Knowledge-oriented modeling for influencing factors of battle damage in military industrial logistics: An integrated method

Xiong Li, Xiao-dong Zhao, Wei Pu

Military Exercise and Training Center, Army Academy of Armored Forces, Beijing 100072, China

Keywords:Battle damage Industrial logistics Entity-relationship approach Social network analysis Agent-based simulation

ABSTRACT Modeling influencing factors of battle damage is one of essential works in implementing military industrial logistics simulation to explore battle damage laws knowledge.However,one of key challenges in designing the simulation system could be how to reasonably determine simulation model input and build a bridge to link battle damage model and battle damage laws knowledge.In this paper,we propose a novel knowledge-oriented modeling method for influencing factors of battle damage in military industrial logistics, integrating conceptual analysis, conceptual modeling, quantitative modeling and simulation implementation.We conceptualize influencing factors of battle damage by using the principle of hierarchical decomposition, thus classifying the related battle damage knowledge logically. Then, we construct the conceptual model of influencing factors of battle damage by using Entity-Relationship approach, thus describing their interactions reasonably. Subsequently, we extract the important influencing factors by using social network analysis, thus evaluating their importance quantitatively and further clarifying the elements of simulation. Finally, we develop an agent-based military industry logistics simulation system by taking the modeling results on influencing factors of battle damage as simulation model input, and obtain simulation model output, i.e., new battle damage laws knowledge,thus verifying feasibility and effectiveness of the proposed method. The results show that this method can be used to support human decision-making and action.

1. Introduction

Nowadays, industrial logistics management has been a hot research issue in production management and industrial engineering. As a military application field of industrial logistics, military industrial logistics is related to wartime application of industrial logistics, in which battle damage is a key for decision makers, prediction of battle damage before battle and assessment of battle damage in and after battle are the core problems.

Battle damage refers to the equipment damage caused in the fight between opposed forces, consisting of two kinds, direct and indirect. The former means direct consequences of the opponent weapons systems,for example,the engine of a tank being damaged due to enemy's strike. The latter means collateral damages caused by involving in the battle activities,for example,the track of a tank being damaged owing to obstacles on the battlefield.Battle damage is mainly caused by man-made factors,that is,influencing factors of battle damage essentially reflect human behavior. When one explores battle damage laws knowledge,he must disclose influencing factors of battle damage firstly by rational and scientific data and knowledge management. Thus, problems to be resolved form:which factors can influence battle damage and which are the leading influencing factors? They are complicated problems,because equipment damage is the consequence of multiple influencing factors. They interact mutually and form a typical complex system.In fact,battle damage is influenced by some human factors such as combat mode, operational mission and logistics support.Accordingly, these aspects increase difficulties to modeling for influencing factors of battle damage in military industrial logistics,since battle damage is a key for decision makers when planning and performing military industrial logistics. In other words, decision makers need to construct an appropriate and useful model and method, with following goals: (1) to describe the causes and influencing factors of battle damage; (2) to illustrate the structure of influencing factors of battle damage; (3) to find the important influencing factors of battle damage; (4) to explore the intrinsic functional interactions of influencing factors of battle damage; (5)to support military industrial logistics simulation for obtaining new battle damage laws knowledge.

From the point of view of modeling and simulation, the abovementioned modeling problems are essentially embodied in the following aspects:(1)conceptual analysis on battle damage and its influencing factors,that is,what is battle damage and how it comes into being, and we can refine influencing factors of battle damage into the concept of what level to understand according to the needs of research; (2) conceptual modeling on influencing factors of battle damage,that is,what conceptual model can we construct to determine the composition of influencing factors of battle damage;(3) quantitative modeling on influencing factors of battle damage,that is,how to find out the core factors on the basis of mastering the composition of influencing factors,and how to find out appropriate simulation input conditions to support subsequent simulation implementation; (4) simulation experiment on influencing factors of battle damage, that is, on the basis of simulation model input,how to carry out military industry logistics simulation to demonstrate the formation of battle damage and the interaction mechanism of influencing factors, from which new battle damage laws knowledge is deduced and generated.

Despite the lack of systematic research on battle damage laws knowledge, we classify the existing methods on modeling influencing factors of battle damage into three categories: formal semantics, object-oriented methods and analytic methods. All the previous methods have shown benefits for the purpose they were conceived.However,they did not specifically focus on modeling for influencing factors of battle damage in military industrial logistics,due to the difficulties that are different from common social and technical systems. Thus, knowledge-oriented modeling process was not taken into consideration.Although some current methods have been used in military fields, they can not meet the requirements of modeling for influencing factors of battle damage usually. For example, object-oriented methodologies and concepts are unable to effectively model the tactics of entities involved in complex battlefield systems, which require better problem decomposition, more powerful abstraction mechanism and better representation of organizational hierarchy [1]. As an important analytic method, linearization, which “l(fā)inearizes” military problems to derive an analytical solution,comes at the price of realism[2]. In terms of simulation models, agent-based simulation for industry logistics has attracted the interest of researchers [3-7].However, there are still a lot of difficulties when the models are designed and implemented, since agents and multi-agent systems are complex and have many properties. It is impossible to take all factors into account [8]. Moreover, most current models and systems can not provide enough detail to examine important dynamics in military industrial logistics, i.e., the intrinsic functional interactions of influencing factors of battle damage due to military entity interactions. How to clarify simulation model input with more conveniences and higher effectiveness is a technical challenge.

