# Evaluation of MAV/UAV Collaborative Combat Capability Based on Network Structure

Authors: Jieru Fan; Dongguang Li; Rupeng Li
Journal: International Journal of Aerospace Engineering
 (2018)

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## Abstract

The collaborative combat of manned/unmanned aerial vehicles (MAVs/UAVs) is a popular topic in combat application research. It maximizes the autonomous combat capability of UAVs and the control capability of MAVs. Furthermore, it improves the comprehensive combat effectiveness. The quantitative description of intercommunication in different aircrafts along with the evaluation of the collaborative combat capability is an emphasis in military research. This paper analyzes the collaborative combat process. Node and edge models are established in the MAV/UAV collaborative network. The intercommunication and combat behaviors among combat entities are analyzed. Based on the information entropy, the effect of capability uncertainties on the collaborative combat is described quantitatively. An evaluation method of the MAV/UAV collaborative combat capability is proposed. Finally, an example is given to demonstrate the proposed model and evaluation method that prove its feasibility and effectiveness.


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## Body

## 1. Introduction

With the development of aviation technology and the increasing military demands, the research and development (R&D) of unmanned aerial vehicles (UAVs) has gradually developed trends of generalization and serialization [1]. The role of UAVs on the battlefield has gradually transitioned from reconnaissance to aerial battle [2]. However, because the intelligent systems of UAVs cannot replace human thinking and judgment, UAVs cannot easily perform complex combat missions independently [3]. Therefore, a mode of collaborative combat of manned/unmanned aerial vehicle (MAV/UAV) has emerged.The collaborative combat systems of MAV/UAV make full use of the advantages of UAVs, such as their low cost, zero life risk, strong maneuverability, and powerful survival ability [4], which compensate for their disadvantages, such as their low intelligence and weak ability in handing emergencies. Collaborative combat systems reduce the cost of using manned aircrafts to execute dangerous tasks and changes in air combat patterns. The collaborative combat capability of MAV/UAV in systemic confrontation has been significantly improved in the information age.MAV/UAV collaborative systems are becoming a new area of research in the field of aviation, but experts generally concentrate on the equipment itself. For future air combat, relevant research results about how to determine index systems of MAV/UAV collaborative combat and evaluate their combat capability have not been found.Developing a reasonable model and description of the collaborative combat architecture is the primary task for collaborative combat systems. With the deepening knowledge of equipment systems, the Department of Defense Architecture Framework (Do DAF) [5, 6], proposed by the US Army, has been unable to reflect the complexity, connectivity, and networking features of the combat process. To remedy this limitation, experts have explored new methods to make the model more reasonable. Boyd proposed an OODA model [7] that regards the combat process as a dynamic cycle consisting of the following four links: observe, orient, decide, and act. Based on this model, Cares established a static model [8, 9]. Military equipment were abstracted into four types of network nodes, and the transmissions of information, material, and energy in the battle process were expressed by the edges. By combining the complex network with the agent method, Dekker extended the traditional network method and proposed a C4ISR model [10], showing that the use of complex networks to study combat processes could improve decision-making. The model not only determined the key elements in the combat cycle but also improved the communication and workflow of the combat systems. Tolk et al. [11] improved the information age model established by Cares but did not consider the impact of node performance on combat effectiveness [12, 13]. Most current research on capability assessments is based on the model of a traditional index system [14, 15], which is decomposed by a hierarchy analysis process. Such research ignores the influence of interactions among entities on the capability of the overall collaborative combat systems.The advancement of information technology has improved the strength of the interactive relationship between military equipment, which has a significant impact on modern warfare. This improvement was motivated by the consideration that the simple superposition of the equipment performances alone cannot adequately evaluate the ability of a whole system. Therefore, when representing the combat capability of the systems, the coordination relationship among the military equipment must be considered. In particular, during the MAV/UAV collaborative combat process, different types of aircraft have great discrepancies in flight speed, information transmission, and applicable combat tasks, which form a heterogeneous feature. The heterogeneous node integration and collaborative combat capability evaluation are not discussed in the literatures.When studying collaborative combat systems, the primary task is to reasonably model and describe the collaborative combat architecture. The systems are used to evaluate the MAV/UAV collaborative combat capability via the construction of reasonable indexes or the adoption of effective methods and to locate the flaws and deficiencies of the combat capability. The results can be used as a theoretical basis to optimize the architecture to effectively improve the combat capability of the entire system.In summary, for a deeper understanding of the MAV/UAV collaborative combat systems, this paper describes the information transmission relationship among military equipment. Based on the operation loop, network node and edge models of the MAV/UAV collaborative combat systems are established and analyzed. The uncertainty influence on the capability of the collaborative combat is measured according to information entropy [16, 17]. A new method for evaluating the MAV/UAV collaborative combat capability is proposed. Research on the modeling and capability evaluation methods of MAV/UAV collaborative combat systems is the cornerstone of research on the complete collaborative combat systems. The research provides a quantitative decision basis for military R&D and the procurement of new aircraft types. Moreover, it delivers a reliable basis for the R&D of the combat guiding ideology and tactics.


## 2. Network Model of MAV/UAV Collaborative Combat

Establishing a network model is a precondition for studying MAV/UAV collaborative combat systems. According to network theory, nodes and edges are the most essential factors. Since the combat network is an abstract based on military equipment and enemy targets, each element must be described as a node or edge of the combat network.


### 2.1. Combat Network Model

In collaborative combat systems, combat equipment with different functions, such as detection, communication, command, and attack, are closely linked and constitute a network through unidirectional edges. The systems include a collaborative sensing network, collaborative decision network, and collaborative attack network.This paper regards the enemy targets and combat equipment that can independently accomplish combat activities as network nodes and regards the information transformation and combat activities as network edges.


### 2.2. Network Nodes

According to the combat network model [8, 9] proposed by Cares and the OODA cycle model [7], the nodes are divided into the sensors (manned reconnaissance aircraft S1 and unmanned reconnaissance aircraft S2), decision-makers (manned director aircraft D1 and unmanned director aircraft D2), influencers (manned fighter I1 and unmanned fighter I2), and the target T. The network nodes are shown in Figure 1.Figure 1
Network nodes.φNφ is used to represent all of the nodes, φ represents the type of the node, φ∈T,S,D,I, and Nφ represents the number of φ in the network. Different types of nodes have various technology indexes. The technology indexes for node φi can be denoted as x1φi,x2φi,…,xnφφi.The target nodeT and its properties are expressed as xT=x1T,x2T,⋯,x7T, where xjTj=1,2,⋯,7 is the camouflage coefficient, survivability coefficient, maneuvering velocity, warning time, anti-infrared coefficient, antiradar coefficient, and antioptical coefficient, respectively.The sensor nodeS and its properties are expressed as xS=x1S,x2S,⋯,x10S, where xjSj=1,2,⋯,10 is the maneuvering velocity, scan frequency, maximum detection range, detection precision, identification probability, communication coverage, transmission rate, communication quality, capacity, and delay, respectively.The decision-maker nodeD and its properties are expressed as xD=x1D,x2D,⋯,x8D, where xjDj=1,2,⋯,8 is the response time, throughput, precision, communication coverage, transmission rate, communication quality, capacity, and delay, respectively.The influencer nodeI and its properties are expressed as xI=x1I,x2I,⋯,x8I, where xjIj=1,2,⋯,8 is the maneuvering velocity, killing radius, firing accuracy, communication coverage, transmission rate, communication quality, capacity, and delay, respectively.


