Risk Assessment Model Based on Set Pair Analysis Applied to Airport Bird Strikes

Abstract

In order to comprehensively evaluate the risk of bird strike at airports and effectively prevent the occurrence of bird strike events, this paper constructs the risk assessment index system of airport bird strike from five perspectives of “personnel-bird-equipment-environment-management”. For the purpose of maximizing variances, the Analytic Hierarchy Process (AHP) and the entropy weight method are combined and used to obtain the comprehensive weights. The five-element connection number of Set Pair Analysis (SPA) is introduced to establish the identical-discrepancy-contrary airport bird strike risk assessment model, and the risk trend is analyzed according to the partial connection number for each order. The experiment results show that the combined weighting method can minimize the weight deviation and demonstrate good accuracy in determining the weights of indicators at all levels. The established airport bird strike risk assessment model can reasonably predict the risk trend, which is significant for airport personnel to carry out bird strike prevention works.

1. Introduction

“Bird strike” refers to the safety accidents caused by the collision between birds and aircrafts at high speed in the air [1]. Flight accidents caused by bird strike not only cause huge economic losses to life, property, and national economy, but also seriously threaten aviation safety. This is an international problem which has plagued the aviation industry for a long time [2,3]. Therefore, it is the key to the current bird strike risk assessment research when considering the scientific and comprehensive paths to assess the risks of bird strike at airports, and to ensure flight safety.

Domestic and foreign scholars have continuously carried out bird strike risk assessment research from new perspectives. Reference [4] summarized the collision frequency between different types of birds and aircrafts, and evaluated the bird strike risk based on the bird strike database system constructed by nine airports in Australia. Reference [5] analyzed a large number of bird strike events over years, obtained the potential correlation of bird strike events based on the FP-Growth data mining algorithm, and judged the factors that led to the occurrence of bird strike through historical data. Reference [6] developed the Generalized Linear Models (GLMs) with binomial distribution in order to further quantify the risk degree of the airport bird strike events. Reference [7] developed a collision avoidance algorithm through the bird strike advisory system, and studied the efficacy of the system for air traffic control. Reference [8] calculated the risk of bird strike by predicting tracks of birds and esteeming the severity of a collision. They also evaluated the impacts on the safety and capacity of an airport when implementing the bird strike advisory system. Reference [9] conducted an investigation regarding the birds’ living and activity situation at an airport in North China, and constructed the ecological security pattern of high-risk birds by using landscape ecology theory. Reference [10] obtained the spatial distribution of the birds’ risk in different seasons by improving the feature importance assessment method, and found that the risk of bird strike has both seasonal and spatial differences. Reference [11] predicted the probability of bird strike through radar data from the US NEXRAD network. Reference [12] used the Geographically Weighted Regression (GWR) model, based on the least squares method, to evaluate the key factors of the density distribution of birds at an airport. This makes some contributions to the sustainable and safe development of the ecological environment near the airports. Reference [13] made a more reasonable prediction of bird strike risk factors based on Artificial Neural Network (ANN); however, this did not consider the special environmental impact factors of airports. Reference [14] used real-time bird status information from the airport bird detection radar to quantitatively analyze and calculate bird strike risks. However, this method is limited to specific bird detection radar equipment, without the universal characteristic. Reference [15] established a real-time bird strike risk assessment model based on associated factors, such as bird detection radar and flight data; however, the model was not dynamic, and the early established bird situation database was not considered. In addition, several common airport bird strike risk assessment methods also provide feasible ideas and methods for carrying out bird strike risk assessment according to the ecological works at airports and surrounding areas, mainly including the feature importance assessment method [16,17], grey fuzzy assessment method [18,19], and risk matrix assessment method [20,21].

Although domestic and foreign scholars have conducted relatively comprehensive research on bird strike risk assessments, furthermore, the mentioned methods can play a certain role in airport bird strike risk assessments. However, these cannot comprehensively evaluate certain and uncertain factors, and cannot make reasonable predictions on the risk trends. The set pair analysis method is a comprehensive analysis method to study the interaction between certainty and uncertainty of the system [22], which has been widely used in many fields, such as environmental assessment [23,24] and engineering technology [25,26]. The main contributions of this paper can be summarized as follows.

(1)

From the perspective of “personnel-bird-equipment-environment-management”, this paper established a risk assessment index system related to airport bird strike.