Aiming at the challenge, we propose the definitions of equipment damage and battle damage, and describe the causes and influencing factors of battle damage. Then, we present the conceptual model by Entity-Relationship (ER) diagrams and achieve quantitative extraction of the important influencing factors by social network analysis,as well as perform agent-based simulation by taking these influencing factors as simulation model input. Thus,we discuss an integrated, knowledge-oriented method of influencing factors analysis of battle damage in military industrial logistics. The results show that our method can be used to solve actual logistics analysis problems and provide scientific references for logistics planning and decision-making.

The remainder of this paper is structured as follows. Current related work is introduced in Section 2. Problem description and research methodology are presented in Section 3. Conceptual analysis and conceptual modeling for influencing factors of battle damage are proposed in Section 4. Quantitative model of influencing factors of battle damage is illustrated in details in Section 5.In Section 6, the proposed method is applied to a case study to show its application in military industrial logistics simulation.Section 7 discusses the conclusion and future work.

2. Related work

2.1. Industrial logistics and military industrial logistics

Industrial logistics plays a major role in providing a competitive advantage for companies in a networked economy and market[9].Industrial logistics is concerned with the physical inflow and outflow of goods and associated services [10]. In terms of analysis and assessment on industrial logistics,Tang and Veelenturf discuss the strategic role of logistics for creating economic,environmental and social values in the industry 4.0 era [11], Aziz et al. analyze some research activities on industrial logistics, such as logistics service, logistics performance, green logistics/reverse logistics, logistics management,logistics systems and logistics models[12].In terms of modeling and simulation on industrial logistics,Kang et al.focus on provision of idle logistics resource sharing for promoting logistics product service system and build an integer programming model for logistics product service allocation [13], Chen, Wu and Hsu develop a pricing model for alleviation of congestion in ecommerce logistics and demonstrate its usability in dealing with logistics congestion with numerical illustration [14], Trappey et al.provide a field tested method for deriving industrial logistics hub reference models for manufacturing based economies [15], Furmann et al. describe interconnection of the real logistic elements with interactive projection planning system and process simulation[16], Lang et al. review mixed reality in logistics and discuss the application potentials of Microsoft HoloLens?in this field [17].Military industrial logistics is intended for military purposes,and is used to meet wartime demands[18,19].In the information era,how to make scientific logistics planning and forecasting has attracted high attentions from logistics departments at all levels. This is not only the focus of the military, but also the important basis for planning and operations of manufacturing and service industries.It is even a great event of national production and industrial system construction.

2.2. Battle damage and influencing factors analysis

Previous researches have been conducted on equipment damage. Nowlen et al. discuss some work associated with the investigation of equipment damage induced by the application of fire suppressants[20].Schober,Loer,and Schwarte report a unique case of airway obstruction due to unexpected equipment damage [21].Xu et al.provide a potential approach to properly evaluate damage accumulation in practice [22].Focusing on accident hazards, Necci et al.construct a model for process equipment damage probability assessment due to lightning[23].Gomes and Diego discuss an issue of human hazards and equipment damage [24]. However, so far,most current studies are limited in peacetime equipment damage.Although some researches relate to the topic of battle damage[25,26], as a whole, in most cases there are almost no systematic studies of battle damage laws knowledge.

Saulwick and Trentelman define social influence and answer questions concerned with social influence by providing a formal definition [27]. However, this work lacks quantitative analysis of influence values, and thus is inconvenient to final application in managing organizational knowledge. In terms of industrial logistics, some researchers have discussed the issue of influencing factors [28-31]. Glock et al. conduct a systematic review of human factors in industrial and logistics system design[32].Unfortunately,current research usually lacks analysis on influencing factors of battle damage. Moreover, there is deficiency in research on the relationships model of influencing factors of battle damage.

2.3. Qualitative and quantitative modeling

The essential means of conceptual modeling is mainly qualitative modeling.Conceptual model is the first abstraction of an actual system.It serves as a reference framework for the development of simulation system, extracts the basic information of important entities and their main actions and interactions related to task execution,and states the content and internal representation of the model. Through qualitative modeling, developers can obtain detailed information of the simulated actual system problems or processes,so as to facilitate object analysis and model construction of the simulation system.Thus,domain experts can understand the internal structure of the simulation system, so as to verify the system. As an effectual method of identifying key application objects and their relationships [33], qualitative modeling has been widely used in recent years, such as in the fields of information supply[34],enterprise resource planning[35],and business models in industrial networks [36].