### 2.3. Network Edges

The edge model is based on the capability index of the weapon interaction, which is derived from the respective weapon performances. The environmental factor is ignored here.A unidirectional edge between nodes represents the information exchange or combat tasks. According to the description of the main tasks, eight edges between the four nodes are generally considered, namely,T-S, S-S, S-D, D2-D1, D1-D2, D-S, D-I, and I-T. The network edges are shown in Figure 2.
(1)
T-S: the T-S edge mainly measures the reconnaissance ability of sensor node S, which can be measured from the following three aspects: finding, tracking, and recognition.Figure 2
Network edges.The finding abilitypf is expressed as follows:
(1)pf=1−1−gix2S,where gi represents the probability that S can find T in its ith detection. If the search probability of sensor node S psearch and the hiding probability of enemy target T phide are considered, then
(2)gi=k⋅psearchx1T⋅phide,0<k<1,psearch=exp−∑i=14ωxiSln1RxiS,phide=exp−∑i=57ωxiTln1RxiT,where k is an environmental parameter (here, k=0.9), Rxiφ represents the membership function of xiφ, and ωxiφ represents the weight of each index.Regarding the tracking abilitypt, if the tracking probability of sensor node S ptr and the antitrack probability of enemy target T pz are considered, then
(3)pt=kz⋅ptrx1T⋅pz,0<kz<1,ptr=exp−∑i=13ωxiSln1RxiS,pz=exp−ωx3Tln1Rx3T−ωx4Tln1Rx4T,where kz is an environmental parameter (here, k=0.9).The recognition abilitypr is equal to the membership function Rx5S.ET−S represents the reconnaissance ability of T-S and is expressed as follows:
(4)ET−S=exp−∑i∈f,t,rωiln1pi,where ωii∈f,t,r represents the weights of finding, tracking, and recognition.
(2)
S-S: the S-S edge indicates that unmanned reconnaissance aircraft S2 sends information (Inform2) to manned reconnaissance aircraft S1. On the one side, S1 searches for enemy target information (Inform1), and on the other side, Inform2 is combined with Inform1 to obtain other important information. These two steps embody the emergence and cooperativity of the combat systems. The S-S edge mainly measures the information transmission ability of sensor node S. pii=1,2,⋯,5 represents the communication coverage, transmission rate, communication quality, capacity, and delay, respectively, as follows:
(5)p1=1,dS1−S2≤minx6S1,x6S2,0,dS1−S2>minx6S1,x6S2,(6)p2=minx7S1,x7S2,(7)p3=x8S1⋅x8S2,(8)p4=minx9S1,x9S2,(9)p5=x10S1+x10S2.
ES−S represents the information transmission ability of S-S and is expressed as follows:
(10)ES−S=p1∗exp−∑i=25ωiln1Ri,where Ri represents the membership function of pii=1,2,⋯,5.
(3)
S-D: the S-D edge indicates that information collected by sensor node S is transmitted to decision-maker node D. According to the characteristics of S-D, the information transmission ability between these nodes is mainly considered. The information transmission ability of S-D is shown as follows:
(11)ES−D=p1∗exp−∑i=25ωiln1Ri.
(4)
D2-D1: the D2-D1 edge indicates that information analyzed by unmanned director aircraft D2 is transmitted to manned director aircraft D1. When determining the information sharing ability of D2-D1, the information transmission ability E1 and information processing ability E2 must be considered. The information transmission ability of D2-D1 is shown as follows:
(12)E1=p1∗exp−∑i=25ωiln1Ri.
E2 represents the information processing ability of D2 and is expressed as follows:
(13)E2=exp−∑i=13ωiln1Ri,where Ri represents the membership function of xiD2i=1,2,3.
ED2−D1 represents the information sharing ability of D2-D1 and is expressed as follows:
(14)ED2−D1=E1⋅E2.
(5)
D1-D2: the D1-D2 edge indicates that manned director aircraft D1 conveys commands to unmanned director aircraft D2. When determining the command and control ability of D1-D2, the information transmission ability of D1-D2 and information processing ability of D1 must be considered. ED1−D2 represents the command and control ability of D1-D2 and can be expressed as follows:
(15)ED1−D2=E1⋅E2.
(6)
D-S: the D-S edge indicates that decision-maker node D conveys commands to sensor node S such that S can further detect, track, and identify the enemy targets to obtain more specific information. When determining the command and control ability of D-S, the information transmission ability of D-S and information processing ability of D must be considered. ED−S represents the command and control ability of D-S and can be expressed as follows:
(16)ED−S=E1⋅E2.
(7)
D-I: the D-I edge indicates that decision-maker node D conveys attack commands to influencer node I. The D-I edge depends on the information transmission ability, which is shown as follows:
(17)ED−I=p1∗exp−∑i=25ωiln1Ri.
(8)
I-T: the I-T edge mainly measures the attack ability of influencer node I, which can be measured by hit probability ph and damage probability pd. ph is defined as follows:
(18)ph=0,x1I⋅tI−T+x2I<dI−T+x3T⋅x4T,1,x1I⋅tI−T+x2I≥dI−T+x3T⋅x4T.For the damage probabilitypd, if the damage ability of influencer node I pa and the survival ability of enemy target T po are considered, then
(19)pd=ka∗papo,0<ka<1,pa=exp−∑i=13ωxiIln1RxiI,where kais an environmental parameter (here, ka = 0.85).The survival abilitypo is equal to the membership function Rx2T.EI−T represents the attack ability of I-T and can be expressed as follows:
(20)EI−T=ph⋅pd.


## 2.1. Combat Network Model

In collaborative combat systems, combat equipment with different functions, such as detection, communication, command, and attack, are closely linked and constitute a network through unidirectional edges. The systems include a collaborative sensing network, collaborative decision network, and collaborative attack network.This paper regards the enemy targets and combat equipment that can independently accomplish combat activities as network nodes and regards the information transformation and combat activities as network edges.


## 2.2. Network Nodes

According to the combat network model [8, 9] proposed by Cares and the OODA cycle model [7], the nodes are divided into the sensors (manned reconnaissance aircraft S1 and unmanned reconnaissance aircraft S2), decision-makers (manned director aircraft D1 and unmanned director aircraft D2), influencers (manned fighter I1 and unmanned fighter I2), and the target T. The network nodes are shown in Figure 1.Figure 1
Network nodes.φNφ is used to represent all of the nodes, φ represents the type of the node, φ∈T,S,D,I, and Nφ represents the number of φ in the network. Different types of nodes have various technology indexes. The technology indexes for node φi can be denoted as x1φi,x2φi,…,xnφφi.The target nodeT and its properties are expressed as xT=x1T,x2T,⋯,x7T, where xjTj=1,2,⋯,7 is the camouflage coefficient, survivability coefficient, maneuvering velocity, warning time, anti-infrared coefficient, antiradar coefficient, and antioptical coefficient, respectively.The sensor nodeS and its properties are expressed as xS=x1S,x2S,⋯,x10S, where xjSj=1,2,⋯,10 is the maneuvering velocity, scan frequency, maximum detection range, detection precision, identification probability, communication coverage, transmission rate, communication quality, capacity, and delay, respectively.The decision-maker nodeD and its properties are expressed as xD=x1D,x2D,⋯,x8D, where xjDj=1,2,⋯,8 is the response time, throughput, precision, communication coverage, transmission rate, communication quality, capacity, and delay, respectively.The influencer nodeI and its properties are expressed as xI=x1I,x2I,⋯,x8I, where xjIj=1,2,⋯,8 is the maneuvering velocity, killing radius, firing accuracy, communication coverage, transmission rate, communication quality, capacity, and delay, respectively.


