Aviation Accident Causation Analysis Based on Complex Network Theory

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College of Air Traffic Management，Civil Aviation University of China，Tianjin 300300，P.R.China

Abstract:Accident causation analysis is of great importance for accident prevention.In order to improve the aviation safety，a new analysis method of aviation accident causation based on complex network theory is proposed in this paper.T hrough selecting 257 accident investigation reports，45 causative factors and nine accident types are obtained by the three-level coding process of the grounded theory，and the interaction of these factors is analyzed based on the“2-4”model.Accordingly，the aviation accident causation network is constructed based on complex network theory which has scale-free characteristics and small-world properties，the characteristics of causative factors are analyzed by the topology of the network，and the key causative factors of the accidents are identified by the technique for order of preference by similarity to ideal solution（TOPSIS）method.The comparison results show that the method proposed in this paper has the advantages of independent of expert experience，quantitative analysis of accident causative factors and statistical analysis of a lot of accident data，and it has better applicability and advancement.

Key words：aviation safety；accident causation；complex network theory；grounded theory；“2-4”model

0 Introduction

Air transportation system is a complex system with high safety requirements.The Annual Statistical Report on Aviation Safety in 2019 released by International Civil Aviation Organization（ICAO）［1］shows that with the rapid development of air transportation，the accident rate is also rising.Consequently，it is very important to improve aviation safety level through accident causation analysis.

The early research on the causation of aviation accidents focused on human factors.After the application of system science in the study of accident causation，some system accident models have been proposed，such as：Systems-theoretic accident modeling and process（STAMP）［2］，failure mode and effect analysis（FMEA）［3］and“2-4”model［4］.Besides，there are other methods to analyze the causation of aviation accidents.For example，a Bayesian network of aviation accidents is established to analyze the change of accident probability［5］.

The complex network theory is applied to the field of safety management.And the event analysis of systemic teamwork（EAST）methodology is proposed to analyze the aviation accidents［6］.The key risk factors of seaplane take-off and landing safety are identified and the accident prevention measures are proposed through the network attack experiments［7］.Based on the complex network and the cascading failure theory，a new accident causation model is proposed for the railway accidents analysis［8］.

In this paper，the causation of aviation accidents is analyzed by the complex network theory.Firstly，the aviation accident investigation reports are collected to classify and sort out the causative factors of aviation accidents based on the grounded theory［9］，and then，the causative chain of each accident is analyzed to determine the relationship between factors based on the“2-4”model［4］.According to the complex network theory，the causationanalysis network of aviation accident is constructed.Secondly，according to the topological properties of complex network theory，the aviation accident causation network is analyzed from degree，average path length，network diameter and clustering coefficient［7-8，10］.Thirdly，combining with the technique for order of preference by similarity to ideal solution（TOPSIS）method，a method for determining the critical causative factors of aviation accidents is proposed.Finally，several aviation accident causation analysis models are compared.

1 Construction of Aviation Accident Causation Network

Aviation accident causation network is constructed by taking the causative factors of aviation accidents as the nodes and the relationship between the causative factors as the edges.

The Report of Aviation Accident Investigation can be used as the data source for the study，because it records in detail of the accident.And 257 investigation reports published in Ref.［11］from 2009 to 2019 are selected as the data source for the study.

1.1 Determination of network nodes

There are a lot of factors described in the investigation report of accidents，and the same or similar factors may be described differently due to the difference of accident investigation institutions.If the exhaustive method is used to list all causative factors，it is not conducive to the subsequent analysis work.

Therefore，the causative factors of 257 aviation accidents are extracted by the coding method based on the grounded theory as nodes for the network.The core process of the extraction is data analysis，which includs three steps：Open coding，axial coding and selective coding.The causative factors extracted by the grounded theory is shown in Fig.1.

Fig.1 Causative factors extracted by grounded theory

Based on the grounded theory，the causative factors of aviation accidents and the accident types are sorted out.SupposeP={P1，P2，…，Pn}is a set of human causative factors，A={A1，A2，…，A n}a set of facilities and equipment causative factors，E={E1，E2，…，E n}a set of environment causative factors，M={M1，M2，…，M n}a set of management causative factors，andZ={Z1，Z2，…，Zn}a set of accident types，shown in Table 1.