(2)

A variance maximization-based combined weighting method is designed by coupling subjective and objective factors, and has better accuracy in determining the weights of indicators at all levels.

(3)

Based on the SPA theory, the identical-discrepancy-contrary airport bird strike risk assessment model is established, and the risk trend of airport bird strike is predicted according to the partial connection numbers.

The rest of this paper is organized as follows. Section 2 describes the methods associated with set pair analysis. Section 3 proposes an airport bird strike risk assessment model. Section 4 presents a more detailed case study and results analysis. Finally, the conclusions are drawn in Section 5.

2. Materials and Methods

2.1. Set Pair Analysis and Connection Number

The set pair analysis method uses the connection number to effectively analyze the uncertainty factors in the system, whose core idea is to establish two sets with certain connections [27]. The characteristics of each set include terms identity, difference, and opposite. Take two sets as an example, shown in Figure 1.

In order to meet the multi-level complex requirements of the practical problems, the connection number can be extended to different levels. The multi-element connection number equation is given by Equation (1).

$$\mu =a+b_1{\tau }_1+b_2{\tau }_2+\cdots +b_{t-2}{\tau }_{t-2}+c\eta$$

(1)

where μ is the connection number. a is the degree of identity, b_t−2 are the degrees of difference, and c is the degree of opposite, which satisfies a + b₁ + b₂ + … + b_t−2 + c = 1(t ≥ 3). The difference uncertainty coefficients are τ_t−2 and τ_t-2 ∈ [–1, 1] (t ≥ 3), and η is the opposite coefficient, which usually equals to –1.

When t = 3, the general expression for the connection number is shown as follows.

$$\mu =a+b_1{\tau }_1+c\eta$$

(2)

When t = 5, the five-element connection number equation can be obtained as follows.

$$\mu =a+b_1{\tau }_1+b_2{\tau }_2+b_3{\tau }_3+c\eta$$

(3)

2.2. Partial Connection Number

The partial connection numbers represent the trends of identities, differences, and opposites. When carrying out the risk assessments of bird strike at airports, the partial connection numbers of different orders can be introduced in order to analyze the trends of risks. The partial connection numbers of various orders are shown as follows [28].

The first-order partial connection number is

$$\partial \mu =\partial a+{\tau }_1\partial b_1+{\tau }_2\partial b_2+{\tau }_3\partial b_3$$

(4)

where $\partial a=\frac{a}{{a+b}_1},\partial b_1=\frac{b_1}{b_1{+b}_2},\partial b_2=\frac{b_2}{b_2{+b}_3},\partial b_3=\frac{b_3}{b_3+c}$.

The second-order partial connection number is

$${\partial }^2\mu =\partial \left(\partial \mu \right)={\partial }^{2}a+{\tau }_1{\partial }^2{b}_1+{\tau }_2{\partial }^2{b}_2$$

(5)

where ${\partial }^{2}a=\frac{\partial a}{\partial a+\partial b_1},{\partial }^2{b}_1=\frac{\partial b_1}{\partial b_1+\partial b_2},{\partial }^2{b}_2=\frac{\partial b_2}{\partial b_2+\partial b_3}$.

The third-order partial connection number is

$${\partial }^3\mu ={\partial }^2\left(\partial \mu \right)={\partial }^{3}a+{\tau }_1{\partial }^3{b}_1$$

(6)

where ${\partial }^{3}a=\frac{{\partial }^{2}a}{{\partial }^{2}a+{\partial }^2{b}_1},{\partial }^3{b}_1=\frac{{\partial }^2{b}_1}{{\partial }^2{b}_1+{\partial }^2{b}_2}$.

The fourth-order partial connection number is

$${\partial }^4\mu ={\partial }^3\left(\partial \mu \right)={\partial }^{4}a$$

(7)

where ${\partial }^{4}a=\frac{{\partial }^{3}a}{{\partial }^{3}a+{\partial }^3{b}_1}$.

When ${\partial }^{\theta }\mu$ > 0, it presents an upward trend, which indicates that the risk is decreasing. When ${\partial }^{\theta }\mu$ = 0, it indicates that the risk is constant. When ${\partial }^{\theta }\mu$ < 0, it presents a downward trend, which indicates that the risk is increasing.

