that the survival rate Srof the aircraft improves with the increase of the laser weapon output power P, the laser launcher diameter D, and the photoelectric sensor pixel Pix,so as the enemy casualty rate Ckand the SoS effectiveness E.However, with the increase of the three indicators,the slope of the curve gradually decreases.When P increases from 250 kW to 300 kW or the diameter D from 60 cm to 70 cm, the changes of Srand Ckare the smallest.The E promotion will diminish from an increase in P and D,and it basically reaches the inflection point of 0.83 when Pix increases to 186.62 × 105.The above result shows that the E promotions caused by P, D and Pix are limited.This suggests a limited promotion of E regarding the laser weapon performance.

Results of the average dwell time Tdurand the number of killed missiles m are shown in Fig.12 and Fig.13,respectively.By increasing the laser weapon output power P, the laser launcher diameter D can shorten the dwell time of the laser weapon, thereby increasing the killed number of missiles m.

Table 1 Combat simulation experiment design.

In the simulation,the max Tdurregarding P and D is about 8 s with Pix=80.94×105.By increasing Pix,the distance for launching the laser can be increased, resulting in a decrease in the delivered power density.

However, there is an increase in the distance when the target is killed, leaving the aircraft more time to deal with other missiles.This is why m increases with Pix.The increase in Pix will greatly affect Tdur, while it has the same impact on m as P and D.

Fig.9 Impact of airborne laser performance on aircraft survival rate.

Fig.10 Impact of airborne laser performance on enemy casualty rate.

Fig.11 Impact of airborne laser performance on SoS effectiveness.

Fig.12 Impact of airborne laser performance on average dwell time.

Fig.13 Impact of airborne laser performance on the number of killed missiles.

Fig.14 Impact of carrier aircraft performance on aircraft survival rate.

5.3.Impact analysis of aircraft performance on SoS effectiveness

Under the changes of aircraft performance,the corresponding survival rate and the enemy casualty are shown in Fig.14 and Fig.15 respectively.The increase in the aircraft Ma and flying altitude H, and the decrease in RCS all help to improve the survival rate Sr, the casualty rate Ckon the blue side, and the effectiveness E.A faster speed results in a shorter penetration time and fewer missiles to launch.The thin air at high H will help the transmission of the laser weapon and increase the range of the laser beam and Ck.

The results of the combat effectiveness regarding the combat aircraft performance are shown in Fig.16.When Ma increases from 1.6 to 2.0,E increases from 0.8 to 1.6.The promotion of E with the changes of H is smaller than Ma,and the max value is 0.79 with H=14 km.Additionally,the reduction of RCS can significantly improve E.When RCS = -20 dB and 0 dB, E = 2.1 and 0.55.

Fig.15 Impact of carrier aircraft performance on enemy casualty rate.

Fig.16 Impact of carrier aircraft performance on SoS effectiveness.

When Ma increases from 0.4 to 2.0, correspondingly, the increment of Sr, Ckand E are 240.9%, 159.67%, and 700%respectively.When H increases from 6 km to 14 km,the increment of Sr, Ckand E are 65.71%, 58.02%, and 152.46%respectively.When RCS decreases from 20 dB to -20 dB,the increment of Sr, Ckand E are 110.52%, 84.78%, and 467.57% respectively.Then, Ma, H, and RCS can greatly change the combat effectiveness, and it can be found that the magnitude of the combat effectiveness caused by Ma is greater than that of H or RCS.Though the high Ma and H can promote E, they cannot be increased all the time in the practice,and the aircraft with stealth design has a high capacity for the SoS effectiveness of E.

The number of killed missiles regarding the performance of the aircraft is shown in Fig.17.A high Ma allows the aircraft to quickly pass the dangerous area while reducing the number of interceptions and m.The low air density at high H leaves more time for the laser weapon to work.When RCS = 20 dB, there is a fewer number of killed missiles than with RCS of 10 dB.This is because the survivability of the aircraft is greatly reduced and many red aircraft are destroyed.

5.4.Impact analysis of formation on SoS effectiveness

Fig.17 Impact of carrier aircraft performance on the number of killed missiles.

Fig.18 Impact of aircraft formation on SoS effectiveness and capability.

The results of the SoS effectiveness and capability regarding the aircraft formation are shown in Fig.18.When the formation distance RB= 0.1 km, the laser weapon can only hit the radome of the missile.It takes a long dwell time to cause damage,leading to lower Srand Ck.When RB=5 km,the aircraft can fire laser beams to strike weak parts of the missile and quickly kill the blue targets.However, when RB= 20 km,the effectiveness E is small because of the low laser power density delivered to the target.Therefore, the ideal RBis 5 km,resulting in E = 1.17, Sr= 0.68, and Ck= 0.75.The impact of the formation distance RBof aircraft on the system capability is shown in Fig.19.When RB=5 km,a minimum average dwell time of 4 s is required to kill the most missiles.

It illustrates that the formation mode of combat aircraft equipped with laser weapon is greatly different from traditional combat aircraft.The scattered formation is more conducive to the cooperation of the laser weapon.The design of the formation can be further investigated by taking the attack angle and the target distance into consideration.

6.Conclusions

To evaluate the cooperative SoS effectiveness with airborne laser weapon,this paper proposes a hierarchical indicator construction method by combining the weapon capability and the ABMS simulation.The main conclusions are made as follows:

(1) From the aspect of laser weapon, increasing the output power P,the launcher diameter D,and the sensor pixel Pix can decrease the dwell time of the laser weapon,increase the killed number of missiles m,and significantly improve the SoS effectiveness E.

Fig.19 Impact of formation distance on average dwell time and the number of killed missiles.

(2) From the aspect of aircraft performance, increasing the aircraft Ma and the altitude H, and decreasing RCS can improve the SoS effectiveness E.In particular,the effectiveness promotion brought by the reduction of RCS is greater than that from speed v and altitude H.

(3) From the aspect of aircraft formation, an appropriate formation distance, being 5 km in this study, is essential for cooperation combat and the increase of the SoS effectiveness E.

The indicator system construction method proposed in this paper is capable of evaluating the SoS effectiveness with laser weapon.The cooperative task planning algorithm of airborne laser weapons in complex combat scenarios and the impact of different combat scenarios can be studied in the future.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.