Identification of flight accidents causative factors base on SHELLO and improved entropy gray correlation method

Abstract

In order to effectively identify the key causative factors of civil aviation flight accidents, and establish a forward-looking effective prevention mechanism for flight accidents. Firstly, Corrected SHELLO model is established to classify the causes of civil aviation accidents in China (2015–2019) based on the integration of SHELL analysis model and Reason organization system concept. Secondly, in view of the randomness and uncertainty gray characteristics of the flight accidents inducing factors, the improved entropy gray correlation algorithm is established for the purpose of importance recognition, which combined with the characteristics of the data sample of inducement classification. Finally, the improved entropy gray correlation algorithm is used to identify and rank the key causative factors of flight accidents. The results showed that the flight accidents crucial causative factor is the human factors which we should pay more attention including the pilot perceptual errors, skill-based errors, decision errors and violation main factors, environmental and organizational factors also play an important role in inducing flight accidents, including complex terrain for approach landing and poor safety management mechanism factors. The method has great practical significance for identifying critical causative factors of flight accidents and improving flight safety.

1. Introduction

Civil aviation transportation is an important part of the comprehensive transportation system, the development of civil aviation transportation is one of the important reference indicators for the country's comprehensive transportation establishment and modernization level. Its rapidity makes international exchanges closer and global village come true, the public's demand for aviation safety is increasing [1,2]. Since the beginning of the new century, China's civil aviation has experienced rapid development, taking 2006–2015 as an example, the average annual growth rate of China's civil aviation transport fleet is about 10.3% and the average annual growth rate of total transportation turnover was about 10.8%, the average annual growth rate of total aircraft movements is about 9.4% [3], but the transportation and general aviation accidents almost always exist every decade between 1950 and 2019 (Table 1). In 2019, there were 16 fatal flight accidents of civil aviation transport aircraft in the world, with 298 deaths (including 12 on the ground). In 2019, there were 2 accidents with more than 40 deaths, including 1 flight accident with more than 100 deaths. In 2019, North America became the continent with the largest number of 6 accidents, followed by 4 in Asia. In 2019, the entire civil aviation industry in China achieved 12.309 million hours of transport flights and 4.965 million sorties. The 10,000-h rate of transport aviation incidents was 0.462, the 10,000-h rate of serious transport aviation incidents was 0.008, and the 10,000-h rate of transport aviation incidents was 0.008. The 10,000-h rate was 0.022, and the 10,000-h rate for transport aviation machinery was 0.019 [4]. From the statistics of the flight accidents rate of ten thousand hours (1950–2019) (Fig. 1), China's flight accidents are constantly decreasing. However, due to the increase in the number of flight time, if the accident rate is still maintained, the absolute value of the total number of accidents will continue to rise. This result is unacceptable. Aviation safety has always been the basis for the healthy and sustainable development of the aviation industry, as well as an important condition and foundation for building a strong civil aviation country. With the rapid development of civil aviation, as the lifeline of the aviation industry, safety has always been the focus of attention in the development process. With the development of civil aviation in the world, more and more countries are facing the pressure of flight safety, paying more attention to the risk management of civil aviation flight [5,6]. On March 21, 2022, one Boeing 737–800 aircraft of China Eastern Airlines crashed, 132 people died on board, including 123 passengers and 9 crew members. This aviation accident broke the longest civil aviation safety operation record of China's civil aviation, causing heavy loss of life and property, and also had a negative impact on the safe operation of civil aviation in the world.

Table 1.

Statistics of China's flight accidents from 1950 to 2019 (per 10 years).

year	Number of accidents			Major aviation accidents		General aviation fatal flight accident per ten thousand hour rate	Transport aviation
	Transport aviation	General aviation	Total	Ten thousand hour rate	Ten thousand times rate		Passenger deaths	The number of passenger-kilometer deaths
1950–1959	17	23	40	0.271	1.255	1.26	18	2.802
1960–1969	12	41	53	0.068	0.209	0.52	17	0.921
1970–1979	16	57	73	0.076	0.192	0.83	73	0.535
1980–1989	15	37	52	0.045	0.098	0.63	220	0.193
1990–1999	17	29	46	0.015	0.021	0.35	536	0.092
2000–2009	3	25	28	0.0011	0.0021	0.0669	207	0.0104
2010–2019	3	78	81	0.0001	0.0003	0.0481	41	0.0006
Total	83	290	373	0.0035	0.0076	0.1283	1112	0.0110

Fig. 1.