3. Airport Bird Strike Risk Assessment Model

The airport bird strike risk assessment process is shown in Figure 2. The corresponding index system is constructed. The risk assessment process also includes the corresponding levels’ divisions of the airport bird strike risks, the indicators’ weights determination, the identical-discrepancy-contrary airport bird strike risk assessment model construction, and the situation and trend of the risk analysis.

3.1. Airport Bird Strike Risk Assessment Index System and Risk Classifications

As References [13,19,29] analyzed, the hierarchical structure of the airport bird strike risk assessment index system includes a target layer, criterion layer, and indicator layer, respectively. First, the ultimate target layer is the airport bird strike risk assessment. Second, the criterion layer includes five factors that affect the airport bird strike risks: personnel factors, bird factors, equipment factors, environmental factors, and management factors. Finally, the indicator layer is mainly refined based on the key points of the criterion layer. A total of 22 secondary indicators with typical representatives are selected as shown in Figure 3.

According to the “Guidelines for the Precaution of Common Birds in Civil Airports” (AC-140-CA-2010-1), “Measures for the Precaution of Bird Strike and Animal Intrusions in Transport Airports” (AP-140-CA-2022-02), “Guidelines for the Construction of Safety Management System (SMS) in Transport Airports” (AC-139/140-CA-2019-3), and “Catalogues of Dangerous Bird Species for the Precaution Bird Strike Aircrafts in Transport Airports” (AC-140-CA-2022-01), the airport bird strike risks are divided into 5 levels: Level I (lower), Level II (low), Level III (medium), Level IV (high), and Level V (higher) as shown in

Table 1. Risk level evaluation standards for airport bird strike.

Risk Levels	Descriptions
Level I	Negligible, airport managers do not need to take risk control measures
Level II	Tolerable, airport managers do not need to take risk control measures, but need to pay attention
Level III	Acceptable, airport managers need to take appropriate risk control measures
Level IV	Partially acceptable, airport managers must take risk control measures
Level V	Unacceptable, airport managers must attach great importance and take risk control measures

.

3.2. Indicators’ Weights Determination Method

The existing index weight calculation methods have their own advantages and disadvantages [30,31]. The entropy weight method is relatively objective. However, its application scope is limited [30]. The AHP method, as shown in Reference [31], cannot reflect the objectivity of the calculation results. Therefore, inspired by the maximum variance introduced in Reference [32], the methods mentioned above are combined to construct the linear programming model.

$$max {\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{(x_{ij}-\overline{x_{ij}})}^2}}{W}_j=max{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{(x_{ij}-\overline{x_{ij}})}^2}}(\alpha U_j+\beta V_j)$$

(8)

where x_ij are the normalization results of the elements of the risk judgment matrix Z, which can be calculated by Equation (9), and $\overline{x_{ij}}$ is the arithmetic mean of x_ij, that is $\overline{x_{ij}}=\frac{1}{v}{\displaystyle \sum _{j=1}^v{x}_{\mathrm{ij}} \left(i=1,2,\cdots m,j=1,2,\dots v\right)}$. The risk judgment matrix Z can be constructed by the nine-scale method as shown in

Table 2. Scales and meanings of the nine-scale method.

Scales	Meanings
1	i is as important as j
3	i is slightly more important than j
5	i is more important than j
7	i is very much more important than j
9	i is more important than j
2, 4, 6, 8	The importance is in the middle of the 1, 3, 5, 7, 9 scales
reciprocal	If the importance relationship between i and j is zij, the importance relationship between j and i is zji = 1/zij.

. Both α and β are linear positive coefficients that satisfy ${\alpha }^2+{\beta }^2=1$; U_j are the objective weights determined by the entropy weight method and calculated by Equations (10) and (11); V_j are the subjective weights determined by AHP and calculated by Equations (12)–(14).

$$x_{ij}=\{\begin{array}{c}\frac{z_{ij}}{{\displaystyle \sum _{i=1}^m{z}_{ij}}}{z}_{ij}\ne 0\\ \frac{1+z_{ij}}{{\displaystyle \sum _{i=1}^m(1+z_{ij})}}{z}_{ij}=0\end{array}$$

(9)

The entropy weights H_j are determined by Equation (10).

$$H_j=-{\left(\ln m\right)}^{-1}{\displaystyle \sum _{i=1}^m{x}_{ij}\times \ln \left(x_{ij}\right)}$$

(10)

The objective weights U_j are calculated by Equation (11).

$$U_j=\frac{1-H_j}{{\displaystyle \sum _{j=1}^v\left(1-H_j\right)}}$$

(11)

A consistency test is carried out on the risk judgment matrix Z, and the consistency indicator is set as CI.

$$CI=\frac{{\lambda }_{max}-n}{n-1}$$

(12)

where ${\mathsf{\lambda }}_{max}$ is the largest eigenvalue of the judgment matrix Z, and n is the order of the judgment matrix Z.