As far as qualitative models of influencing factors are concerned,they can be summarized as formal method and object-oriented method. As mentioned earlier, Saulwick and Trentelman's approach is a typical formal method [27]. However, it is inconvenient only by formalizing semantics to implement a nuanced representation on social interactions. Object-oriented method are widely used in system analysis and modeling.For example,Koyama and Suzuki propose the real object-oriented communication method[37].Bergesio et al.propose an object-oriented model able to describe any kind of smart object [38]. Object-oriented models are also used in construction method selection in buildings[39]and cost-based scheduling method [40]. As another useful objectoriented method, the Entity-Relationship (ER) approach plays a fundamental role in conceptual modeling [41,42]. For system analysis purposes,the ER model and its accompanying ER diagrams are the tools used mostly [43-45]. Since an ER diagram is a visual representation of different entities within a system and how they relate to each other, this method can be applied to modeling and analysis of complex process system similar to battle damage factors.

Quantitative modeling, sometimes referred to as mathematical modeling, is the use of mathematical language to describe the model.Quantitative calculation is used to describe the relationship or causality among the variables of system.A quantitative model is further abstracted on the basis of simplification of a qualitative model, quantifying and describing the relationship between the relevant task space elements, laying the foundation for building computer simulation model. As for the quantitative modeling of influencing factors, the traditional methods commonly used are mainly the analytic hierarchy process (AHP) and Lanchester equation. They all belong to the principles of linearization in essence.

As a structured technique for organizing and analyzing complex decisions,AHP has been widely valued by researchers.For instance,the AHP is used to valuate decision making for sustainable development [46], distributed available Internet of Things databases[47], and respiratory protection program in petrochemical industries [48]. Of course, this method needs the judgments of a decision maker.Lanchester equations theory has been widely used to predict the results of military operations by the quantitative analysis [49-51]. However, Lanchester-type combat models need big sample spaces since they are based on differential equations.With the recognition of the importance of complex networks,social network analysis has been proposed and used in this research area.Social network analysis, which focuses on relationships among social entities,and aims to investigate social structures and uncover the patterning of social interactions, has emerged as a key technique in modern sociology and been widely used in industrial engineering and technological forecasting in recent years [52,53].Because of the characteristics of describing social structures and modeling a group of individuals and their relationships, social network analysis method can be used for quantitative analysis of influencing factors, mainly extracting important influencing factors.

2.4. Agent-based industry logistics simulation

With high flexibility in design, agents are used to map intelligent entities in a real world system. In recent years, many agentbased models have been developed. Agent-based simulations can be performed to identify results such as the percentage of procurement covered and the number of tasks generated [54], to observe the effects of ordering parameters on a supply chain [55],to study horizontal cooperation in logistics and transportation[56],and to explain the related problems of scheduling and synchronization on intelligent e-commerce logistics [57]. From the previous works [54-59], we can sum up the important role of agent-based industry logistics simulation. The attributes (variables) of agents can be used to describe multi-agent interactions, which represent social relationships of entities in industry logistics system.Thus,we can explore actual industry logistics system behaviors by running agent-based industry logistics simulation. Note that these attributes (variables) and interaction model depend on simulation inputs.However,in the actual design of agent-based model systems,simulation inputs are not clear to some extent,and sometimes they are too complicated, especially for military system simulation.

3. Problem description and solution approach

3.1. Problem description: solution requirement

As a multi-technology field in production management and industrial engineering, industrial logistics focuses on planning and forecasting of equipment and maintenance materials. Military industrial logistics is the general term of support measures and corresponding activities that are adopted and implemented by national industrial system to common weapons, weapon systems and military technical equipment in order to fulfill various tasks.These measures and activities mainly cover all support behaviors,including production, planning & control, allocation, storage &supply, maintenance and management by mobilizing and employing manufacturing and service industries. Military industrial logistics can be divided into peacetime logistics and wartime logistics.The former mainly includes organizing and implementing military industry system construction, general equipment maintenance, technical transformation and integrated supporting reforms. Its main objective is to ensure comprehensiveness of military industry system, meet needs of army construction and training for preparedness against war, as well as afford logistics support for military operations other than war (MOOTW). The latter mainly includes organizing and implementing allocation support, maintenance support, technical improvement and operations management. It aims to maintain and recover quantitative and qualitative level of military equipment,provide efficient and stable logistics for a force, and ultimately accomplish tasks of operations.

One of key tasks of military industrial logistics is to dispose damaged equipments. In wartime, equipment damages come into being and engagement of the opposed forces inevitably engenders battle damages [60]. Thus, in this paper, the influencing factors model of war damage is taken as the research object.Our research focuses on the following three aspects: (1) How to conduct conceptual analysis and conceptual modeling of the impact factors of war damage, and then refine and form its internal relationship model from the aspects of knowledge classification and expression.(2)How to find out the key influencing factors of battle damage,so as to find the relationship between direct battle damage simulation input and its output.(3)How to use the above knowledge of battle damage influencing factors model to form the transformation mechanism from simulation input to simulation output. Through simulation execution, the output of simulation model is obtained,thus new battle damage laws knowledge is obtained.

