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

Abstract: In order to reduce the accident rate of consumer-grade unmanned aerial vehicles（UAVs）in daily use scenarios，the accident causes are analyzed based on the accident cases of consumer-grade UAVs.By extracting accident causing factors based on the Grounded theory，the relationship between these factors is analyzed.The Bayesian network for consumer-grade UAV accidents is constructed.With the Grounded theory-Bayesian network，the probability of four types of accidents is inferred：fall，air collision，disappearance，and personal injury.With the posterior probability of each factor being reversely reasoned，the causal chain with the maximum probability of each accident is obtained.After the sensitivity of each factor is analyzed，the key nodes in the network accordingly are inferred.Then the causing factors of consumer-grade UAV accidents are analyzed.The results show that the probability of fall accident is the highest，the fall accident is associated with the probabilistic maximum causal chain of personal injury，and the sensitivity analysis results of each type of accident as the result node are inconsistent.

Key words：consumer-grade UAV；Grounded theory；Bayesian network；key nodes；accident causes

0 Introduction

With the continuous advancement of technolo?gy，the performance of unmanned aerial vehicles（UAVs）has been significantly improved，but flight accidents of consumer-grade UAVs with low entry barriers and the largest holdings still exist.Most of the existing consumer-grade UAV operators have not received systematic skill training and safety edu?cation，resulting in a high risk of UAV operation.In addition，these UAVs are prone to accidents，which brings high risks to air transportation.The production standards of UAV manufacturers are not uniform and the quality is not up to standard，which also lays a hidden danger for the safe use of consum?er-grade UAVs.Therefore，it is necessary to ana?lyze the causes of consumer?grade UAV accidents to improve the operation safety level.

In UAV collision risk field，many new UAV collision models through mathematical analysis have proposed，which have achieved relative success［1?3］.The fall risk of logistics UAVs is used to analyze the main reasons for the failure of UAVs［4］.Based on the system theoretic accident model and process（STAMP），a safety control model is built for UAV low-altitude conflict resolution，and systemstheoretic process analysis（STPA）is used to identi?fy and analyze key causes of unsafe behavior in the relief process［5］.By fully considering various envi?ronmental factors，new evaluation models are estab?lished for identifying UAV operation risk，which has achieved good results in application［6-8］.Based on the deep learning technology，a new model is built to solve the collision problem of drones with non-stationary objects during operation［9］.

Operational risk is a hotspot in the field of UAVs，and some positive research results are ob?tained.Markov chains and equivalent safety level principles are used to model and validate accidentbased UAV safety analysis［10］.Based on the analysis of the UAV accidents，the direct and indirect causes of the accidents are identified，and then the method is applied to the accident scene of a UAV target crash，which proves the effectiveness of this meth?od［11］.Developed on the fault tree analysis model，the main hazards are determined for a UAV crash accident by analyzing the minimum cut set and struc?tural importance of the model［12］.

The key limitations of the above mentioned studies are：（1）These studies mainly focus on the UAV collision model and UAV safety risk assess?ment，while few studies pay attention to the causa?tion analysis of UAV accidents；（2）many studies fail to notice the huge difference in safety levels be?tween consumer-grade UAVs and industrial UAVs；（3）some studies just consider a certain ac?cident，and the conclusions provided by them are not persuasive enough to analyze the causation theo?ry of UAV accidents adequately［10］.To address these problems，the method of Grounded theory-Bayesian network for UAV accidents cause analysis is put forward with the following contributions：（1）208 cases of consumer-grade UAV accidents are an?alyzed by the Grounded theory，and the rich acci?dent cases make the extraction of accident causing factors more accurate；（2）a Bayesian network for consumer-grade UAV accidents is constructed，which fully considers the relationship between caus?al factors and the occurrence mechanism of each ac?cident；（3）the maximum causal chain of various ac?cidents is inferred by the Bayesian network，so the key factors of various accidents are obtained，which provides a reference for improving the safety level of consumer-grade UAV operation in the future.

