An operational effectiveness evaluation method of the swarming UAVs air combat system

. In this paper, we propose an operational effectiveness evaluation method of the swarming UAVs air combat system. The system network model is firstly established before the evaluation. We divide the edges in the network into nine types according to the Generalized Operation Loop and give the edge attribute of operational information entropy based on node attributes. When calculating the system operational effectiveness, we focus on the striking ability and propose the concept of Operation Loop Capability to represent the target-attack effectiveness of a certain operational loop, which can be calculated from the edge operational information entropies. We can get the combat effectiveness to a certain target from the Operation Loop Capability, and the combat effectiveness of the swarming UAVs air combat system is represented by the sum of the striking capabilities to all targets. Finally, the scene of swarming UAVs air combat is taken as a case study to apply and verify our evaluation method. This paper gives a quantitative perspective on swarming UAVs combat system assessment and can help to analyze the contribution of UAVs and other weapons in the system.


Introduction
four types [4] [5]. The research team in National University of Defense Technology proposed a network description and evaluation method of the weapon system called Operation Loop (OL) [6]. They divided the system weapons into sensors, decision-makers, attackers and targets, which provided a good perspective for combat system modeling and evaluation.
Based on the present studies on military systems, in this paper, we propose an operational effectiveness evaluation method of the swarming UAVs air combat system through network modeling. This work gives a new perspective for modeling and assessing the swarming UAVs air combat system quantitatively.

The concept of Generalized Operation Loop (GOL)
The concept of Generalized Operation Loop (GOL) is based on Operation Loop (OL). Tan Yuejin firstly proposed OL theory and defined the combat process as a closed loop consisting of one or more sensors, deciders, attack weapons and targets [6]. In the swarming UAVs combat system, in addition to the basic relationships in OL, there may be more relationships among the same kind of weapons. We add these relationships to the standard OL theory and define it as Generalized Operation Loop.
Definition 1: Generalized Operation Loop (GOL) is a modified closed loop based on traditional Operation Loop (OL), besides the cycle of sensors (S), decision-makers (D), attackers (A) and targets (T), it contains more weapon relationships, including the information sharing relationships between sensors, the coordination of command and control relationships between decision-makers, and the autonomous coordinated attack relationships between attackers.

Nodes definition
In the system network, the weapons are abstracted as nodes and can be classified as Where, , , , S D A T represents the weapon of sensor, decider, attacker and target entity respectively. The attributes of the four types of nodes are set in figure 3-6.

Edges definition
The types of edges represent different relationships between S, D, A and T nodes. This part aims to find out all the possible relationships (edge types) among the system weapons and give corresponding edge attributes for further effectiveness evaluation. During the modeling process, we mainly consider the information sharing and the complex communication relationships between UAVs.

Edge types
As shown in table 1, we carefully analyzed the relationships between S, D, A, and T, and the edges with practical meanings are listed.

One-way Directed
The command nodes can control the actions of attack weapons and sensor devices.

One-way Directed
This edge type represents the feedbacks of battlefield information to the decision nodes.

A T 
One-way Directed It represents the attack task to the target.

One-way Directed
The information of the targets can be detected, and it means the information flow from targets to sensors.

Bidirectional
This edge means the command cooperation between the decisionmakers.

Bidirectional
It mainly represents the information sharing between the reconnaissance UAVs in the combat process.

Attack coordination edge
It mainly represents the attack cooperation between the attack UAVs in the combat process.