Table 1 Causative factors of aviation accidents

1.2 Determination of networ k edges

The relationship between accident causative factors is abstracted as the edge of the network and the aviation accident causation network should be a directed weighted network.

The occurrence path of the“2-4”model is described as system network，where“2”means two levels（individual，organization）and“4”means four stages（guidance，operation，unsafe behavior and individual factors）.The model is suitable to construct the accident causation network for its network structure，and makes the analysis more comprehensive.So，the“2-4”model is applied to the analysis of the relationship between the factors.

The“2-4”model is taken as the logical framework to get an event chain composed of causative factors based on each aviation accident.According to the complex network theory，each causative factor is regarded as an independent node.However，it can be found that some factors do not completely form the causal relationship but promotion and interaction.Therefore，the causal relationship or the promotion relationship between factors is regarded as a directed edge，and the number of co-occurrence between the same factors is taken as the weight of the edge.Moreover，the corresponding adjacency matrix is established.

An aviation accident investigation report is selected as an example to analyze the relationship between the accident causative factors based on the“2-4”model.On January 25，2010，at 00：41：30 UTC，Ethiopian Airlines Flight ET 409，B737-800，crashed into the southwest region of Beirut Rafik in the Mediterranean Sea.Analysis for this accident by the“2-4”model is shown in Fig.2.

Fig.2 Analysis for an accident by the“2-4”model

When the flight took off，there were thunderstorms and low clouds in the area.At this time，the controller gave the instruction of a right turn，then the aircraft bumped，and finally the aircraft went through two recoverable stalls.During this period，the pilots were fatigued and lost situation awareness due to the poor crew scheduling.In addition，the pilots’capability declined under the bad weather condition.For the poor CRM level，the pilots failed to correctly operate the aircraft，and the flight control inputs of the captain and the co-pilot were inconsistent.In the final stage，the aircraft made an uncontrolled spiral dive.

According to the causation analysis process for 257 aviation accidents，the adjacent matrix can be established as the basis of constructing the accident causation network.

2 Analysis of Topological Characteristics

According to the network nodes identified in Table 1 and the network edges identified in the“2-4”model，the aviation accident causation network is constructed by the Pajek software［12］.

The aviation accident causation network is comprised of 45 nodes（causative factors）and 304 edges.Most of the factors are affected by others，which proves that the occurrence of accidents is not the result of a single factor.

According to the in-degree analysis of accident type nodes，the runway safety accounts for 38.5%of the total accidents，and it can be seen that the approach and landing are the critical nature of those flight phases.Moreover，the ground safety accounts for 19%of the total accidents，indicating that it is also an important factor of aviation accident causation.

The causative process of aviation accidents can be analyzed from different topological characteristics，which provides some theoretical basis for the accident prevention.Therefore，combined with the topology characteristic formula of complex network，the node degree，the average path length，the network diameter and the clustering coefficient are selected for analysis.

2.1 Node degr ee

The aviation accident causation network is a directed-weighted network，so the node degree of the network can be analyzed from three aspects：Outdegree，in-degree and total degree.The total degree is equal to the sum of in-degree and out-degree.The total degree varies from 1 to 41.In Fig.3，the causative factors of aviation accident with the total degree greater than 15 are displayed respectively.Besides，about 30%of total node-degrees account for 53%of all total-node degrees.

Fig.3 Causative factors with total degree greater than 15

In Fig.3，the total degree of the human factor accounts for the largest proportion of all factors，indicating that the pilot factor is more related to other factors.In addition，the factors with larger total node-degree are the aircraft-related factors，management factors and weather factors in turn.

Among them，the nodes with larger in-degree are as follows：Pilot errorP3，pilot violationP2，insufficient flight skillsP1，airframe damageA7，lack of CRMP9.These factors are easily affected by other factors and become the direct accident causation.

The nodes with larger out-degree are as follows：Pilot violationP2，pilot errorP3，bad weatherE2，lacks supervision in airlinesM4，incomplete rules and regulations for airlinesM3.These factors can easily promote other factors and become the essential accident causation.

Especially，in-degree and out-degree of the nodes，pilot errorP3and pilot violationP2，are nearly the largest nodes，which shows that the two factors are easy to interact with other factors and are the key causative factors of aviation accidents.