3.2. Solution approach: research methodology

To attack this critical challenge, we propose a knowledgeoriented modeling method of influencing factors analysis of battle damage. Our method is completed firstly by a definition and description of some concepts on battle damage,their relationships and attributes, subsequently by application in an agent-based simulation system which is used to solve actual battle damage analysis problems and provide scientific references for logistics planning and forecasting.Its general process is illustrated in Fig.1,including the following steps.

(1) Conceptual analysis. Specific objective of this step is to identify and classify knowledge on battle damage. In this work, we need to perform the first conceptualization from real system, i.e., form concepts of equipment damages and obtain categorised knowledge on battle damage, which lays the foundation for follow-up work.

(2) Conceptual modeling. This work is related to knowledge representation and has the potential to assist the development of new computerized methodologies and industrial engineering techniques. By this work, we can fulfill the second conceptualization from categorised knowledge on battle damage and construct the conceptual model for influencing factors of battle damage to represent entities,attributes and their inherent functional relationships.

(3) Quantitative modeling. This work means quantitative description and handling of influencing factors of battle damage,aiming to finding the leading influencing factors by quantitative extraction. These results can be used in the agent-based military industrial logistics simulation system design as model input.

(4) Simulation implementation. In an agent-based simulation system, agents are designed to represent the entities'behavior. Therefore, the objective of simulation implementation is to verify feasibility and effectiveness of our method. By the simulation results, we can explore further battle damage laws knowledge.

Compared to related modeling methods, the proposed method has more conveniences and advantages as shown in Table 1.In this study, we use war statistics to collect historical combat data and introduce data driven engineering to form a systematic procedure of knowledge-oriented modeling. Note that our method has three features that form advantages over current other influencing factors analysis methods. First, it is an integrated procedure with conceptual analysis, conceptual modeling, quantitative modeling and simulation implementation Second,it is a knowledge-oriented paradigm.Integration of analysis,modeling and simulation,model verification, validation and accreditation (VV&A) is achieved to classify,represent and describe knowledge on battle damage.Third,it is a common approach.Although the research object in this paper is battle damage in military industrial logistics, the method is generic and practicable to other production management fields.

4. Conceptual analysis and conceptual modeling

4.1. Conceptual analysis

4.1.1. Equipment damage

Equipment damage generally refers to a fault event of equipment that is generated in the entire military operation and needs to be processed and eliminated by military industrial logistics. General speaking, there will be a series of maintenance-oriented military industrial logistics demands because of equipment damages.Therefore, processing and eliminating equipment damages is an important direct reason for developing military industrial logistics.Generally, equipment damages can be divided into battle damage and non-battle damage according to the damage modes. Battle damage will be introduced in Subsection 4.1.2.Non-battle damages include natural losses, random failures of equipment, severe environment-induced damages and manual operational errors.

4.1.2. Battle damage

Battle damage is a unique mode of wartime equipment damage.Further, battle damage can be divided into firepower damage and electronic damage, according to its generation mechanism. The causes and influencing factors of battle damage can be described simply as Fig. 2.

4.2. Conceptual modeling

4.2.1. Modeling method

Because of the intrinsic complexity and dynamic nature of military industrial logistics systems, influencing factors of battle damage involve the functional interactions among some battlefield areas,tactical procedures and logistics infrastructures.To construct the conceptual model of influencing factors,we invite four experts to analyze and evaluate related factors and their functional interactions, and present graphical notation representation for the model.

When consulting with experts, we absorb the principles of the main functional areas (MFA) method. Since a person, area or department which carries out a particular function can be viewed as functional area in an organization or management system, the MFA method has been widely used in both business organizations[61-63]and regional management[64-66].In the former field,the purpose of MFA analysis is to define the relationships of different functional areas and ensure that all important business activities are carried out efficiently, thus implementing the strategy in a business organization and achieving the business objectives[61-63].In the latter field,using MFA,researchers can more easily explore collaborative regional management mechanism for ecoenvironment and socioeconomic development [64-66]. According to the general procedure of operational command, after receiving superior operational order, the commander and command agency have to analyze and identify various objective situations and corresponding influences related with operational mission. Key attention shall be paid to comprehensive analysis,judgment and conclusions of enemy's situation, our situation and battlefield environment. On this basis, they shall determine action objective and combat mode, formulate alternative programs,evaluate and optimize judgments,and finally make decisions.Thus,we regard the above elements as the objectives and subjects of MFA for influencing factors of battle damage,respectively.As a result,we provide key information for the experts to analyze and evaluate these factors. Through this kind of evaluation survey, the invited experts quickly reach an agreement. They approve the causes and influencing factors of battle damage illustrated in Fig. 2. In other words, four groups of factors, i.e., operations, battlefield environment, enemy's situation and our situation, are determined as elements of MFA for influencing factors of battle damage.In addition,the invited experts also propose classification for them and define corresponding functional interactions.