Statistics on the 10,000-h rate of flight accidents per decade (1950–2019).

The importance of flight safety is beyond doubt, civil aviation practitioners and researchers unanimously agree that without safety there is nothing, and the idea of safety first has formed a unified understanding in the global civil aviation transportation. There are many factors affecting flight safety, carrying out causative factors analysis and experience sharing is of great practical significance for national and regional civil aviation flight safety. In previous studies, many civil aviation safety research methods have been formed, and different scholars have carried out research on factors affecting flight safety from different perspectives [7]. established “old” and “new” safety thinking from perspectives of aviation safety investigators. Some scholars have carried out a series of studies on the tools and aspects of civil aviation operation safety management, and developed an effective safety risk decision-making framework, and introduced methods such as safety management system [8,9]. Some scholars also have developed traffic simulation models to identify hazards and analyze unsafe events [[10], [11], [12], [13], [14]]. Ni et al. (2019) made civil aviation safety evaluation based on deep belief network and principal component analysis. Some scholars also use methods such as the establishment of structural equations, bayesian networks, machine learning, and bowtie models for aircraft fault safety diagnosis or safety assessment applications [[16], [17], [18], [19], [20]]. Many scholars have carried out a series of studies on new energy aircraft, human factors and text mining [[21], [22], [23]], found safety voice and safety listening during aviation accidents: cockpit voice recordings reveal that speaking-up to power is not enough [24]. Many scholars have carried out a series of researches on aviation safety mining and application by using modern information technologies such as natural language processing and data mining [[25], [26], [27], [28], [29], [30]]. Aviation safety has always been the basis for the healthy and sustainable development of the industry, as well as an important condition and foundation for building a strong civil aviation country.

In a word, more and more scholars pay attention to civil aviation flight safety research, but key causative risky factors identification researches of aviation safety accidents in a specific country over a longtime span are rare. This paper use the SHELLO model to categorize the causative factors of flight accidents in China (2015–2019), and apply an improved entropy gray correlation method to identify key risk factors and rank importance. Then, according to the key incentives of flight accidents, targeted prevention and control suggestions are put forward, which aims to provide flight risk management reference for civil aviation flight safety management.

2. Materials and methods

2.1. Flight accidents causative factors classification based on SHELLO

The SHELL (Software, Hardware, Environment, Liveware) model is a conceptual model for exploring risky hazards from the perspective of man-machine-environment. It was firstly proposed by Edwards in 1972 and then improved by Hawkins in 1987 [31]. It includes four elements of software(S), hardware(H), environment(E) and liveware(L). In fact, many accidents are also closely related to bad organization and management factors. The Reason model proposed by professor James Reason, and in his psychology monograph “Human Error” pointed out that the occurrence of an accident has not only a reaction chain of the event itself, but also a penetrating the set of organizational defects, accident-causing factors and defects at all levels of the organization exist for a long time and evolve continuously. However, these accident triggers and organizational defects do not necessarily cause unsafe incidents. When multiple levels of organizational defects appear in an accident triggering factor at the same time or for the second time, unsafe incidents will occur because of the multi-level blocking barriers lose [32,33]. Therefore, the organizational system theory of Professor Reason can be incorporated into the SHELL model to form a SHELLO (Software, Hardware, Environment, Liveware, Liveware, Organization) model. As shown in Fig. 2, the main safety risk factors of the pilot (Liveware, L) include perceptual errors, decision errors, skill-based errors and violations risky factors. The main safety risk factors between pilot and software (L-S) include flight procedure error, SOP execution deviation. The main safety risk factors between the pilot and other personnel (L-L) include the crew management deficiencies and air traffic management failure. The main safety risk factors between the pilot and the equipment hardware (L-H) include aircraft/equipment failure and disabling. The main safety risk factors between pilot and organization management (L-O) include poor safety management mechanism, insufficient investment in safety resources. The main safety risk factors between the pilot and the environment (L-E) include the bad weather condition, complex terrain for approach and landing and insufficient airport runway conditions (Table 2).