Edge attribute
For the combat effectiveness evaluation, we define the edge attribute of the operational information entropy using the nodes attributes data of S, D, A and T. In 1948, Shannon proposed the concept of "information entropy" [7] and he described the information entropy as ( ) lg ( ) In the combat process, the low operational information uncertainty (also information entropy) means the better knowledge of the battle situation, which will help to get better combat effectiveness. Thus, we will use the information entropy to make the combat effectiveness evaluation and give the following modified edge operational information entropy definition.
Definition 2: Edge operational information entropy is used to reflect the information uncertainty of the information flow in the combat network, signifying the control and knowledge of battlefield situation, and is defined as e h .
Supposing that the edge e connects the nodes of S1 and S2, then ( 1, 2,..., ) i x i n  represents the comprehensive index calculated from the attributes of S1 and S2. n is the number of i x and i w is the weights of i x . i f is a membership function to guarantee . For different types of edges, there is a subtle difference in the number of i x and its calculation method, thus the edge operational information entropies will also be different slightly. Here we just take the S S  edge for example and give its edge operational information entropy calculation method. Supposing that there are two reconnaissance UAVs S1 and S2, which are all sensor nodes (S) and their attributes are shown in figure 3. 1 x is set to mark whether there is a communication connect between the two UAVs, the information capacity of the communication link is set to be 2 x , the information quality of the communication link is 3 x , and 4 x means the information transmission delay, then 1  where, 1 2 S S d means the distance of UAV S1 and S2, 1 j s and 2 j s represent the attributes of node S1 and S2, as figure 3 shows. i w is the weight of i x . 1 2 , e S S h is the operational information entropy of the edge S S  , meaning the information uncertainty and reflecting the combat effectiveness.

The operational effectiveness evaluation for the swarming UAVs air combat system
Based on the above network model, we put forward the concept of Operation Loop Capability and evaluate the target-attack effectiveness of the swarming UAVs air combat system. Definition 3: Operation Loop Capability is an index to quantify the impact of a certain Operation Loop (both standard and generalized loop) to a particular target in the combat system network.
As is mentioned in 2.4.2, the edge operational information entropy is a measure of the combat information uncertainty. A low operational information entropy means smaller information uncertainty of the target and will lead to stronger combat capability. Therefore, there is an inverse relationship between the information entropy and the combat capability. Hence Supposing that an attack is launched to target p , the number of participated operational loops is r , then the striking effectiveness to p is equal to the sum of the combat capabilities of all the corresponding operational loops. Namely, where l is the number of the targets in the system,

Case study
In this part, we take the attack to enemy ground command centers and infrastructures as an example.

Network model
To build the system network model, we have to figure out all the combat weapons and clarify their types. The weapons in the swarming UAVs air combat scene are listed in table 2.  The second step of the network model is to determine edges among the above weapons. The attack weapons undertake the combat mission to the enemy and the strike relationships are as follows:

Operational effectiveness evaluation
The effectiveness of the swarming UAVs air combat system ( C ) is defined as the sum of the striking capabilities to all targets, so we have to firstly calculate the operational effectiveness to a certain target. Just take the target of "Antiaircraft gun launch location" as an example, table 4 shows its attribute data. Notably, all the weapon attributes' (as figure 3-6) data is from relevant literatures or Internet, and due to the space limitation, we didn't list all the data.  (16) Although the proposed system combat effectiveness index is a figure and sometimes cannot be certified, it provides a quantitative method of assessing the swarming UAVs combat scene. Besides, it may live a foundation for weapon contribution or importance evaluation by changing node quantities.

Conclusion
In this paper, we propose an operational effectiveness evaluation method of the swarming UAVs air combat system. Before the effectiveness evaluation, the system network model is firstly established. Considering the unique weapon relationships in UAVs system, the concept of Generalized Operation Loop (GOL) is put forward and the edge operational information entropy is proposed to reflect the information uncertainty and combat effectiveness based on the network nodes attributes. As for the system operational effectiveness evaluation, we mainly focus on the striking capability and give the concept of Operation Loop Capability to evaluate the system target-attack effectiveness, which can be calculated from the edge operational information entropies. The combat effectiveness of the swarming UAVs air combat system is represented by the sum of the striking capabilities to all targets. Finally, the scene of swarming UAVs air combat is taken as a case study to apply and verify the proposed operational effectiveness evaluation method. It provides a good quantitative perspective for swarming UAVs system performance assessment and can help to evaluate weapon contribution or importance.
In the future works, we will make a further analyzation of the equipment importance in the system and their influence on the network structure invulnerability.