## 2.3. Network Edges

The edge model is based on the capability index of the weapon interaction, which is derived from the respective weapon performances. The environmental factor is ignored here.A unidirectional edge between nodes represents the information exchange or combat tasks. According to the description of the main tasks, eight edges between the four nodes are generally considered, namely,T-S, S-S, S-D, D2-D1, D1-D2, D-S, D-I, and I-T. The network edges are shown in Figure 2.
(1)
T-S: the T-S edge mainly measures the reconnaissance ability of sensor node S, which can be measured from the following three aspects: finding, tracking, and recognition.Figure 2
Network edges.The finding abilitypf is expressed as follows:
(1)pf=1−1−gix2S,where gi represents the probability that S can find T in its ith detection. If the search probability of sensor node S psearch and the hiding probability of enemy target T phide are considered, then
(2)gi=k⋅psearchx1T⋅phide,0<k<1,psearch=exp−∑i=14ωxiSln1RxiS,phide=exp−∑i=57ωxiTln1RxiT,where k is an environmental parameter (here, k=0.9), Rxiφ represents the membership function of xiφ, and ωxiφ represents the weight of each index.Regarding the tracking abilitypt, if the tracking probability of sensor node S ptr and the antitrack probability of enemy target T pz are considered, then
(3)pt=kz⋅ptrx1T⋅pz,0<kz<1,ptr=exp−∑i=13ωxiSln1RxiS,pz=exp−ωx3Tln1Rx3T−ωx4Tln1Rx4T,where kz is an environmental parameter (here, k=0.9).The recognition abilitypr is equal to the membership function Rx5S.ET−S represents the reconnaissance ability of T-S and is expressed as follows:
(4)ET−S=exp−∑i∈f,t,rωiln1pi,where ωii∈f,t,r represents the weights of finding, tracking, and recognition.
(2)
S-S: the S-S edge indicates that unmanned reconnaissance aircraft S2 sends information (Inform2) to manned reconnaissance aircraft S1. On the one side, S1 searches for enemy target information (Inform1), and on the other side, Inform2 is combined with Inform1 to obtain other important information. These two steps embody the emergence and cooperativity of the combat systems. The S-S edge mainly measures the information transmission ability of sensor node S. pii=1,2,⋯,5 represents the communication coverage, transmission rate, communication quality, capacity, and delay, respectively, as follows:
(5)p1=1,dS1−S2≤minx6S1,x6S2,0,dS1−S2>minx6S1,x6S2,(6)p2=minx7S1,x7S2,(7)p3=x8S1⋅x8S2,(8)p4=minx9S1,x9S2,(9)p5=x10S1+x10S2.
ES−S represents the information transmission ability of S-S and is expressed as follows:
(10)ES−S=p1∗exp−∑i=25ωiln1Ri,where Ri represents the membership function of pii=1,2,⋯,5.
(3)
S-D: the S-D edge indicates that information collected by sensor node S is transmitted to decision-maker node D. According to the characteristics of S-D, the information transmission ability between these nodes is mainly considered. The information transmission ability of S-D is shown as follows:
(11)ES−D=p1∗exp−∑i=25ωiln1Ri.
(4)
D2-D1: the D2-D1 edge indicates that information analyzed by unmanned director aircraft D2 is transmitted to manned director aircraft D1. When determining the information sharing ability of D2-D1, the information transmission ability E1 and information processing ability E2 must be considered. The information transmission ability of D2-D1 is shown as follows:
(12)E1=p1∗exp−∑i=25ωiln1Ri.
E2 represents the information processing ability of D2 and is expressed as follows:
(13)E2=exp−∑i=13ωiln1Ri,where Ri represents the membership function of xiD2i=1,2,3.
ED2−D1 represents the information sharing ability of D2-D1 and is expressed as follows:
(14)ED2−D1=E1⋅E2.
(5)
D1-D2: the D1-D2 edge indicates that manned director aircraft D1 conveys commands to unmanned director aircraft D2. When determining the command and control ability of D1-D2, the information transmission ability of D1-D2 and information processing ability of D1 must be considered. ED1−D2 represents the command and control ability of D1-D2 and can be expressed as follows:
(15)ED1−D2=E1⋅E2.
(6)
D-S: the D-S edge indicates that decision-maker node D conveys commands to sensor node S such that S can further detect, track, and identify the enemy targets to obtain more specific information. When determining the command and control ability of D-S, the information transmission ability of D-S and information processing ability of D must be considered. ED−S represents the command and control ability of D-S and can be expressed as follows:
(16)ED−S=E1⋅E2.
(7)
D-I: the D-I edge indicates that decision-maker node D conveys attack commands to influencer node I. The D-I edge depends on the information transmission ability, which is shown as follows:
(17)ED−I=p1∗exp−∑i=25ωiln1Ri.
(8)
I-T: the I-T edge mainly measures the attack ability of influencer node I, which can be measured by hit probability ph and damage probability pd. ph is defined as follows:
(18)ph=0,x1I⋅tI−T+x2I<dI−T+x3T⋅x4T,1,x1I⋅tI−T+x2I≥dI−T+x3T⋅x4T.For the damage probabilitypd, if the damage ability of influencer node I pa and the survival ability of enemy target T po are considered, then
(19)pd=ka∗papo,0<ka<1,pa=exp−∑i=13ωxiIln1RxiI,where kais an environmental parameter (here, ka = 0.85).The survival abilitypo is equal to the membership function Rx2T.EI−T represents the attack ability of I-T and can be expressed as follows:
(20)EI−T=ph⋅pd.


## 3. Evaluation of MAV/UAV Collaborative Combat

### 3.1. Evaluation Method

Based on the definition of the nodes and edges, the operation loop is used to integrate combat activities, such as detection, command, and attack. An operation loop is a closed network comprising of a series of nodes and unidirectional edges connected by material, energy, or information. For a given enemy targetT, our combat entities can build an operation loop OL. The impact of a series of combat activities on T is the capability of the operation loop OL.The improved information entropy is used to measure the combat activities, and the operation loop capability is evaluated by this information. Next, the uncertainty contained in the combat activities of each edge is analyzed, and the formulas for improved information entropy are given.(1)
T-S: the stronger reconnaissance capability ET−S of the T-S edge means that the information uncertainty of the target is lower and that the collaborative combat capability is stronger when more accurate information on the enemy targets is obtained by S. ET−S represents the reconnaissance capability of T-S; therefore, the self-information entropy of T-S is expressed as follows:
(21)ST−S=−logET−S.
(2)
S-S: the S-S edge implies a synergic relationship between the S nodes, which refers to the relationship between S2-S1 and T-S1. This edge mainly reflects the information fusion ability of S1. The information entropy after synergy can be represented by the joint entropy method.
(22)HX,Y=HX+HY−IX;Y.X and Y represent the operational activities of S2-S1 and T-S1, respectively.
(23)HX=ES2−S1,(24)HY=ET−S1,(25)HX,Y=ES−S,(26)IX;Y=−∑y∑xpx,ylogpx,ypxpy=−∑y∑xpy∣xpxlogpy∣xpy.According to the definition of mutual information in equation (26), the impact that the information obtained and transmitted by S2 to the reconnaissance ability of S1 is measured by py∣x. px and py represent the completion degree of S2-S1 and T-S1, respectively, which are equal to ES2−S1 and ET−S1. Then, py∣x is defined as follows:
(27)py∣x=ks⋅ET−S11−ES2−S1,where ks is an influence coefficient (here, ks = 0.2). S1 is more likely to obtain more information through fusion when the information transmitted by S2-S1 is more accurate.
(28)IX;Y=−ks⋅ET−S11−ES2−S1⋅ES2−S1⋅logks1−ES2−S1.Therefore, the self-information entropy ofS-S is expressed as follows:
(29)SS−S=−logES−S=−logHX,Y.
(3)
S-D: the information uncertainty of S-D mainly originates from communication. Thus, the self-information entropy of S-S combat activities is expressed as follows:
(30)SS−D=−logES−D.
(4)
D2-D1: unmanned director aircraft D2 analyzes the information of the enemy and sends it to manned director aircraft D1. The uncertainty inherent in this process mainly lies in the information transmission ability and information processing ability.
(31)SD2−D1=−logED2−D1=−logE1⋅E2.
(5)
D1-D2: considering the current situation, manned director aircraft D1 further determines the targets and provides appropriate measures. Similarly, the uncertainty inherent in this process mainly lies in the information transmission ability and information processing ability.
(32)SD1−D2=−logED1−D2=−logE1⋅E2.
(6)
D-S: the D-S edge describes the process of director aircraft D communicating surveillance commands to sensor node S, which is based on the data analysis results. Similarly, the uncertainty inherent in this process mainly lies in the information transmission ability and information processing ability.
(33)SD−S=−logED−S=−logE1⋅E2.
(7)
D-I: the D-I edge describes the process of director aircraft D communicating attack commands to influencer node I. The uncertainty inherent in this process mainly lies in the information transmission ability. Therefore, the self-information entropy of D-I can be expressed as follows:
(34)SD−I=−logED−I.
(8)
I-T: the I-T edge describes the process of influencer node I attacking enemy target T. The uncertainty inherent in this process mainly lies in the hit probability ph and damage probability. Therefore, the self-information entropy of I-T is expressed as shown as follows:
(35)SI−T=−logEI−T=−logph⋅pd.At this point, the description of the self-information entropy of each edge has been completed. Next, the length of each edge, that is, the distance between two adjacent nodes, is defined.Definition 1. The length ofeij.
The length of the unidirectional edgeeij between nodes xi and xj is expressed as lij=Si−j.Definition 2. The distance fromxi to xj.
If there are some intermediate nodesxi,xj∉x1,x2,⋯,xk,i≠j and a set of unidirectional edges Eij=xix1,x1x2,⋯xk−1xk,xkxj between xi and xj, then a path rij exists from xi to xj. The distance dij is related to the length of path rij, which can be described as follows:
(36)dij=N−1N∏epq∈EijlpqN=N−1N∏epq∈EijSp−qN,where N=k+1.According to the distancedij, the distance between the two nodes in the combat network is equal to the total uncertainties of all combat activities. For a given enemy target Tm, the length of operation loop OLmn is described as follows:
(37)dOLmn=N−1N∏epq∈EmnlpqN=N−1N∏epq∈EmnSp−qN,where N is the number of edges in the operation loop and Emn is the set of all unidirectional edges.The length of the operation loop can be used to measure the combat capability to the given target. The length is proportional to the information uncertainty and inversely proportional to the combat capability. The operation loop is expressed as follows:(38)OLCmn=exp−dOLmn.For different military actions againstTm, the combat capability is the comprehensive uncertainty of all operation loops. Suppose that M military actions are formulated for target M, that is, M operation loops are made. Then, the comprehensive uncertainty of all operation loops is described as follows:
(39)dOLm=1∑j=1M1/dOLmj.The combat capability AOC for targetTm is calculated as follows:
(40)AOC=exp−1∑j=1M1/dOLmj.Based on the weighted calculation, the evaluation indexes of the MAV/UAV collaborative combat capability can be obtained as follows:(41)Y=∑i=1NTωi⋅AOCi.