Fig.1. Knowledge-oriented modeling process of influencing factors of battle damage in military industrial logistics.

To further mark off the functional interactions,in this paper the conceptual model of influencing factors of battle damage is built by using ER approach represented by ER diagrams. The conceptual model of ER diagrams can provide an insight to extracting the important influencing factors of battle damage. In fact, the presented conceptual model here is the input of the following quantitative model in Section 5.

As one of the main diagrammatic representations of a conceptual data model, an ER diagram consists of *-entity type, *-relationship type and *-attributes.

*-entity type with key attributes is called strong entity, while*-entity type without key attributes is weak entity. They are expressed by a rectangle and a double-line rectangle in an ER diagram, respectively. Name of an entity is denoted in the rectangle framework.

Table 1 Comparison of related methods and our method.

Fig. 2. Causes and influencing factors of battle damage.

*-relationship type is expressed by a diamond in an ER diagram.Name of relationship is written in the diamond framework. Relationships are connected with related entities by undirected edges.

*-attributes of an *-entity is useful to define specific attributes for different subsets of entity instances. Similarly, *-attributes of a*-relationship type are useful to define attributes for multiple relationship instances between the associated entity types [45].Multiple-valued attribute, derived attribute, and key attribute are expressed by a double-line oval, a dotted oval and an oval,respectively. Name of attribute is denoted with underlines. If an attribute has sub-attributes, it is a composite attribute and is expressed by connection of an undirected edge between ovals.

4.2.2. Conceptual model

Based on Fig.2 and the above process,four groups of influencing factors of battle damage in assault of a combined army force are chosen as follows. More importantly, through the analysis and evaluation from experts, these influencing factors and corresponding functional interactions have been further differentiated.

(1) Operations.Operations factors include combat type,combat mode, operational mission and operational activities. In the ER diagram,the first three are strong entities and the last one is a weak entity.

(2) Battlefield environment. Battlefield environment is composed of natural environment and artificial environment. Natural environment includes terrain type (key attribute), vegetation distribution, hydrological distribution,meteorological conditions and road conditions. Artificial environment includes position construction (key attribute),obstacle settings and electromagnetic environment. In the ER diagram,natural environment and artificial environment are strong entities, whereas battlefield environment is a weak entity. The rests are attributes.

(3) Enemy's situation. Factors related with enemy's situation include enemy's equipment, enemy's military strength and enemy's equipment support.Enemy's equipment consists of equipment type (key attribute), equipment quantity, information ability, strike ability, maneuver ability and defense ability. Enemy's military strength includes code designation(key attribute), command ability, tactics application ability,training degree, distribution of personnel and morale. Enemy's equipment support includes equipment support code designation (key attribute), enemy's technical support and enemy's allocation support. In the ER diagram, enemy's equipment, enemy's military strength and enemy's equipment support are strong entities,while enemy's situation is a weak entity. The rests are attributes.

(4) Our situation.The influencing factors of our situation include our equipment, our military strength and our equipment support. Their attributes are same with those of enemy's situation. In the ER diagram, our equipment, our military strength and our equipment support are strong entities,and our situation is a weak entity. The rests are attributes.

In assault of a combined army force, artificial environment is mainly set by the enemy to retard our military actions.Therefore,it is one part of enemy's situation. Moreover, *-relationship types of entities in the selected influencing factors are mainly generated by combat interactions. Thus, we get a list of influencing factors of battle damage, as shown in Table 2.

Accordingly,we can further build the final conceptual model of influencing factors of battle damage for a combined army force by ER diagram modeling method, as shown in Fig. 3.

5. Quantitative modeling

Although equipment damage is caused by many factors in wartime, different factors have different weights when studying a specific problem.As a result,the influencing factors shall be further analyzed according to specificity of the problem. In the following text, some important influencing factors of battle damage are extracted through a case of assault of a combined army force. In information war, a combined army force might suffer firepower attacks from the enemy that will cause damages of mechanical equipment and electronic equipment, and encounter electronic attack from the enemy that will cause damages to electronic equipment.Due to different mechanisms of firepower damages and electronic damages, there will be different influencing factors.Therefore,they are discussed separately in this paper.

5.1. Extraction of important influencing factors of firepower damage

Social network analysis characterizes networked structures in terms of nodes in the network (social entities) and the ties, edges,links or relationships (social interactions) that connect them. In a social network, centrality is an important concept that refers to a group of metrics that aim to quantify the “importance” or “influence”(in a variety of senses)of a particular node(or group)within the network. This character can be used to extract the important influencing factors of firepower damage in our study.