Fig. 2.

SHELLO model.

Table 2.

Statistics of flight accident causative factors based on SHELLO (2015–2019).

	Risk Factor	Description	Example	2015	2016	2017	2018	2019
L	Perceptual errors Xm1 (m = 1,2,3,4,5)	Errors caused by deviations between the perception and understanding of objective objects and the actual situation.	Visual hallucinations, lack of sense of orientation, misjudgment of distance, size, and color, etc.	9	4	3	12	10
	Decision errors Xm2 (m = 1,2,3,4,5)	The executed behavior plan does not meet the requirements of the current situation	Decision-making errors in selecting procedures, options, and problem-solving	13	5	9	14	12
	Skill-based errors Xm3 (m = 1,2,3,4,5)	A skill error that occurs when a person responds spontaneously or spontaneously to a specific task	Inappropriate attention	10	7	6	12	15
	Violations Xm4 (m = 1,2,3,4,5)	Long-lasting violations, high frequency behaviors, and incidental violations that have nothing to do with personal behavior habits or organizational management systems	Habitual violations and occasional violations, such as not wearing seat belts in the cockpit, sleeping, etc.	9	9	2	5	9
L—L	Crew management deficiencies Xm5 (m = 1,2,3,4,5)	Insufficient team communication and assistance between crews	The standard crew dialogue is not adopted, and the monitoring of manipulation behavior is not in place.	5	13	3	12	10
	Air traffic management failure	There is a defect in the communication and assistance between the pilot and the air traffic controller	The land-air dialogue is not standard, disturbed, and inaccurate recitation	3	3	1	2	1
L—H	Aircraft/equipment failure or disabling Xm6 (m = 1,2,3,4,5)	Aircraft or ground equipment are disabled, such as aircraft electronic navigation equipment and airport navigation equipment failure; aircraft design and manufacturing, resulting in poor human-computer interaction	Such as aircraft wing jam, airport navigation light failure, cockpit display system failure, etc.	2	1	1	2	4
L—E	Bad weather condition Xm7 (m = 1,2,3,4,5)	Adverse weather conditions that seriously affect flight operations and safety	Bad flight weather conditions, such as thunderstorms, wind shear, heavy rainfall, etc.	3	4	1	3	2
	Complex terrain for approach and landing Xm8 (m = 1,2,3,4,5)	The terrain and complex geographical conditions that affect the aircraft approach, take-off and landing route operation and safety.	The terrain of the aircraft approach and landing route is complex, such as plateaus, mountains, etc.	9	16	5	12	3
	Insufficient airport runway conditions	Bad airport runway conditions affecting aircraft takeoff and landing	For example, the airport is not airworthy, such as water and snow at the airport, non-airport construction, etc. That affect flight safety.	3	4	1	1	3
L—O	Poor safety management mechanism Xm9 (m = 1,2,3,4,5)	The organization's establishment of flight safety management agencies and management systems are unscientific, resulting in an unhealthy and safety culture of the company	The setting of safety supervision agencies is unscientific, and the responsibilities and rights are inconsistent	8	7	9	13	12
	Insufficient investment in safety resources Xm10 (m = 1,2,3,4,5)	The organization's insufficient investment in safety funds has led to insufficient flight training, etc.	Insufficient safety management personnel, money input	2	3	3	4	4
L—S	Flight procedure error Xm11 (m = 1,2,3,4,5)	The flight procedure is set incorrectly	Incorrect flight procedure settings lead to deviations in the flight approach and landing process	3	6	5	9	3
	SOP execution deviation Xm12 (m = 1,2,3,4,5)	Part of the checklist procedures were ignored during the flight, and the SOP was not strictly followed	The flight crew did not strictly abide by the SOP, and the control procedures are not implemented in place	7	8	11	12	7

2.2. Improved entropy gray correlation algorithm

There are usually many conditions that affect research goals, and different impact conditions have different contributions to the research object, and their proportions are different [34], so it is extremely important to scientifically determine the weight of each evaluation index. Weight analysis can adopt objective weight, subjective weight or mixed weight processing methods. From a mathematical perspective, the entropy method belongs to the category of objective weight methods [35,36].