### 3.2. Evaluation Procedure

Based on the above evaluation method, the evaluation procedure of the MAV/UAV collaborative combat capability can be summarized as follows:Step 1:
Analyze the strategic missions and define the set of enemy targetsT=T1,T1,⋯TNT
Step 2:
According to the targets, determine the combat entities and establish the model of nodes and edges
Step 3:
Identify the operation loops and calculate their combat capabilities
Step 4:
Calculate the combat capability of all operational loops for each target
Step 5:
Obtain the MAV/UAV collaborative combat capability by calculating the combat capabilities of the operation loops aimed at all the targets


## 3.1. Evaluation Method

Based on the definition of the nodes and edges, the operation loop is used to integrate combat activities, such as detection, command, and attack. An operation loop is a closed network comprising of a series of nodes and unidirectional edges connected by material, energy, or information. For a given enemy targetT, our combat entities can build an operation loop OL. The impact of a series of combat activities on T is the capability of the operation loop OL.The improved information entropy is used to measure the combat activities, and the operation loop capability is evaluated by this information. Next, the uncertainty contained in the combat activities of each edge is analyzed, and the formulas for improved information entropy are given.(1)
T-S: the stronger reconnaissance capability ET−S of the T-S edge means that the information uncertainty of the target is lower and that the collaborative combat capability is stronger when more accurate information on the enemy targets is obtained by S. ET−S represents the reconnaissance capability of T-S; therefore, the self-information entropy of T-S is expressed as follows:
(21)ST−S=−logET−S.
(2)
S-S: the S-S edge implies a synergic relationship between the S nodes, which refers to the relationship between S2-S1 and T-S1. This edge mainly reflects the information fusion ability of S1. The information entropy after synergy can be represented by the joint entropy method.
(22)HX,Y=HX+HY−IX;Y.X and Y represent the operational activities of S2-S1 and T-S1, respectively.
(23)HX=ES2−S1,(24)HY=ET−S1,(25)HX,Y=ES−S,(26)IX;Y=−∑y∑xpx,ylogpx,ypxpy=−∑y∑xpy∣xpxlogpy∣xpy.According to the definition of mutual information in equation (26), the impact that the information obtained and transmitted by S2 to the reconnaissance ability of S1 is measured by py∣x. px and py represent the completion degree of S2-S1 and T-S1, respectively, which are equal to ES2−S1 and ET−S1. Then, py∣x is defined as follows:
(27)py∣x=ks⋅ET−S11−ES2−S1,where ks is an influence coefficient (here, ks = 0.2). S1 is more likely to obtain more information through fusion when the information transmitted by S2-S1 is more accurate.
(28)IX;Y=−ks⋅ET−S11−ES2−S1⋅ES2−S1⋅logks1−ES2−S1.Therefore, the self-information entropy ofS-S is expressed as follows:
(29)SS−S=−logES−S=−logHX,Y.
(3)
S-D: the information uncertainty of S-D mainly originates from communication. Thus, the self-information entropy of S-S combat activities is expressed as follows:
(30)SS−D=−logES−D.
(4)
D2-D1: unmanned director aircraft D2 analyzes the information of the enemy and sends it to manned director aircraft D1. The uncertainty inherent in this process mainly lies in the information transmission ability and information processing ability.
(31)SD2−D1=−logED2−D1=−logE1⋅E2.
(5)
D1-D2: considering the current situation, manned director aircraft D1 further determines the targets and provides appropriate measures. Similarly, the uncertainty inherent in this process mainly lies in the information transmission ability and information processing ability.
(32)SD1−D2=−logED1−D2=−logE1⋅E2.
(6)
D-S: the D-S edge describes the process of director aircraft D communicating surveillance commands to sensor node S, which is based on the data analysis results. Similarly, the uncertainty inherent in this process mainly lies in the information transmission ability and information processing ability.
(33)SD−S=−logED−S=−logE1⋅E2.
(7)
D-I: the D-I edge describes the process of director aircraft D communicating attack commands to influencer node I. The uncertainty inherent in this process mainly lies in the information transmission ability. Therefore, the self-information entropy of D-I can be expressed as follows:
(34)SD−I=−logED−I.
(8)
I-T: the I-T edge describes the process of influencer node I attacking enemy target T. The uncertainty inherent in this process mainly lies in the hit probability ph and damage probability. Therefore, the self-information entropy of I-T is expressed as shown as follows:
(35)SI−T=−logEI−T=−logph⋅pd.At this point, the description of the self-information entropy of each edge has been completed. Next, the length of each edge, that is, the distance between two adjacent nodes, is defined.Definition 1. The length ofeij.
The length of the unidirectional edgeeij between nodes xi and xj is expressed as lij=Si−j.Definition 2. The distance fromxi to xj.
If there are some intermediate nodesxi,xj∉x1,x2,⋯,xk,i≠j and a set of unidirectional edges Eij=xix1,x1x2,⋯xk−1xk,xkxj between xi and xj, then a path rij exists from xi to xj. The distance dij is related to the length of path rij, which can be described as follows:
(36)dij=N−1N∏epq∈EijlpqN=N−1N∏epq∈EijSp−qN,where N=k+1.According to the distancedij, the distance between the two nodes in the combat network is equal to the total uncertainties of all combat activities. For a given enemy target Tm, the length of operation loop OLmn is described as follows:
(37)dOLmn=N−1N∏epq∈EmnlpqN=N−1N∏epq∈EmnSp−qN,where N is the number of edges in the operation loop and Emn is the set of all unidirectional edges.The length of the operation loop can be used to measure the combat capability to the given target. The length is proportional to the information uncertainty and inversely proportional to the combat capability. The operation loop is expressed as follows:(38)OLCmn=exp−dOLmn.For different military actions againstTm, the combat capability is the comprehensive uncertainty of all operation loops. Suppose that M military actions are formulated for target M, that is, M operation loops are made. Then, the comprehensive uncertainty of all operation loops is described as follows:
(39)dOLm=1∑j=1M1/dOLmj.The combat capability AOC for targetTm is calculated as follows:
(40)AOC=exp−1∑j=1M1/dOLmj.Based on the weighted calculation, the evaluation indexes of the MAV/UAV collaborative combat capability can be obtained as follows:(41)Y=∑i=1NTωi⋅AOCi.