Based on obtaining the list of influencing factors of battle damage and corresponding functional interactions by conceptual modeling, we further consult experts to specify the internal relationships between influencing factors.On the advice of experts,we judge the logic relationship between any two influencing factors, one by one. If there's logic correlation between two influencing factors,the value is 1;otherwise,no value is assigned(or the value is 0). Thus, we can establish a relationship matrix of influencing factors of battle damage.The results are listed in Table 3,and Appendix A containing all data information, which are used as data-input of the subsequent social network analysis.

The influencing factors network of battle damage is formed from visualization by using social network analysis software UCINET,displayed in Fig.4.The overall connections of different influencing factors can be seen intuitively from Fig. 4. Battle damage, combat mode,battlefield environment,enemy's situation and our situation occupy central positions, indicating that they play the key role in the whole network system.This conforms to the judgment content in command program.

In social network analysis, centrality is a structural location index that evaluates node importance, status advantage and social reputation. It discloses whether the node is in the central position of network. There are many centrality analysis methods, mainly including degree centrality, closeness centrality and between centrality. Degree centrality analyzes individual or overall connection based on node degree.Degree centrality is the major index.Higher degree centrality implies closer connection between the individual and other individuals and higher importance of the individual in the network. Degree centrality can be divided into absolute centrality and relative centrality according to computing methods,and divided into individual centrality and overall centrality in view of analysis objects.In this paper,degree centrality is applied to study effects of the influencing factors on firepower damages. Higher node centrality means stronger effects of the influencing factor.Meanwhile, absolute centrality and relative centrality of every influencing factor are analyzed.

The absolute centrality of an influencing factor can be calculated as

where niis the No.i influencing factor,xijis a numerical value(0 or 1) that represents whether there's direct connection between the No. i influencing factor and the No. j influencing factor, d and CDrepresent the absolute centrality of a certain influencing factor.

The relative centrality of an influencing factor refers to the ratio between its centrality and the total number of connections.Different from absolute centrality, relative centrality is a standardized data and can be used directly in contrast analysis of different influencing factors in the same network.In an undirected graph, the relative centrality of an influencing factor can be expressed as:

where niis the No.i influencing factor, N represents network size,i.e., number of the influencing factors, d represents the absolute centrality of a certain influencing factor,while C’Dand d′represent the relative centrality of a certain influencing factor.

A quantitative analysis on centralities of the influencing factors network of battle damage is performed by UCINET software. The results are listed in Table 4.

It can be seen from Table 4 that the first 20 influencing factors of battle damage have high absolute centrality(≥5)and high relative centrality (≥9). They can be regarded as important factors. The relationships among them are illustrated in Fig. 5.

Table 2 Classification for influencing factors of battle damage.

Fig. 3. ER diagram model of influencing factors of battle damage.

Table 3 Relationship matrix of influencing factors of battle damage.

From the above study, we extract the important influencing factors of battle damage in assault of a combined army force.Firstly,influencing factors of firepower damage are analyzed deeply. Subsequently, repeated indices are combined and simplified to determine the important influencing factor indices as follows.

(1) Combat mode.As previously described,different equipment damage laws come into being because of different combat modes. Meanwhile, different influencing factor indices can be extracted from different combat modes.Therefore,we can discuss battle damage laws under a certain combat mode to increase the prediction accuracy of equipment damage. In this paper,assault of a combined army force is chosen as the certain combat mode.

Fig. 4. Influencing factors network of battle damage.

Table 4 Centrality analysis results of influencing factors of battle damage.

(2) Battlefield environment.It is the material carrier of the entire military operation.It is divided into natural environment and artificial environment. Key influencing factors vary for different operational missions. Therefore, they have to be analyzed thoroughly according to specific combat mode. In assault of a combined army force, terrain type, hydrological distribution and road situations in natural environment will influence traveling speed of equipment. Meteorological conditions and vegetation distribution will influence observation ability and firing accuracy of equipment. Since these five indices have high centrality in Table 4, they shall be considered comprehensively. In artificial environment, position construction and obstacle settings are determinants of combat intensity and duration.They shall be considered and analyzed carefully.

(3) Enemy's situation. It reflects involved equipment and soldiers of the enemy in the battle. It mainly includes enemy's equipment and enemy's military strength. Equipment type,equipment quantity and equipment attacking ability are the important factors related with enemy's equipment. Therefore, enemy's equipment can be estimated by firepower attacking ability of enemy's equipment.For enemy's military strength,it can be seen from Table 4 that tactics application ability and training degree of the enemy force have relatively high centrality and shall be quantified.

(4) Our situation. It reflects involved equipment and soldiers of our side in the battle. It mainly includes our equipment and our military strength,which are same with those of enemy's situation.

Fig. 5. ER diagram model of important influencing factors of battle damage.

In general, the important influencing factors of firepower damage in assault of a combined army force and their quantitative measures are listed in Table 5.