• (1)Calculation steps of improve entropy method

• Step 1: Build an evaluation matrix $X_{mn}^{\prime }$, as show in equations [1].

$$X_{mn}^{\prime }=\left[\begin{array}{cccc}{x}_{11}^{\prime }& x_{12}^{\prime }& \cdots & x_{1n}^{\prime }\\ x_{21}^{\prime }& x_{22}^{\prime }& \cdots & x_{2n}^{\prime }\\ ⋮& ⋮& ⋮& ⋮\\ x_{m1}^{\prime }& x_{m2}^{\prime }& \cdots & x_{mn}^{\prime }\end{array}\right]$$ (1)

In the formula: $m$ is the number of evaluation indicators, and $n$ is the number of evaluation objects.

• Step 2: Standardize processing

Obviously, the different dimensions of each evaluation index cannot be directly analyzed and compared. Using a processing method similar to the standard value, the non-dimensional processing of each index is done. There are two evaluation indicators, forward and reverse. The small increment of the positive index is consistent with the direction of the change increment of the evaluation object, and the negative index is just the opposite. The specific processing methods for the two types of indicators are shown in equations [2,3].

$$x_{ik}=\frac{x_{ik}^{\prime }-x_{\mathit{min}}^{\prime }}{x_{\max }^{\prime }-x_{\min }^{\prime }}$$ (2)

$$x_{ik}=1-\frac{x_{ik}^{\prime }-x_{\mathit{min}}^{\prime }}{x_{\max }^{\prime }-x_{\min }^{\prime }}$$ (3)

Where: $x_{ik}$ is the standardized value of the row $i$ and column $k\left(i=\mathrm{1,2},\cdots ,m;k=\mathrm{1,2},\cdots ,n\right)$; $x_{\max }^{\prime }$ and $x_{\min }^{\prime }$ are the maximum and minimum values of the index respectively.

• Step 3: Calculate information entropy

Calculate information entropy according to equations [4]-(6).

$$H_i=-\beta \sum _{k=1}^n{f}_{ik}.\ln f_{ik}$$ (4)

among them

$$f_{ik}=x_{ik}/\sum _{k=1}^n{x}_{ik}$$ (5)

$$\beta =1/\ln n$$ (6)

This paper makes the following assumptions: in the process of $H_i$ calculation the situation may occur, such if $f_{ik}=0$, $\ln f_{ik}$ is meaningless in mathematics. it has no mathematical meaning, so if $x_{ik}=0$ and $f_{ik}=0$, define $f_{ik}.\ln f_{ik}=0$.

• Step 4: Calculate the entropy weight

When calculating the entropy weight, the traditional entropy weight method uses a standardized processing method, as shown in equation [7].

$$w_i=\frac{1-H_i}{\sum _{i=1}^m\left(1-H_i\right)}=\frac{1-H_i}{m-\sum _{i=1}^m{H}_i}$$ (7)

But after doing this, when $H_i\to 1\left(i=\mathrm{1,2},\cdots ,m\right)$, there will be an abnormal phenomenon that the difference in entropy value of different evaluation indicators is small, but the entropy weight value is quite different. For example, the entropy value of 3 indicators of a scheme set is 0.999,0.998 and 0.997, The entropy weights of the three indicators are 0.1667,0.3333 and 0.5000. According to the principle of entropy weight, if the entropy value of the analysis objects is not much different, it means that the amount of available information provided by these objects should be equivalent, and the corresponding weights should be basically at the same level, the above situation is obviously unreasonable.