## 3.2. Evaluation Procedure

Based on the above evaluation method, the evaluation procedure of the MAV/UAV collaborative combat capability can be summarized as follows:Step 1:
Analyze the strategic missions and define the set of enemy targetsT=T1,T1,⋯TNT
Step 2:
According to the targets, determine the combat entities and establish the model of nodes and edges
Step 3:
Identify the operation loops and calculate their combat capabilities
Step 4:
Calculate the combat capability of all operational loops for each target
Step 5:
Obtain the MAV/UAV collaborative combat capability by calculating the combat capabilities of the operation loops aimed at all the targets


## 4. Example

The network framework provided in this example is an ideal model. To simplify the model and highlight the process of the cooperative combat capability evaluation, we considered the simplest one. In the example, only eight nodes are considered, that is, each node represents an UAV or an MAV with different functions. In practical applications, nodes can be added based on the specific combat environment, and the edges can be determined by the specific combat assignments.Some of the parameter assignments in this example come from experience summarization. After much investigation and calculation of statistics, the most representative parameters are selected from the functional parameters of reconnaissance aircrafts and combat aircrafts, such as the maneuvering velocity, scan frequency, and maximum detection range of the sensor nodeS. The other part is imaginary scene representation, such as the anti-infrared coefficient, antiradar coefficient, and antioptical coefficient of the target node T. The parameters selected in this example are just used as examples. In practical applications, the correct parameters for the actual model can be substituted.


### 4.1. Nodes of the Network

Based on the above modeling process, the MAV/UAV collaborative combat network shown in Figure3 can be obtained.Figure 3
An MAV/UAV collaborative combat network.The technical indexes of each node are assigned according to the description of the nodes in the collaborative combat network. In calculating the information entropy and combat capability of each edge, the membership functions are determined in combination with actual combat and expert experience.(1)
Target nodeT: the hypothetical target nodes and their technical indexes in this example are shown in Table 1.Table 1
Tactical indexes ofT.
Name
Code
T1
T2
Camouflage coefficient
x1
3
3
Survivability coefficient (mm)
x2
800
500
Maneuvering velocity (km/h)
x3
70
50
Warning time (s)
x4
0.6
0.5
Anti-infrared coefficient
x5
8
7
Antiradar coefficient
x6
6
5
Antioptical coefficient
x7
7
7The membership function of the survivability coefficient is shown as follows:(42)Rx2T=1,800≤x2T,0.7,500≤x2T<800,0.3,300≤x2T<500,0.1,x2T<300.The weights of the maneuvering velocity and warning time areωx3T=0.3 and ωx4T=0.7, and their membership functions are shown, respectively, as follows:
(43)Rx3T=1,70≤x3T,0.5,50≤x3T<70,0.3,30≤x3T<50,0.1,x3T<30,(44)Rx4T=1,0.7≤x4T,0.7,0.5≤x4T<0.7,0.3,0.3≤x4T<0.5,0.1,x4T<0.3.The anti-infrared, antiradar, and antioptical weights areωx5T=0.25, ωx6T=0.6, and ωx7T=0.15, and their membership functions are shown, respectively, as follows:
(45)Rx5T=1,6<x5T,0.6,4<x5T≤6,0.2,x5T≤4,(46)Rx6T=1,5<x6T,0.5,2<x6T≤5,0.2,x6T≤2,(47)Rx7T=1,10≤x7T,0.6,5≤x7T<10,0.1,x7T<5.When calculating the reconnaissance capability ofT-S, the weights of finding, tracking, and identification are each equal to 1/3.
(2)
Sensor nodeS: the technical indexes of the S nodes mentioned above are shown in Table 2.Table 2
Tactical indexes ofS.
Name
Code
S1
S2
Maneuvering velocity (km/h)
x1
1000
700
Scan frequency (Hz)
x2
7
8
Maximum detection range (km)
x3
3500
2500
Detection precision (m2)
x4
5
6
Identification probability
x5
0.65
0.85
Communication coverage (km)
x6
3000
2500
Transmission rate (bps)
x7
15
12
Communication quality
x8
0.2
0.3
Communication capacity (MHz/s)
x9
40
30
Communication delay (ms)
x10
5.5
4The maneuvering velocity, scan frequency, maximum detection range, and detection precision weights areωx1S=0.2, ωx2S=0.3, ωx3S=0.15, and ωx4S=0.35, respectively, and their membership functions are shown, respectively, as follows:
(48)Rx1S=1,900≤x1S,0.8,700≤x1S<900,0.5,500≤x1S<700,0.2,x1S<500,(49)Rx2S=1,6≤x2S,0.8,5≤x2S<6,0.5,3≤x2S<5,0.2,x2S<3,(50)Rx3S=1,3000≤x3S,0.8,2000≤x3S<3000,0.3,x3S<2000,(51)Rx4S=0.2,7≤x4S,0.5,5≤x4S<7,0.8,4≤x4S<5,1,x4S<4,(52)Rx5S=1,0.9≤x5S,0.8,0.8≤x5S<0.9,0.4,0.6≤x5S<0.8,0.2,x5S<0.6.
(3)
Decision-maker nodeD: the technical indexes of the decision-maker nodes in our collaborative combat systems are shown in Table 3.Table 3
Tactical indexes ofD.
Name
Code
D1
D2
Response time (s)
x1
0.02
0.04
Throughput (bps)
x2
8
4
Precision
x3
0.9
0.6
Communication coverage (km)
x4
2600
2000
Transmission rate (bps)
x5
8
5
Communication quality
x6
0.1
0.12
Communication capacity (MHz/s)
x7
60
30
Communication delay (ms)
x8
4
4When considering the information processing capability ofD, the following three tactical indexes exist: response time, throughput, and precision; their weights are ωx1D=0.3, ωx2D=0.25, and ωx3D=0.45, respectively, and their membership functions are shown, respectively, as follows:
(53)Rx1D=0.2,0.06≤x1D,0.5,0.03≤x1D<0.06,0.8,0.01≤x1D<0.03,1,x1D<0.01,(54)Rx2D=1,8≤x1D,0.7,6≤x1D<8,0.3,4≤x1D<6,0.1,x1D<4,(55)Rx3D=1,0.9≤x3D,0.7,0.7≤x3D<0.9,0.5,0.4≤x3D<0.7,0.2,x3D<0.4.
(4)
Influencer nodeI: the technical indexes of I are shown in Table 4.Table 4
Tactical indexes ofI.
Name
Code
I1
I2
Maneuvering velocity (km/h)
x1
1600
2000
Killing radius (km)
x2
20
30
Firing accuracy (m)
x3
3
5
Communication coverage (km)
x4
2000
2000
Transmission rate (bps)
x5
8
7.5
Communication quality
x6
0.1
0.12
Communication capacity (MHz/s)
x7
50
25
Communication delay (ms)
x8
3
2When considering the attack ability ofI, the following three tactical indexes exist: maneuvering velocity, killing radius, and firing accuracy; their weights are ωx1I=0.3, ωx2I=0.3, and ωx3I=0.4, respectively. Their membership functions are shown, respectively, as follows:
(56)Rx1I=1,2000≤x1I,0.8,1500≤x1I<2000,0.5,1000≤x1I<1500,0.25,x1I<1000,(57)Rx2I=1,30≤x2I,0.8,20≤x2I<30,0.5,10≤x2I<20,0.25,x2I<10,(58)Rx3I=0.1,6≤x3I,0.5,4≤x3I<6,0.8,2≤x3I<4,1,x3I<2.In addition, when considering the information transmission capacity between nodes, the following four tactical indexes are considered: transmission rate, communication quality, capacity, and delay, with weights ofω3=0.3, ω4=0.2, and ω5=0.2, respectively. Their membership functions are shown, respectively, as follows:
(59)R2=1,15≤p2,0.8,10≤p2<15,0.6,5≤p2<10,0.2,p2<5,(60)R3=0.2,0.3≤p3,0.6,0.2≤p3<0.3,0.8,0.1≤p3<0.2,1,p3<0.1,(61)R4=1,60≤p4,0.8,50≤p4<60,0.6,40≤p4<50,0.2,p4<40,(62)R5=0.25,4≤p5,0.6,3≤p5<4,0.8,2≤p5<3,1,p5<2.