5.2. Extraction of important influencing factors of electronic damage

Similarly as the above process in extracting the important influencing factors of firepower damage, we achieve extraction of ones of electronic damage and obtain two important influencing factors by using the above extraction method. As for assault of a combined army force, these two important influencing factors ofelectronic damage and their quantitative measures are listed in Table 6.

Table 5 Important influencing factors of firepower damage and their quantitative measures.

Table 6 Important influencing factors of electronic damage and their quantitative measures.

6. Computer simulation

6.1. Design and implementation by simulation model input

Industry logistics simulation is actively being applied in production management and industrial engineering.Especially,multiagent system emerged, as a scientific area, from the previous research efforts in distributed artificial intelligence started in 1980s. Military industry logistics simulation centers on battle damage laws knowledge and needs influencing factors analysis of battle damage. Thus, we take an agent-based military industry logistics simulation system as a real-world example to show application of the above method and results of influencing factors analysis of battle damage.

Simulation model input is precondition in industry logistics simulation.Military industry logistics simulation using multi-agent paradigm needs simulation model input that can connect influencing factors of battle damage and agents mapped from logistics support entities. It may be more accessible in simulation system design to take those results of influencing factors analysis of battle damage as simulation model input. Internally the agents implement appropriate empirical and semi-empirical methods to describe their behavior and interaction with other agents [67].Based on our previous study in agent-based simulation[3-5,68],a computer simulation system for military industry logistics of a combined army force that plays as Red Force is developed. This system focuses on combat mode,battlefield environment,enemy's situation, our situation and their relationships. Application of the above extracted important influencing factors of battle damage canbe listed as Table 7.

Table 7 Application of important influencing factors of battle damage.

On information battlefield, military industry logistics system is composed of a geographically dispersed organization of heterogeneous elements. All elements are tied together by a communications network with command and control applied at tactical centers. These elements are multi-level logistics support entities,such as superior commander, logistics support element commanders, equipment support force, and logistics support element vehicles.In this agent-based simulation,these elements have been mapped into respective agents, for example, logistics support element vehicle →logistics support element vehicle agent, and logistics support element commander →logistics support element commander agent. In other words, it is platform-level simulation,meaning that the model granularity is single vehicle (platform).Thus, multi-platform interaction behaviors can be simulated to describe the generation process of battle damage.By implementing this platform-level agent-based simulation, we can observe interaction behaviors in military industry logistics system, analyze battle damage results, and explore further battle damage laws knowledge.

When designing the simulation system, we select an appropriate battle event from warfare experiments.As an effective way to test combat effectiveness in peacetime,war experiments with real equipment and real forces have been regarded as real fights by armies around the world and used to guide future warfare practice.Although this selected battle event was not a warfare between two hostile countries, it was a typical tactical fight between two opposed combined army forces wielding conventional weapons.It happened in RHZ region in northern China, a geographical region like plain and hilly area, in August 2011. Then, we draw on the principles of a statistical method and extract useful historical data on battle damage in military industrial logistics from this battle event.These data include static and dynamic data.The former,such as Number of useable equipments before combat and Number of useable parts before combat, can be obtained through military documents. The latter can be acquired by battlefield sensors and manual means. Usually, complex dynamic data need be collected manually and processed comprehensively by using templates.Although this process involves a lot of random variables,when we do this work, we focus on distribution of battle damages and statistical parts consumption data of Red Force,which are used as not only data-inputs to achieve data driven engineering in modeling,but also parameters to perform comparisons with simulation results. The designed template on battle damages and parts consumption consists of four sub-modules,as illustrated in Fig. 6.

Based on war statistics from collected historical real-world combat data, a simulation scenario for military industrial logistics of a combined army force is designed here. It involves settings of combat mode, battlefield environment, combat strength and objective mission, logistics resources and logistics strength.Specifically,on a plain with mild slopes,Red Force initiates assault to Blue Force from south to north, and Blue Force is deployed in northern defensive position to carry out positional battle of defending. With the advance of Red Force, battle damage occurs.Accordingly,logistics resources and logistics strength are scheduled to perform repair tasks.

The simulation system is implemented by Qt 4.7 graphic interface library and its interface is shown in Fig. 7. From Fig. 7, we can see the generation process of battle damage. At some point, the engine of No.1Y2L6 vehicle in Red Force was damaged because of Blue Force's strike,then,logistics support element vehicles received order from a logistics support element commander, subsequently reached the spot and repaired the damaged engine. In the simulation system, this multi-platform interaction mechanism is represented by multi-agent interaction process.

6.2. Simulation results and discussion

The system is run 30 times and the results are automatically recorded by Simulation Results Data subsystem. The simulation results on battle damage of a certain combined army force are shown in Fig. 8. In Fig. 8, NDE, BDR, PC and MPCPE represent Number of damaged equipments, Battle damage rate, Parts consumption and Mean parts consumption per equipment,respectively.