Therefore, in this paper, equation [8] is used to calculate the entropy weight to replace equation [7].

$${{\omega }_i}^{\prime }=\frac{\sum _{k=1}^m{H_k}_i+1-2H}{\sum _{i=1}^m\left(\sum _{k=1}^m{H_k}_i+1-2H\right)}$$ (8)

• (2)Analysis of the rationality of improving the entropy method

In equation [7], when $H_i\to 1\left(i=\mathrm{1,2},\cdots ,m\right)$, we get equation [9].

$$\left|1-H_i\right|<{\epsilon }_i$$ (9)

Thereby we get equation [10].

$$\sum _{i=1}^m\left|1-H_i\right|<\epsilon$$ (10)

${\epsilon }_i$ is an arbitrarily small value, $\epsilon =m.\max \left({\epsilon }_1,{\epsilon }_2,\cdots ,{\epsilon }_m\right)$.

When the numerator and denominator in equation [10] converge to infinitesimal respectively, there will be slight changes in different indexes, and the weight of entropy may cause big changes. In the improved method, for different indicators (for example, two evaluation indicators $p$ and $q$), the corresponding entropy weight difference becomes, and we get equation [11].

$$\Delta {\omega }^{\prime }=\frac{2\Delta H}{C}$$ (11)

Where equation [12]:

$$C=\sum _{i=1}^m\left(\sum _{k=1}^m{H_k}_i+1-2H\right)$$ (12)

When $\left|\Delta H\right|<\epsilon$, $\left|\Delta {\omega }^{\prime }\right|<2\cdot \epsilon /C$, it means that the entropy value changes slightly, and the corresponding entropy weight will also change slightly. Using equation [8] to calculate the above example, the entropy weights are respectively $0.3330$, $0.3333$, $0.3337$.Obviously, for indicators that contain equivalent useful information, the weight information obtained by the improved entropy weight method is consistent with the corresponding entropy level.

2.3. Improved entropy gray relational analysis algorithm

Gray relational analysis is a quantitative analysis of the similarity between influencing factors and behavioral results. The core mathematical idea is to use the degree of similarity between the change curve of the object to be analyzed and the ideal data curve, to judge the level of association, and it is easy to deal with the relationship between elements with uncertain and incomplete information.

• Step 1: Determine the reference series and comparison series

Firstly, collect data, determine the indicators, determine the original evaluation matrix and determine the reference series as $X_0^{\prime }=\left(x_{01}^{\prime },x_{02}^{\prime },\cdots ,x_{0n}^{\prime }\right)$, we get equation [13].

$$X^{\prime }=\left[\begin{array}{c}{X}_0^{\prime }\\ X_{mn}^{\prime }\end{array}\right]=\left[\begin{array}{cccccc}{x}_{01}^{\prime }& x_{02}^{\prime }& \cdots & x_{0k}^{\prime }& \cdots & x_{0n}^{\prime }\\ x_{11}^{\prime }& x_{12}^{\prime }& \cdots & x_{1k}^{\prime }& \cdots & x_{1n}^{\prime }\\ x_{21}^{\prime }& x_{22}^{\prime }& \cdots & x_{2k}^{\prime }& \cdots & x_{2n}^{\prime }\\ ⋮& ⋮& & ⋮& & ⋮\\ x_{i1}^{\prime }& x_{i2}^{\prime }& \cdots & x_{ik}^{\prime }& \cdots & x_{in}^{\prime }\\ ⋮& ⋮& & ⋮& & ⋮\\ x_{m1}^{\prime }& x_{m2}^{\prime }& \cdots & x_{mk}^{\prime }& \cdots & x_{mn}^{\prime }\end{array}\right]$$ (13)

• Step 2: Standardization $X$

• Step 3: Calculate the absolute difference, as show in equation [14].

$$\left|X_i-X_0\right|=\left|X_{ik}-X_{0k}\right|$$ (14)