The research objects of this paper are consum?er-grade UAVs such as aerial photography.Com?pared with industrial UAVs，consumer-grade UAVs have more quantity and lower security，are more difficult to operate，supervise and certify pi?lots’qualifications，and operate in a more complex environment with a much higher accident rate than industrial UAVs.Therefore，in order to reduce UAV accidents and promote the development of the industry，it is necessary to conduct further research and analysis on the causing factors of consumergrade UAV accidents.

1 Accident Cause Identification

Accident cases are collected through interviews and questionnaire surveys.There are 32 interviews and 176 questionnaires，a total of 208 cases.The ac?cidents are caused by consumer-grade UAVs en?gaged in aerial photography activities.

The Grounded theory is a qualitative research method.It emphasizes the development of theoreti?cal ideas based on data，suitable for research fields lacking theoretical explanations or insufficient exist?ing explanations.The core of Grounded theory is the process of data collection and analysis，which mainly analyzes data through three steps：Open cod?ing，axial coding，and selective coding［13］.

1.1 Open coding

Open coding refers to coding the original data so that it presents the original attributes.Correctly reflecting the data content according to the concept and category，combining the same or similar types to extract the concept category.The initial appeared concepts are selected and categorized to gain 45 causing factor concepts and four accident concepts.With the acquired initial concepts being further inte?grated，33 initial categories of causing factors and four initial categories of accident categories are ob?tained.

1.2 Axial coding

Axial coding is a deepening of open coding，which is continuously merged and clustered to estab?lish relationships and express the association be?tween various parts of the data.The categories ob?tained by open coding are further summarized and classified to form 13 independent categories of caus?ing factors and two categories of accidents.

1.3 Selective coding

Selective coding is used to select the core cate?gory，process the relationship between the main cat?egories，then analyze the relationship between the main categories.The essence of selective coding is to analyze the concept category system and select a core category.On the basis of the above-mentioned open coding and axial coding analysis，generaliza?tion，extraction，reorganization，and integration are carried out.Finally，three core categories of causing factors and one core category of accidents are sum?marized.

The extraction process of category develop?ment and coding implementation for the three types of codes is shown in Table 1.

Table 1 Process of category development and coding implementation

2 Accident Cause Modeling

2.1 Principle of Bayesian network

Bayesian network is the product of the combi?nation of probability theory and graph theory.It is an uncertain causal correlation model［14］，a two-tu?pleB=（G，θ）represents the Bayesian network，whereG=（V，E）represents the directed acyclic graph，Vis the node set in the graph，andEthe di?rected edge connecting two nodes in the graph，rep?resenting qualitative information；andθrepresents the probability distribution between variables，i.e.conditional probability table，representing quantita?tive information.Under the given premise，the Bayesian network can update the probability of vari?ables through probability propagation or reasoning under incomplete and uncertain conditions.

Assuming that the variable set in the Bayesian network isV=｛X1，…，Xn｝，according to the condi?tional independence assumption and chain rule in the Bayesian network structure，the joint probability dis?tributionP（V）of Bayesian network nodes can be expressed as

wherePa(Xi)is the parent node set ofXi.

When the new premiseE=eis given，the pos?terior probability of variableVcan be inferred through the Bayesian network，which is defined as

whereE=eindicates that the value of variableEise.

The node sensitivity analysis in the Bayesian network can find out the nodes that have an impor?tant influence on the result nodes.The formula is as follows

whereMrepresents the sensitivity of a node，Ythe posteriori probability of a node，andXthe priori probability of a node.

2.2 Construction of Bayesian network

Based on the consumer-grade UAV accident cases，by analyzing and sorting out the causal chain of the accident，the causal factors and the final acci?dent are connected through a directed acyclic graph，then a Bayesian network graph is constructed.The steps are as follows：

（1）Determine the basic events in the network and take them as the root node.

（2）The relationship between nodes is deter?mined according to the causal chain in the accident case，which is regarded as a directed arc in the net?work.

（3）Determine prior probability and conditional probability.

Four types of accidents and 33 causing factors are obtained from the cases.The four types of acci?dents are fall，air collision，disappearance，and per?sonal injury，including 109 cases of fall，47 cases of air collision，36 cases of disappearance，and 16 cas?es of personal injury.Among the 33 cause factors，18 factors are used as root nodes and 15 factors as intermediate nodes.The prior probability of the root node is obtained through accident cases.For exam?ple，there are 100 cases of low altitude obstacles in 208 accident cases，so the prior probability of low al?titude obstacles is 48%.The prior probability of the root node is shown in Table 2.