Derived from warfare experiment practice in the typical battle event, the obtained templated data on battle damages and parts consumption can be illustrated in Appendix B,in which(a),(b),(c)and(d)represent these data in four operational stages,respectively.Thus, we present comparisons between actual combat data and simulation data,shown in Fig.9.Fig.9(a),(b),(c)and(d)represent comparisons on NDE, BDR, PC and MPCPE in four operational stages, respectively.

The simulation results basically coincide with actual combat data, indicating high credibility of the results. Moreover, the conceptual model of influencing factors of battle damage described by ER diagrams builds a bridge between real military industrial logistics system and the simulation system. The ER diagram model and the corresponding influencing factors network of battle damage depict appropriately interactions of different elements. Especially,the extracted important influencing factors of battle damage reflect reasonably not only the corresponding operation functions of logistics support entities but also the simulation results of multiagent interaction running. This is a procedure of verifying each other.

Fig. 6. Template on battle damages and parts consumption.

Fig. 7. Agent-based military industrial logistics simulation system interface.

Fig. 8. Simulation results on battle damage of a certain combined army force.

For instance,from Figs.8 and 9 we can see that NDE and BDR in stage 1 are larger than others, and the parameters in stage 2 are second,while the parameters in stage 3 are the minimum.As far as PC and MPCPE are concerned, they are the largest in stage 1, followed by stage 2.Actually,according to the simulation scenario for military industrial logistics,in stage 1 Red Force is designed to carry out joint operations with firepower attacks and electronic attacks,which are the most complex and violent combat mode.Besides,in stage 1 it is very difficult for Red Force to acclimatize itself to new battlefield environment and enemy's situation. Stage 2 represents the battle phase of break through in which the intensity is only inferior to joint operations, while stage 3 means combat in depth with the minimum resistance from Blue Force.Of course,in stage 3,multi-dimensional defense tasks need to be completed simultaneously, and adequate spare parts should be carried accordingly.Thus,PC and MPCPE are ranked third in stage 3 and the smallest in stage 4.

Fig. 9. Comparisons between actual combat data and corresponding simulation data.

In a word, the simulation experiment proves validity of the method and results of influencing factors analysis of battle damage.Thus we can obtain some battle damage laws knowledge on different stages in a command cycle.For example,for a certain force it forms usually probable maximum battle damage during joint operations with firepower attacks and electronic attacks. The next is operation of break through.When a commander makes military industrial logistics planning and forecasting, he should highly emphasize these operations and try to provide adequate support resources.

7. Conclusion and future work

Influencing factors analysis of battle damage is the basis to master battle damage laws knowledge. Systematic study on influencing factors of battle damage lays a foundation for comprehension of the knowledge. It provides scientific references for prediction, allocation, usage and supplementation of equipment,materials and devices to support logistics planning and forecasting.

With consideration to actual needs of battle damage prediction and estimation in military industrial logistics, the conceptual model of influencing factors of battle damage is constructed in this paper. The important influencing factors are extracted reasonably.Validity of influencing factors analysis results is verified by a case study. Research results provide a design basis for developing models of battle damage simulation. Thus, an approach to exploring human behavior in military industrial logistics is presented. Compared with other current methods, our method has some characteristics: (1) establishing a qualitative conceptual model of influencing factors of battle damage by using E-R diagrams modeling method, thus giving a view to exploring the causation of battle damages; (2) extracting the important influencing factors of battle damage by building a quantitative social network model,thus forming a means of evaluating the influencing factors and their intrinsic functional interactions; and (3) presenting a real-world example of military industrial logistics simulation system design and implementation by taking the results of influencing factors analysis as input, thus building a bridge to link battle damage analysis and battle damage laws knowledge.Besides,our method has three advantages. (1) It is the first to offer researchers a systematic procedure for knowledge-oriented influencing factors analysis of battle damage in military industrial logistics. The specific characteristics of battle damage are considered and the corresponding resolutions are presented,thus forming a framework of military industrial logistics analytics. (2) It is a knowledge-oriented methodology. From knowledge classification,knowledge representation,extraction of the important influencing factors, to application, it centers on exploring battle damage laws knowledge, thus giving a view for scientific logistics planning and forecasting.(3)In this study,historical real-world combat data are collected and used to design our model, i.e., data driven engineering are introduced in model construction, thus proposing a novel industrial logistics modeling approach to exploring issues on industrial management, supply and support systems.

This analysis method will be perfected in future researches.Key attentions will be paid to display the nonlinear relationships of different influencing factors more scientifically and accurately. At the same time, the computer simulation system for logistics of a combined army force will be improved centering on function expansion in order to meet more requirements of military industrial logistics analysis and demonstration, and to provide better service for human decision-making and action.

Acknowledgement

This research was funded by National Natural Science Foundation of China (grant number 61473311, 70901075), Natural Science Foundation of Beijing Municipality (grant number 9142017), and military projects funded by the Chinese Army.

Appendix A. Relationship matrix of influencing factors of battle damage

Appendix B. Templated data on battle damages and parts consumption