• Step 4: Calculate the correlation coefficient

Use the correlation formula to calculate the correlation coefficient value between the first evaluation index (comparison series) and the reference series (evaluation object), as show in equation [15].

$${\xi }_{ik}=\left\{\stackrel{m}{\underset{i=1}{\min }}\left[\stackrel{n}{\underset{j=1}{\min }}\left(\left|x_{ik}-x_{0k}\right|\right)\right]+\eta \stackrel{m}{\underset{i=1}{\max }}\left[\stackrel{n}{\underset{j=1}{\max }}\left(\left|x_{ik}-x_{0k}\right|\right)\right]\right\}/\left\{\left|x_{ik}-x_{0k}\right|+\eta \stackrel{m}{\underset{i=1}{\max }}\left[\stackrel{n}{\underset{j=1}{\max }}\left(\left|x_{ik}-x_{0k}\right|\right)\right]\right\}$$ (15)

Among them, $\eta$ is the resolution coefficient, and its value is between $\left(\mathrm{0,1}\right)$. Usually take $\eta =0.5$.

• Step 5: Calculate the gray entropy correlation degree using equations [16]-(17), obtain the average correlation coefficient between the evaluation index to be analyzed and the evaluation object, and then obtain the original correlation degree. Reuse equation [18] and include the entropy weight of the evaluation index to get the final degree of relevance.

$$p={\left(p_{01},p_{02},\cdots p_{0i,\cdots }{p}_{0m}\right)}^T$$ (16)

$$p_{0i}=\frac{1}{n}\sum _{k=1}^n{\xi }_{ik}$$ (17)

$${\mathrm{p}}_{\mathrm{i}}=\frac{1}{\mathrm{n}}\sum _{\mathrm{k}=1}^{\mathrm{n}}\omega {{\left(\mathrm{k}\right)}_{\mathrm{i}}}^{\prime }{\xi }_{\mathrm{i}\mathrm{k}}$$ (18)

The influencing factors are sorted from large to small through the gray entropy correlation degree $p_{0i}$, and the influencing factors with large correlation degree have a greater impact on the reliability index.

3. Results

Select the civil aviation safety information report of China from 2015 to 2019 to count the original data of the flight accident investigation report information, eradicate the SHELLO model for classification (Table .2), and use the improved entropy gray correlation method to explore the key flight accidents causative factors.

According to equations [1]-(2), the non-dimensional processing of the index data of the risk factors of flight accidents, we can get

$$X_{mn}^{\prime }=\left[\begin{array}{cccccccccccccc}0.7500& 0.9286& 0.6667& 1.0000& 0.3846& 1.0000& 0.5000& 0.7500& 0.5625& 0.7500& 0.6154& 0.5000& 0.3333& 0.5833\\ 0.3333& 0.3571& 0.4667& 1.0000& 1.0000& 1.0000& 0.2500& 1.0000& 1.0000& 1.0000& 0.5385& 0.7500& 0.6667& 0.6667\\ 0.2500& 0.6429& 0.4000& 0.2222& 0.2308& 0.3333& 0.2500& 0.2500& 0.3125& 0.2500& 0.6923& 0.7500& 0.5556& 0.9167\\ 1.0000& 1.0000& 0.8000& 0.5556& 0.9231& 0.6667& 0.5000& 0.7500& 0.7500& 0.2500& 1.0000& 1.0000& 1.0000& 1.0000\\ 0.8333& 0.8571& 1.0000& 1.0000& 0.7692& 0.3333& 1.0000& 0.5000& 0.1875& 0.7500& 0.9231& 1.0000& 0.3333& 0.5833\end{array}\right]$$