The conditional probability of the intermediate node is inferred from the causal relationship between the nodes in the accident case and further improved based on expert experience.For example，the prob?ability of satellite signal loss is 100% in all accident cases with simultaneous satellite positioning system failure and low altitude obstacles，100% in the acci?dent cases with only satellite positioning system fail?ure and no low altitude obstacles，and 23% in the case with only low altitude obstacles and no satellite positioning system failure，but the probability with no satellite positioning system failure and low alti?tude obstacles is 0%.However，because of the small number of accident cases，there may be in?complete coverage of accident causes.In compre?hensive consideration，the probability of 0% here is too absolute，so expert experience correction is in?troduced to set the probability of occurrence to 0.1%.To sum up，the conditional probability of the satellite signal loss node is shown in Table 3（T indi?cates occurrence and F otherwise）.

Table 3 Conditional probability of satellite signal loss node

3 Accident Cause Analysis

The causing factors are the nodes in the net?work，the active relationship between the causal fac?tors is the edge，reasoning down in turn，and the factors are connected to form the Bayesian network diagram of consumer-grade UAV accidents.

In the constructed Bayesian network，accidents are divided into four situations：Disappearance，air collision，fall，and personal injury.Air collision acci?dents may further deteriorate into fall accidents，and fall accidents may produce secondary accidents and personal injury under the condition of dense person?nel.Therefore，it is necessary to analyze the rela?tionship between causal factors and the occurrence mechanism of each accident in order to reduce the occurrence of accidents.The Bayesian network dia?gram is shown in Fig.1，which is simulated by the Netica software.

3.1 Forward reasoning and analysis

By inputting the prior probability or conditional probability of the node into the Bayesian network，the probability of final fall accident can be inferred to be 15%，the probability of air collision accident is 8.6%，the probability of disappearance accident is 4.85%，and the probability of personal injury acci?dent is 1.71%.As shown in Fig.1，the probability of fall accident is the highest，followed by air colli?sion，then disappearance and personal injury，which is consistent with the statistical results of accident cases used in this paper，indicating that the con?structed Bayesian network is effective.

Fig.1 Bayesian network diagram of consumer-grade UAV accidents (unit:%)

The highest probability of basic events is the existence of low-altitude obstacles.The main rea?sons are that the flight airspace of consumer-grade UAVs is mostly ultra-low altitude or low altitude.There are many obstacles，such as buildings，trees，and wires，and the flight environment is complex.Secondly，the probabilities of lack of experience and skills and lack of safety awareness are also high.The main reasons are that the acquisition cost and operation threshold of consumer-grade UAVs are low，leading many operators have not received sys?tematic skills and safety education，which are con?sistent with the current situation.Through the Bayesian network，the accident probability of the combination of the factors causes the operators，UAV system and flight environment can be deduced forward.Taking the low altitude obstacle with the highest priori probability in the root node as an ex?ample，this paper researches the occurrence proba?bility of various accidents when there are different combinations of operator and flight environment fac?tors in the root node in the presence of low altitude obstacles.The results are shown in Fig.2.

Fig.2 Occurrence probability of various accidents with low altitude obstacles

Fig.2 shows that when low altitude obstacles（E7），lack of experience and skills（L4），and auto?matic flight mode（H19）occur at the same time，the most likely accident is air collision，with a probabili?ty of 61%.When low altitude obstacles（E7），lack of experience and skills（L4），and motor fault（H1）occur at the same time，the most likely accident is fall，with a probability of 72.2%.The comparative analysis shows that the automatic flight model（H19）has a greater influence on air collision，and motor fault（H1）has a greater influence on falls.By analo?gy，the probability of various accidents is analyzed when different causing factors interact，and those ac?cidents are more affected by various causal factors.

3.2 Reverse reasoning and analysis

The posterior probability reverse reasoning function of the Bayesian network is used to analyze the generation process of consumer-grade UAV ac?cidents.The probability of disappearance，air colli?sion，fall，and personal injury is set to 100%，and then the posterior probability distribution of each node in four cases is obtained，as shown in Fig.3.