### 4.2. Network Edges

According to the technical indexes of the different nodes in the MAV/UAV collaborative combat network, the capability and information entropy of each edge can be calculated when combined with the analysis of the relationships among the nodes. The capability of each edge can be obtained by substituting the technical indexes of the different nodes into equations (4)-(20). Then, the information entropy of each edge can be obtained by substituting the capabilities of the different edges into equations (21)-(35), as shown in Table 5.Table 5
Edge capability and length.
Number
Edge
Capability
Length
Number
Edge
Capability
Length
1
T1-S1
0.5120
0.6694
13
D1-S1
0.7131
0.3382
2
T1-S2
0.6312
0.4601
14
D1-S2
0.6216
0.4755
3
T2-S1
0.5681
0.5655
15
D2-S1
0.4189
0.8700
4
T2-S2
0.6982
0.3592
16
D2-S2
0.4189
0.8700
5
T1-S2-S1
0.8750
0.1335
17
D1-I1
0.5886
0.5301
6
T2-S2-S1
0.8658
0.1441
18
D1-I2
0.4162
0.8766
7
S1-D1
0.5477
0.6020
19
D2-I1
0.4162
0.8766
8
S1-D2
0.4162
0.8766
20
D2-I2
0.4162
0.8766
9
S2-D1
0.4162
0.8766
21
I1-T1
0.8246
0.1928
10
S2-D2
0.4162
0.8766
22
I1-T2
0.9856
0.0145
11
D1-D2
0.6216
0.4755
23
I2-T1
0.8026
0.2199
12
D2-D1
0.4189
0.8700
24
I2-T2
0.9593
0.0416


### 4.3. Capability Evaluation

The MAV/UAV collaborative combat network aimed at targetT1 can be formed by the military activities for target T1, as shown in Figure 4.Figure 4
MAV/UAV collaborative combat network aimed at targetT1.Referring to Table5, the information entropy of the operation loops can be obtained by substituting the lengths of the corresponding edges into equation (37). According to equation (38), the capability of the operation loop can be obtained.Table6 shows the operation loops and the capability and length results aimed at target T1.Table 6
Capability and length of operation loops aimed at targetT1.
Number
Operation loop
Number of nodes
Length of operation loop
Capability of operation loop
1
T1-S2-S1-D1-I1-T1
5
0.2503
0.7786
2
T1-S2-S1-D1-I2-T1
5
0.2817
0.7545
3
T1-S2-D1-I1-T1
4
0.3165
0.7287
4
T1-S1-D1-I1-T1
4
0.3188
0.7270
5
T1-S2-D2-I1-T1
4
0.3550
0.7011
6
T1-S2-D1-I2-T1
4
0.3669
0.6929
7
T1-S2-D2-I2-T1
4
0.3669
0.6929
8
T1-S2-D1-D2-I1-T1
5
0.3679
0.6922
9
T1-S1-D1-I2-T1
4
0.3696
0.6910
10
T1-S2-D1-D2-I2-T1
5
0.3777
0.6854
11
T1-S2-D2-D1-I1-T1
5
0.3824
0.6822
12
T1-S2-D2-D1-D2-I1-T1
6
0.4191
0.6575
13
T1-S2-D2-D1-D2-I2-T1
6
0.4284
0.6515
14
T1-S2-D2-D1-I2-T1
5
0.4304
0.6503
15
T1-S1-D2-D1-D2-I1-T1
6
0.4461
0.6401
16
T1-S1-D2-D1-D2-I2-T1
6
0.4560
0.6338Similarly, the MAV/UAV collaborative combat network aimed at targetT2 can be formed by the military activities for target T2, as shown in Figure 5.Figure 5
MAV/UAV collaborative combat network aimed at targetT2.Table7 shows the operation loops and the capability and length results aimed at target T2.Table 7
Energy and length of operation loops aimed at targetT2.
Number
Operation loop
Number of nodes
Length of operation loop
Capability of operation loop
1
T2-S2-S1-D2-I1-T2
5
0.1693
0.8442
2
T2-S2-S1-D2-I2-T2
5
0.2091
0.8113
3
T2-S2-D2-I2-T2
4
0.2275
0.7966
4
T2-S1-D2-D1-I1-T2
5
0.2375
0.7886
5
T2-S1-D2-I2-T2
4
0.2548
0.7751
6
T2-S2-D2-D1-D2-I1-T2
6
0.2613
0.7701
7
T2-S2-S1-D2-D1-D2-I1-T2
7
0.2308
0.757
8
T2-S1-D2-D1-D2-I1-T2
6
0.2818
0.7544
9
T2-S2-D2-D1-D2-I2-T2
6
0.3115
0.7324
10
T2-S1-D2-D1-I2-T2
5
0.3215
0.7251
11
T2-S2-S1-D2-D1-D2-I2-T2
7
0.2751
0.7235
12
T2-S1-D2-D1-D2-I2-T2
6
0.3359
0.7147According to equation (39), the comprehensive uncertainties of the operation loops aimed at targets T1 and T2 can be obtained, respectively. If these uncertainties are introduced in equation (40), the combat capability AOC for targets T1 and T2 can be obtained.The combat capabilities synthesized by the operation loops aimed at targetsT1 and T2 are calculated, respectively, as follows:
(63)AOCT1=exp−dOL1=exp−1∑j=1M1/dOLmj=exp−0.0226=0.9777,(64)AOCT2=exp−dOL2=exp−1∑j=1M1/dOLmj=exp−0.0210=0.9792.After analyzing the target weights, the overall combat capability can be determined. In this case, the weights of the two targets areωT1=0.7 and ωT2=0.3; thus, the MAV/UAV collaborative combat capability is calculated as follows:
(65)Y=∑i=12ωTi⋅AOCTi=0.7×0.9777+0.3×0.9792=0.9781.