and according to equations [3]-(5), we get

$$f_{ik}=\left[\begin{array}{cccccccccccccc}0.2368& 0.2453& 0.2000& 0.2647& 0.1163& 0.3000& 0.2000& 0.2308& 0.2000& 0.2500& 0.1633& 0.1250& 0.1154& 0.1556\\ 0.1035& 0.0943& 0.1400& 0.2647& 0.3023& 0.3000& 0.1000& 0.3077& 0.3556& 0.3333& 0.1429& 0.1875& 0.2308& 0.1778\\ 0.0789& 0.1698& 0.1200& 0.0588& 0.0698& 0.1000& 0.1000& 0.0769& 0.1111& 0.0833& 0.1837& 0.1875& 0.1923& 0.2444\\ 0.3158& 0.2642& 0.2400& 0.1471& 0.2791& 0.2000& 0.2000& 0.2308& 0.2667& 0.0833& 0.2653& 0.2500& 0.3462& 0.2667\\ 0.2632& 0.2264& 0.3000& 0.2647& 0.2326& 0.1000& 0.4000& 0.1538& 0.0667& 0.2500& 0.2449& 0.2500& 0.1154& 0.1556\end{array}\right]$$

According to equations [6]-(8), we get

$$w_i=\left(\begin{array}{cccccccccccccc}0.0716& 0.0712& 0.0712& 0.0716& 0.0716& 0.0716& 0.0718& 0.0714& 0.0718& 0.0718& 0.0710& 0.0710& 0.0714& 0.0710\end{array}\right)$$

From equations [9]-(15), the gray correlation matrix can be obtained as:

$${\xi }_{ik}=\left(\begin{array}{ccccc}1.0000& 0.5634& 0.6807& 0.9757& 0.9918\\ 1.0000& 0.5399& 0.9931& 0.7662& 0.8104\\ 1.0000& 0.6915& 0.8883& 0.8720& 0.6627\\ 1.0000& 0.9435& 0.6203& 0.5060& 0.8812\\ 1.0000& 0.3333& 0.8883& 0.4170& 0.4646\\ 1.0000& 0.9435& 0.6807& 0.5455& 0.5018\\ 1.0000& 0.5870& 0.7971& 0.7121& 0.4646\\ 1.0000& 0.7303& 0.6807& 0.7121& 0.6394\\ 1.0000& 0.5151& 0.8453& 0.9757& 0.5018\\ 1.0000& 0.7303& 0.6807& 0.4420& 0.8812\\ 1.0000& 0.8192& 0.6451& 0.7141& 0.6627\\ 1.0000& 0.6314& 0.4919& 0.5310& 0.4646\\ 1.0000& 0.4489& 0.4450& 0.3154& 0.8812\\ 1.0000& 0.8896& 0.4706& 0.6599& 0.8812\end{array}\right)$$

According to equations [16]-(17), the gray relational entropy value can be calculated

$${\mathrm{p}}_{0\mathrm{i}}=\frac{1}{\mathrm{n}}\sum _{\mathrm{k}=1}^{\mathrm{n}}\omega {{\left(\mathrm{k}\right)}_{\mathrm{i}}}^{\prime }{\xi }_{\mathrm{i}\mathrm{k}}=\left(\begin{array}{cccccccccccccc}0.0603& 0.0585& 0.0586& 0.0565& 0.0445& 0.0525& 0.0511& 0.0537& 0.0551& 0.0536& 0.0545& 0.0443& 0.0442& 0.0554\end{array}\right)$$

The gray entropy correlation degree of each factor of the gray entropy correlation degree is obtained from the equation [18] (Fig. 3).

Fig. 3.

Gray entropy correlation degree of flight accidents causative factors.

According to the gray entropy correlation theorem, the gray entropy correlation value determines the influence degree of the index factors, the greater the gray entropy correlation degree value, the greater the influence degree of the index factors. According to the gray entropy correlation value, the main factors that induce unsafe flights in China's civil aviation (2015–2019) are in descending order: perceptual errors, skill-based errors, decision errors, violations, SOP execution deviation, Complex terrain for approach and landing, poor safety management mechanism, bad weather conditions.