Fig.3 Posterior probability of each node

When there is a disappearance accident，the most likely cause chain is shown in Fig.3.Another important reason for the loss of the communication link（H7）is the presence of magnetic interference（E5），with a probability of 31%.In addition，the flight direction error（H17）of UAV is also the main cause of the disappearance，with a probability of 53.2%，and the flight direction error（H17）is usual?ly caused by compass operation failure（H14），with a probability of 43.1%，of which the probability of compass operation failure（H14）caused by magnetic interference（E5）is the highest.

When an air collision accident occurs，the max?imum accident probability is shown in Table 3.The second is the collision caused by the satellite signal loss（H15）.The cause of the collision is the satellite signal loss（H15）and the presence of low-altitude ob?stacles（E7）.The probability of satellite signal loss（H15）is 36.7%.The presence of low altitude obsta?cles（E7）is also the main cause of satellite signal loss（H15）.

When a fall accident occurs，the chain of causes with the largest accident probability is shown in Table 3.Battery failure（H4）and low battery（H5）are also important reasons for losing power（H3），with the probability of 11.3% and 7.59%，re?spectively.Because a part of collision accidents will further deteriorate into fall accidents，when the fall occurs，the probability of air collision is 35.4%.In addition，lose control（H18）is also an important cause of the fall.

As the personal injury is the follow-up accident of UAV fall，they will only occur when the fall and the densely populated area（E9）occur at the same time.At this time，the probabilistic maximum caus?al chain of accidents is shown in Table 4.Unlike fall accident，the probability of fall caused by lose pow?er（H3）and air collision is reduced，and the proba?bility of fall caused by lose control（H18）increases.This is because of lack of safety awareness（L5）.At the same time，it may also cause incorrect load（L2），which may cause attitude loss（H10）and cause an uncontrolled fall.

Table 4 Probabilistic maximum causal chain of accidents

3.3 Sensitivity analysis

Bayesian network sensitivity analysis can be used to measure the influence of cause nodes on re?sult nodes.Different accidents are selected as result nodes respectively.And Netica software is used to analyze the sensitivity of causing factors for consum?er-grade UAV accidents.The results are shown in Fig.4.

Fig.4 Sensitivity analysis of causing factors

When disappearance，air collision，fall，and personal injury accidents are selected as the target nodes，the causing factors with significantly higher sensitivity in the network are selected，as shown in Table 5.Because fall is the precondition of personal injury，the lose power（H3）and lose control（H18）with high sensitivity in fall accidents are also highly sensitive in personal injury accidents.

Table 5 Cause factors with significantly higher sensitivity

For fall accidents and personal injury acci?dents，the sensitivity of lose power（H3）and lose control（H18）is high，so there are 15 high sensitivi?ty nodes in the four types of accidents in the net?work.

Nodes with high sensitivity have a great influ?ence on the Bayesian accident network which are the weak link of the system.When the probability of these node changes，the probability of accident nodes will also change greatly.Therefore，they can be regarded as key nodes in the network and need to be focused on prevention and control.

4 Conclusions

Based on the consumer-grade UAV accident cases，the accidents causing factors are extracted by the Grounded theory，then the Bayesian network is constructed to analyze the relationship between the causal factors and the accident probability according to the accident causal chain.

（1）Based on the accident cases，the causes of consumer-grade UAV accidents are summarized and analyzed by the Grounded theory，which con?sists of 33 initial categories，13 main categories，and three core categories.

（2）Among the four types of accidents，fall has the highest probability，with a probability of 15%，and the probabilistic maximum causal chain of per?sonal injury is similar to that of fall accidents.

（3）There are 15 key nodes in the consumergrade UAV accident cause network.Among them，the factor that has the greatest influence on the dis?appearance accident is flighted direction error，the greatest influence on the air collision is bird strike，the greatest influence on the fall is lose power，and the greatest influence on personnel injury is a dense?ly populated area.

The accident causes of consumer-grade UAVs are studied，while relevant research on the accident causes of other types of UAVs such as industrial UAVs，unmanned helicopters，and fixed-wing UAV needs further consideration.