2.2 Average path length and network diameter

The average path length reflects the influence ability of the factors and indicates the degree of separation between the nodes.If the average path length is short，the information exchange between the causative factors passes through few nodes.The average path length is reflected in the number of causative factors that need to go through in the occurrence of the accident.The obtained results show that the average path length of the accident causation network is 2.543，which indicates that the accident can be reached through three factors on average.

The network diameter of the accident causation network is 7，and the path is from aircraft design and manufacturing defectsA10to loss of abilityP10.In the real situation，A10is difficult to directly lead toP10，but the analysis of the network diameter shows that there is an indirect relationship between the two involved factors.It can be seen that the new accident causation analysis method can effectively identify the causal relationship which is difficult to find directly.

2.3 Clustering coefficient

The clustering coefficient reflects the aggregation of nodes in the complex network.The greater the clustering coefficient of nodes is，the closer the connection between the nodes and the surrounding nodes is.The clustering coefficient is defined as

wherekiis adjacent nodes in the network andE ithe number of edges between adjacent nodes.

In addition，the clustering coefficient and average path length can judge whether the network obeys small world properties［13］.The clustering coefficient of nodes varies from 0.05 to 0.67.The nodes with the clustering coefficient greater than 0.25 are selected，shown in Fig.4.

In Fig.4，nodes with larger clustering coefficients are：Unreasonable crew schedulingM2，malfunction or lack of CNSA11，insufficient crew trainingM1，controller errorP14，loss of situational awarenessP5，lack of safety awarenessP7，and these factors have strong aggregation ability.Ifthese factors are abnormal，it is easy to interact with other factors and lead to the formation of event chain.Therefore，in order to prevent the chain reaction in the network，it is necessary to remove these nodes with larger clustering coefficient.

Fig.4 Network nodes with clustering coefficient greater than 0.25

The clustering coefficient of the network is 0.217 6 and the average path length of the network is 2.543，then it can be concluded that the aviation accident causation network obeys small-world properties.This also means that the connectivity between the causative factors of accidents is random，and the factors propagate quickly in the network.If a factor occurs，it is easy to produce a chain of events，which further aggravates the situation and increases the difficulty of emergency response.

3 Determination and Analysis of Key Nodes

3.1 Determination algorithm based on TOPSIS

According to the analysis of the topological characteristics of the aviation accident causation network，the causation network has both scale-free characteristics and small world properties.The scale-free characteristic reflects that the network follows the Pareto principle，which shows that a small number of nodes control the efficiency of the whole network.The robustness of the network can be achieved by taking deliberate attacks.The key nodes are identified and deleted，which can cut off the formation of event chain，reduce the propagation rate and achieve the purpose of accident prevention.

The network topology feature can be used as the index to determine the key nodes（causative factors），but sometimes it has limitations.TOPSIS is a multicriteria decision-making approach.Degree centrality，betweenness centrality，closeness centrality and clustering coefficient of nodes are normalized and set as four objectives of the TOPSIS method.

The ideal solution and the negative ideal solution of objectives are calculated to obtain the approaching between the node and the ideal solution，which is defined as

whereCTis the value of TOPSIS centrality of nodei，the distance between the node and the negative ideal solution，andthe distance between the node and the ideal solution.

The value of the ideal solution approaching of each node is closer to 1，and the node plays an important role in network.It can be used as the basis for evaluating the key nodes［14］.

3.2 Nor malized results of key nodes and their ranking

According to Eq.（1），the degree centrality，the betweenness centrality，the closeness centrality and the clustering coefficient of each node are normalized.The normalized values，the TOPSIS values and their ranking are shown in Table 2.

From Table 2 we can see that，considering degree centrality，betweenness centrality，closeness centrality and clustering coefficient of nodes，the ranking of nodes has a certain change compared with the single network topology.

Table 2 Normalized and TOPSISvalues of each node and their ranking

According to the TOPSIS value and ranking of each node，it is also seen thatP2，P3，M9，P14，P9are the key causative factors，which focus on the errors of professional of air transportation and also verify the importance of human factors in aviation safety management.

In addition，when an emergency occurs，the multi-party collaborative emergency response fails to work，and the crew resource management is not enough，which indicates that team cooperation，collaborative linkage and decision-making play an im-portant role in dealing with the emergency or avoiding the deterioration of the situation.

From the perspective of various factors，the pilot factor is the most important causative factor among the human factors.Among them，the flight skills are the key to the safe operation of the aircraft.The training of flight skills should be strengthened.The landing gear and engine of aircraft are easy to fail，which may lead to unsafe incidents.