4. Discussion

Combined with the analysis of the SHELLO model, it can be seen that the key factor that induces the occurrence of unsafe flight accidents in China's civil aviation (2015–2019) is the human factor (L) at the core of the SHELLO model. For example, human unsafe behavior includes perceptual errors, skill-based errors, decision errors, and violations. On August 24, 2010, an aircraft accident occurred in Yichun, Heilongjiang, China, killing 44 people and injuring 52 people. The results of the accident investigation showed that the main reason for the accident was pilot human error, including perceptual errors, skill-based errors, decision errors, and violations wait for unsafe behavior. In the implementation of the human factor risk control of flight accidents, it is necessary to focus on the training of human situational awareness to cope with pilot perceptual errors. It is necessary to strengthen the initial training and recurrent training of pilots' flying skills under different operating scenarios to effectively avoid skills -based errors. It is necessary to strengthen crew resource management (CRM) training, optimize effective communication and accurate decision-making to deal with crew decision errors. It is necessary to strengthen pilot selection and company mechanism culture to effectively avoid pilot violations. It can be seen that the human factor is in flight aviation. The issues that need to be focused on in accident prevention are also in line with the current international mainstream requirements for pilot core competency building for the entire life cycle of flight technology.

Secondly, L-S also needs to pay more attention to the SOP execution deviation. Inadequate execution of SOPs during the execution of SOP is the main factor leading to unsafe flight accidents. In terms of effective avoidance, it is necessary to consider the rationality of SOP formulation and establish an effective supervision mechanism for SOP execution.

In addition, the complex terrain for approach and landing and bad weather conditions in L-E are also important factors leading to the occurrence of unsafe flight accidents. For example, the high plateau flight routes located in southwest China are prone to trigger unsafe events, which need to be strengthened. It is necessary to strengthen the risk analysis and prediction of complex terrain and bad weather conditions for airline operations.

In terms of L-O analysis, poor safety management mechanism is a deep potential factor that leads to unsafe flight accidents. In view of the apparent failure causes obtained from each typical unsafe accident, it is necessary to analyze the underlying reasons behind the apparent failure from the organizational level. Establishing an effective organization and management organization and cultivating a good safety culture are effective in preventing flight unsafe accidents.

In terms of L-H, strengthening the quality of aviation maintenance and supply of high-quality aviation materials to avoid Aircraft/equipment failure and disabling, and establishing an effective emergency prevention mechanism can effectively prevent flight accidents.

5. Conclusion

In order to effectively identify the key causative factors in civil aviation flight accidents, explore the inducing laws of flight accidents, and establish a prospective and effective prevention mechanism for flight accidents. This paper firstly establishes a flight accident inducement classification SHELLO model based on human, hardware, software, environment and organization and interaction with the needs of flight accident inducement analysis. Then, in view of the randomness and uncertainty characteristics of civil aviation flight activities, and the gray characteristics of flight accident-inducing factors, an improved entropy gray correlation algorithm is established combined with the characteristics of the data samples for classification of incentives. Finally, the algorithm is used to identify and prioritize the causes of flight accidents. According to the gray entropy correlation value, the main factors that induce unsafe flights in China's civil aviation (2015–2019) are in descending order: perceptual errors, skill-based errors, decision errors, violations, SOP execution deviation, Complex terrain for approach and landing, poor safety management mechanism, bad weather conditions. Finally based on the SHELO model, respectively from L, L—S, L—E, L—O and L—H classified the key causes and put forward targeted prevention and control strategies, and the prediction and early warning for the identification of key risk causing factors need to be further study in the next step.

Author contribution statement

Nongtian Chen: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials and data; Wrote the paper.

Youchao Sun: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials and data.

Zongpeng Wang: Performed the experiments; Analyzed and interpreted the data.

Peng Chong:Analyzed and interpreted the data; Wrote the paper.

Funding statement

Nongtian Chen was supported by Key R&D Program of the Sichuan Provincial Department of Science and Technology [2022YFG0213], Safety Capability Fund Project of the Civil Aviation Administration of China [ASSA2022/17].

Youchao Sun, Zongpeng Wang and Chong Peng were supported by National Natural Science Foundation of China [U2033202].

Data availability statement

Data included in article/supp. Material/referenced in article.

Declaration of interest's statement

The authors declare no competing interests.

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