### 4.4. Analysis of the Result

(1)
Influence of the node in the operation loop on the combat capability: according to Table5, when considering edges 1 to 4, the reconnaissance and detection capabilities of unmanned reconnaissance aircraft S2 are superior to those of S1; when considering edges 11 to 12 and 11 to 16, the command and detection capabilities of manned command aircraft D1 are superior to those of D2; and when considering edges 21 to 24, the fire strike capability of manned combat aircraft I1 is highly similar to that of the unmanned combat aircraft. Therefore, considering such factors as the manned aircraft cost and pilot safety, an unmanned combat aircraft should be selected as much as possible to execute missions.
(2)
Influence of the operation loop length on the combat capability: the observations listed in Tables6 and 7 indicate that the length of the operation loop has a negative relation to its combat capability, which means that a longer operation loop has a lower combat capability. Each equipment in the operation loop brings a time delay, which becomes longer with more equipment, thereby influencing the combat capability of the overall operation loop.
(3)
Influence of collaborative combat on combat capability: the length of operation loops 1 and 2 is greater than that of 3 and 4. Thus, according to the previous conclusion, the combat capability of operation loops 1 and 2 should be inferior to that of 3 and 4; however, the opposite is true. The reason is that during the detection of targetT1 with 1 and 2, unmanned reconnaissance aircraft S2 transmits its information to manned aircraft S1. S1 conducts reconnaissance of an enemy target and integrates information from both sides, which significantly reduces the information uncertainty of target T1. Thus, the combat capability of 1 and 2 does not decrease due to the greater operation loop length but instead increases, which reflects the emergent properties and synergy of the combat systems.


## 4.1. Nodes of the Network

Based on the above modeling process, the MAV/UAV collaborative combat network shown in Figure3 can be obtained.Figure 3
An MAV/UAV collaborative combat network.The technical indexes of each node are assigned according to the description of the nodes in the collaborative combat network. In calculating the information entropy and combat capability of each edge, the membership functions are determined in combination with actual combat and expert experience.(1)
Target nodeT: the hypothetical target nodes and their technical indexes in this example are shown in Table 1.Table 1
Tactical indexes ofT.
Name
Code
T1
T2
Camouflage coefficient
x1
3
3
Survivability coefficient (mm)
x2
800
500
Maneuvering velocity (km/h)
x3
70
50
Warning time (s)
x4
0.6
0.5
Anti-infrared coefficient
x5
8
7
Antiradar coefficient
x6
6
5
Antioptical coefficient
x7
7
7The membership function of the survivability coefficient is shown as follows:(42)Rx2T=1,800≤x2T,0.7,500≤x2T<800,0.3,300≤x2T<500,0.1,x2T<300.The weights of the maneuvering velocity and warning time areωx3T=0.3 and ωx4T=0.7, and their membership functions are shown, respectively, as follows:
(43)Rx3T=1,70≤x3T,0.5,50≤x3T<70,0.3,30≤x3T<50,0.1,x3T<30,(44)Rx4T=1,0.7≤x4T,0.7,0.5≤x4T<0.7,0.3,0.3≤x4T<0.5,0.1,x4T<0.3.The anti-infrared, antiradar, and antioptical weights areωx5T=0.25, ωx6T=0.6, and ωx7T=0.15, and their membership functions are shown, respectively, as follows:
(45)Rx5T=1,6<x5T,0.6,4<x5T≤6,0.2,x5T≤4,(46)Rx6T=1,5<x6T,0.5,2<x6T≤5,0.2,x6T≤2,(47)Rx7T=1,10≤x7T,0.6,5≤x7T<10,0.1,x7T<5.When calculating the reconnaissance capability ofT-S, the weights of finding, tracking, and identification are each equal to 1/3.
(2)
Sensor nodeS: the technical indexes of the S nodes mentioned above are shown in Table 2.Table 2
Tactical indexes ofS.
Name
Code
S1
S2
Maneuvering velocity (km/h)
x1
1000
700
Scan frequency (Hz)
x2
7
8
Maximum detection range (km)
x3
3500
2500
Detection precision (m2)
x4
5
6
Identification probability
x5
0.65
0.85
Communication coverage (km)
x6
3000
2500
Transmission rate (bps)
x7
15
12
Communication quality
x8
0.2
0.3
Communication capacity (MHz/s)
x9
40
30
Communication delay (ms)
x10
5.5
4The maneuvering velocity, scan frequency, maximum detection range, and detection precision weights areωx1S=0.2, ωx2S=0.3, ωx3S=0.15, and ωx4S=0.35, respectively, and their membership functions are shown, respectively, as follows:
(48)Rx1S=1,900≤x1S,0.8,700≤x1S<900,0.5,500≤x1S<700,0.2,x1S<500,(49)Rx2S=1,6≤x2S,0.8,5≤x2S<6,0.5,3≤x2S<5,0.2,x2S<3,(50)Rx3S=1,3000≤x3S,0.8,2000≤x3S<3000,0.3,x3S<2000,(51)Rx4S=0.2,7≤x4S,0.5,5≤x4S<7,0.8,4≤x4S<5,1,x4S<4,(52)Rx5S=1,0.9≤x5S,0.8,0.8≤x5S<0.9,0.4,0.6≤x5S<0.8,0.2,x5S<0.6.
(3)
Decision-maker nodeD: the technical indexes of the decision-maker nodes in our collaborative combat systems are shown in Table 3.Table 3
Tactical indexes ofD.
Name
Code
D1
D2
Response time (s)
x1
0.02
0.04
Throughput (bps)
x2
8
4
Precision
x3
0.9
0.6
Communication coverage (km)
x4
2600
2000
Transmission rate (bps)
x5
8
5
Communication quality
x6
0.1
0.12
Communication capacity (MHz/s)
x7
60
30
Communication delay (ms)
x8
4
4When considering the information processing capability ofD, the following three tactical indexes exist: response time, throughput, and precision; their weights are ωx1D=0.3, ωx2D=0.25, and ωx3D=0.45, respectively, and their membership functions are shown, respectively, as follows:
(53)Rx1D=0.2,0.06≤x1D,0.5,0.03≤x1D<0.06,0.8,0.01≤x1D<0.03,1,x1D<0.01,(54)Rx2D=1,8≤x1D,0.7,6≤x1D<8,0.3,4≤x1D<6,0.1,x1D<4,(55)Rx3D=1,0.9≤x3D,0.7,0.7≤x3D<0.9,0.5,0.4≤x3D<0.7,0.2,x3D<0.4.
(4)
Influencer nodeI: the technical indexes of I are shown in Table 4.Table 4
Tactical indexes ofI.
Name
Code
I1
I2
Maneuvering velocity (km/h)
x1
1600
2000
Killing radius (km)
x2
20
30
Firing accuracy (m)
x3
3
5
Communication coverage (km)
x4
2000
2000
Transmission rate (bps)
x5
8
7.5
Communication quality
x6
0.1
0.12
Communication capacity (MHz/s)
x7
50
25
Communication delay (ms)
x8
3
2When considering the attack ability ofI, the following three tactical indexes exist: maneuvering velocity, killing radius, and firing accuracy; their weights are ωx1I=0.3, ωx2I=0.3, and ωx3I=0.4, respectively. Their membership functions are shown, respectively, as follows:
(56)Rx1I=1,2000≤x1I,0.8,1500≤x1I<2000,0.5,1000≤x1I<1500,0.25,x1I<1000,(57)Rx2I=1,30≤x2I,0.8,20≤x2I<30,0.5,10≤x2I<20,0.25,x2I<10,(58)Rx3I=0.1,6≤x3I,0.5,4≤x3I<6,0.8,2≤x3I<4,1,x3I<2.In addition, when considering the information transmission capacity between nodes, the following four tactical indexes are considered: transmission rate, communication quality, capacity, and delay, with weights ofω3=0.3, ω4=0.2, and ω5=0.2, respectively. Their membership functions are shown, respectively, as follows:
(59)R2=1,15≤p2,0.8,10≤p2<15,0.6,5≤p2<10,0.2,p2<5,(60)R3=0.2,0.3≤p3,0.6,0.2≤p3<0.3,0.8,0.1≤p3<0.2,1,p3<0.1,(61)R4=1,60≤p4,0.8,50≤p4<60,0.6,40≤p4<50,0.2,p4<40,(62)R5=0.25,4≤p5,0.6,3≤p5<4,0.8,2≤p5<3,1,p5<2.