The ranking of TOPSIS values of environmental factors is in the middle part，indicating that environmental factors belong to the transitional causative factors，which are the leading causative factors of human factors and the facilities and equipment factors.Moreover，bad weather is the key causative factor to affect the flight safety，and the operation of apron is the key factor to affect the ground safety.

Among the management factors，the effectiveness and timeliness of the emergency response are the key to avoid the serious situation.Besides，the management factors of the airline company are easy to cause human factors，such as：Unreasonable crew scheduling and insufficient crew training.

In sum，the key factors are those nodes with high importance in the network，so dealing with the key factors preferentially can effectively paralyze the network and achieve the purpose of accident prevention.

4 Comparative Analysis

The software，hardware，environment and liveware（SHEL）model，the Reason model and the functional resonance analysis method（FRAM）are classic aviation accident causation analysis models widely applied in the aviation safety field.They are selected to compare with the method proposed in this paper，shown in Table 3.

Table 3 Comparison of aviation accident causation analysis models

SHEL and Reason models are very common and mature in the field of aviation accident analysis.They have the characteristics of simple structure and easy operation.

The human-centered characteristics of the SHEL model are consistent with the situation of aviation accidents dominated by human factors.The innovation of Reason model lies in its vision of system view.The causation analysis of the accident is extended from the human factors to the potential organizational factors.

However，these two models are not enough for the analysis of accident causation details，and the dynamic interaction description of various factors is insufficient，so they are not suitable for a lot of accident data analysis.In addition，the analysis objects covered by these two models are not comprehensive enough.

Different from the modular structure of the SHEL model and the chain structure of the Reason model，FRAM and the method proposed in this paper adopt a reticular structure，which has the advantage of being able to analyze the evolution path of the accident and the interrelationship between the causative factors and the propagation mechanism in detail，and the analysis objects covered are more comprehensive.

Compared with SHEL and Reason models，the model structure of complex network theory is more advanced，the dynamic interaction and propagation mechanism between causative factors are much clearer，and the accident analysis is more detailed.

Compared with FRAM，the complex network theory model does not rely too much on expert experiences，and is more suitable for analyzing a lot of accident data at the same time with higher efficiency.

In addition，the new method can identify key factors that cannot be achieved by conventional methods.By controlling the identified key factors，the purpose of accident prevention and control can be effectively achieved.

Therefore，the method of analyzing the causation of aviation accidents based on complex network theory described in this paper has better applicability and advancement.

5 Conclusions

The feasibility of applying complex network theory to analyze aviation accident causation is explored.The conclusions are drawn as follows：

（1）The 45 causative factors from 257 aviation accident investigation reports are selected as network nodes based on the grounded theory，and the causative chain of each accident is established as network edge based on the“2-4”model.Then the aviation accident causation network is constructed for analysis.

（2）The topological characteristics of the aviation accident causation network is analyzed.Considering the different characteristics of nodes，the key nodes are identified by the TOPSIS method.

（3）Several aviation accident analysis models are compared and analyzed，and it is concluded that the method proposed in this paper has better applicability and advancement than conventional aviation accident analysis models.

The new method can also analyze the characteristics of different network topologies according to the actual needs of safety management work，and obtain the analysis results of different dimensions.

AcknowledgementT his work was supported by the Civil Aviation Joint Fund of National Natural Science Foundation of China（No.U1533112）.

AuthorDr.YUE Rentian received the B.S.degree in industrial engineering and the M.S.degree in safety technology and engineering from Shandong University of Science and Technology，Tai’an，China，in 2000 and 2003，respectively.He received the Ph.D.degree in safety engineering from China University of Geosciences，Beijing，China，in 2008.In 2003，he joined College of Safety Science and Technology，Civil Aviation University of China，as an assistant.In 2009，he joined College of Air Traffic Management，Civil Aviation University of China，as an assistant researcher，and was employed as an associate researcher in 2011.His main research fields are aviation safety，air traffic planning and management，and so on.

Author contributionsDr.YUE Rentian designed the research，compiled the model，explained the model results，analyzed the results，and wrote the manuscript.Miss LI Junwei provided data and complex network model components.Mr.HAN Meng participated in data analysis and manuscript writing.All authors commented on the manuscript draft and approved the submission.

Competing interestsThe authors declare no competing interests.