## 4.2. Network Edges

According to the technical indexes of the different nodes in the MAV/UAV collaborative combat network, the capability and information entropy of each edge can be calculated when combined with the analysis of the relationships among the nodes. The capability of each edge can be obtained by substituting the technical indexes of the different nodes into equations (4)-(20). Then, the information entropy of each edge can be obtained by substituting the capabilities of the different edges into equations (21)-(35), as shown in Table 5.Table 5
Edge capability and length.
Number
Edge
Capability
Length
Number
Edge
Capability
Length
1
T1-S1
0.5120
0.6694
13
D1-S1
0.7131
0.3382
2
T1-S2
0.6312
0.4601
14
D1-S2
0.6216
0.4755
3
T2-S1
0.5681
0.5655
15
D2-S1
0.4189
0.8700
4
T2-S2
0.6982
0.3592
16
D2-S2
0.4189
0.8700
5
T1-S2-S1
0.8750
0.1335
17
D1-I1
0.5886
0.5301
6
T2-S2-S1
0.8658
0.1441
18
D1-I2
0.4162
0.8766
7
S1-D1
0.5477
0.6020
19
D2-I1
0.4162
0.8766
8
S1-D2
0.4162
0.8766
20
D2-I2
0.4162
0.8766
9
S2-D1
0.4162
0.8766
21
I1-T1
0.8246
0.1928
10
S2-D2
0.4162
0.8766
22
I1-T2
0.9856
0.0145
11
D1-D2
0.6216
0.4755
23
I2-T1
0.8026
0.2199
12
D2-D1
0.4189
0.8700
24
I2-T2
0.9593
0.0416


## 4.3. Capability Evaluation

The MAV/UAV collaborative combat network aimed at targetT1 can be formed by the military activities for target T1, as shown in Figure 4.Figure 4
MAV/UAV collaborative combat network aimed at targetT1.Referring to Table5, the information entropy of the operation loops can be obtained by substituting the lengths of the corresponding edges into equation (37). According to equation (38), the capability of the operation loop can be obtained.Table6 shows the operation loops and the capability and length results aimed at target T1.Table 6
Capability and length of operation loops aimed at targetT1.
Number
Operation loop
Number of nodes
Length of operation loop
Capability of operation loop
1
T1-S2-S1-D1-I1-T1
5
0.2503
0.7786
2
T1-S2-S1-D1-I2-T1
5
0.2817
0.7545
3
T1-S2-D1-I1-T1
4
0.3165
0.7287
4
T1-S1-D1-I1-T1
4
0.3188
0.7270
5
T1-S2-D2-I1-T1
4
0.3550
0.7011
6
T1-S2-D1-I2-T1
4
0.3669
0.6929
7
T1-S2-D2-I2-T1
4
0.3669
0.6929
8
T1-S2-D1-D2-I1-T1
5
0.3679
0.6922
9
T1-S1-D1-I2-T1
4
0.3696
0.6910
10
T1-S2-D1-D2-I2-T1
5
0.3777
0.6854
11
T1-S2-D2-D1-I1-T1
5
0.3824
0.6822
12
T1-S2-D2-D1-D2-I1-T1
6
0.4191
0.6575
13
T1-S2-D2-D1-D2-I2-T1
6
0.4284
0.6515
14
T1-S2-D2-D1-I2-T1
5
0.4304
0.6503
15
T1-S1-D2-D1-D2-I1-T1
6
0.4461
0.6401
16
T1-S1-D2-D1-D2-I2-T1
6
0.4560
0.6338Similarly, the MAV/UAV collaborative combat network aimed at targetT2 can be formed by the military activities for target T2, as shown in Figure 5.Figure 5
MAV/UAV collaborative combat network aimed at targetT2.Table7 shows the operation loops and the capability and length results aimed at target T2.Table 7
Energy and length of operation loops aimed at targetT2.
Number
Operation loop
Number of nodes
Length of operation loop
Capability of operation loop
1
T2-S2-S1-D2-I1-T2
5
0.1693
0.8442
2
T2-S2-S1-D2-I2-T2
5
0.2091
0.8113
3
T2-S2-D2-I2-T2
4
0.2275
0.7966
4
T2-S1-D2-D1-I1-T2
5
0.2375
0.7886
5
T2-S1-D2-I2-T2
4
0.2548
0.7751
6
T2-S2-D2-D1-D2-I1-T2
6
0.2613
0.7701
7
T2-S2-S1-D2-D1-D2-I1-T2
7
0.2308
0.757
8
T2-S1-D2-D1-D2-I1-T2
6
0.2818
0.7544
9
T2-S2-D2-D1-D2-I2-T2
6
0.3115
0.7324
10
T2-S1-D2-D1-I2-T2
5
0.3215
0.7251
11
T2-S2-S1-D2-D1-D2-I2-T2
7
0.2751
0.7235
12
T2-S1-D2-D1-D2-I2-T2
6
0.3359
0.7147According to equation (39), the comprehensive uncertainties of the operation loops aimed at targets T1 and T2 can be obtained, respectively. If these uncertainties are introduced in equation (40), the combat capability AOC for targets T1 and T2 can be obtained.The combat capabilities synthesized by the operation loops aimed at targetsT1 and T2 are calculated, respectively, as follows:
(63)AOCT1=exp−dOL1=exp−1∑j=1M1/dOLmj=exp−0.0226=0.9777,(64)AOCT2=exp−dOL2=exp−1∑j=1M1/dOLmj=exp−0.0210=0.9792.After analyzing the target weights, the overall combat capability can be determined. In this case, the weights of the two targets areωT1=0.7 and ωT2=0.3; thus, the MAV/UAV collaborative combat capability is calculated as follows:
(65)Y=∑i=12ωTi⋅AOCTi=0.7×0.9777+0.3×0.9792=0.9781.


## 4.4. Analysis of the Result

(1)
Influence of the node in the operation loop on the combat capability: according to Table5, when considering edges 1 to 4, the reconnaissance and detection capabilities of unmanned reconnaissance aircraft S2 are superior to those of S1; when considering edges 11 to 12 and 11 to 16, the command and detection capabilities of manned command aircraft D1 are superior to those of D2; and when considering edges 21 to 24, the fire strike capability of manned combat aircraft I1 is highly similar to that of the unmanned combat aircraft. Therefore, considering such factors as the manned aircraft cost and pilot safety, an unmanned combat aircraft should be selected as much as possible to execute missions.
(2)
Influence of the operation loop length on the combat capability: the observations listed in Tables6 and 7 indicate that the length of the operation loop has a negative relation to its combat capability, which means that a longer operation loop has a lower combat capability. Each equipment in the operation loop brings a time delay, which becomes longer with more equipment, thereby influencing the combat capability of the overall operation loop.
(3)
Influence of collaborative combat on combat capability: the length of operation loops 1 and 2 is greater than that of 3 and 4. Thus, according to the previous conclusion, the combat capability of operation loops 1 and 2 should be inferior to that of 3 and 4; however, the opposite is true. The reason is that during the detection of targetT1 with 1 and 2, unmanned reconnaissance aircraft S2 transmits its information to manned aircraft S1. S1 conducts reconnaissance of an enemy target and integrates information from both sides, which significantly reduces the information uncertainty of target T1. Thus, the combat capability of 1 and 2 does not decrease due to the greater operation loop length but instead increases, which reflects the emergent properties and synergy of the combat systems.


## 5. Conclusion

This work models an MAV/UAV collaborative combat system network with a formal representation of the nodes and edges in the system. A capability assessment method and process for collaborative combat is introduced based on information entropy. The combat network modeling and corresponding capability assessment methods are verified by examples. The information entropy and operational capability of the collaborative combat network are calculated, the final combat capability evaluation index is obtained, and the operation loop capability is analyzed. The suggested method allows for a fast and reliable evaluation of the combat capabilities of different MAV/UAV systems as well as for the rapid identification of the key assets and issues that can influence the combat capabilities of such systems. The results of this research are expected to be supplementary to previous research. The new method is useful to the development of collaborative combat system.



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*Source: 5301752-2018-12-05.xml*