The consistency ratio CR is determined by Equation (13).

$$CR=\frac{CI}{RI}$$

(13)

The value of mean consistency index RI is determined by the different orders of the judgment matrix Z, as shown in

Table 3. RI values under different orders.

n	1	2	3	4	5	6	7	8	9	10
RI	0	0	0.52	0.89	1.12	1.26	1.36	1.41	1.46	1.49

. When CR < 0.1, the judgment matrix Z conforms to the consistency test and is regarded as a reasonable judgment matrix; otherwise, the judgment matrix Z needs to be adjusted.

The subjective weights V_j are calculated by Equation (14).

$$V_j=\frac{{({\displaystyle \prod _{i=1}^m{z}_{ij}})}^{\frac{1}{m}}}{{\displaystyle \sum _{p=1}^m{({\displaystyle \prod _{j=1}^v{z}_{pj}})}^{\frac{1}{m}}}}$$

(14)

Lagrangian function is constructed, as shown in Equation (15), to solve the optimization problem.

$$L(\alpha ,\beta ,\delta )={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{(x_{ij}-\overline{x_{ij}})}^2}}(\alpha U_j+\beta V_j)+\delta ({\alpha }^2+{\beta }^2-1)$$

(15)

where δ is the Lagrangian multiplier. The partial derivative of L(α, β, δ) is calculated with respect to the linear coefficients α, β, and the multiplier δ, and it is set at 0 as shown in Equations (16)–(18).

$$\frac{\partial L(\alpha ,\beta ,\delta )}{\partial \alpha }={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{(x_{ij}-\overline{x_{ij}})}^2}}{U}_j+2\delta \alpha =0$$

(16)

$$\frac{\partial L(\alpha ,\beta ,\delta )}{\partial \beta }={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{(x_{ij}-\overline{x_{ij}})}^2}}{V}_j+2\delta \beta =0$$

(17)

$$\frac{\partial L(\alpha ,\beta ,\delta )}{\partial \delta }={\alpha }^2+{\beta }^2-1=0$$

(18)

The linear coefficients α and β are expressed as follows.

$$\alpha =\frac{1}{{\left[1+\frac{{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{\left(x_{ij}-\overline{x_{ij}}\right)}^2{U}_j}}}{{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{\left(x_{ij}-\overline{x_{ij}}\right)}^2{V}_j}}}\right]}^{0.5}}$$

(19)

$$\beta =\frac{1}{{\left[1+\frac{{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{(x_{ij}-\overline{x_{ij}})}^2}}{V}_j}{{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^v{(x_{ij}-\overline{x_{ij}})}^2}}{U}_j}\right]}^{0.5}}$$

(20)

Equations (19) and (20) are substituted into Equation (8) to obtain W₀ = (W₀₁, W₀₂, …, W_0v), and W₀ is normalized to obtain the final comprehensive weights matrix W = (W₁, W_2, …, W_v).

3.3. The Identical-Discrepancy-Contrary Airports Bird Strike Risk Assessment Model

After determining the comprehensive weights W of each indicator, Equation (21) is used in order to estimate the impact of each indicator on the airport bird strike risk assessment.

$$R_s=\frac{N_s}{N}$$

(21)

where R_s represents the risk degree of the evaluation indicator, N_s represents the number of experts who divide the indicator into the corresponding risk level s, and N is the total number of experts.

The identical-discrepancy-contrary airports bird strike risk assessment model is established.

$$\begin{array}{cc}\hfill \mu & =WR{E}^T\hfill \\ & =(W_1,W_2,\dots ,W_v)\left(\begin{array}{ccccc}{R}_{11}& R_{12}& R_{13}& R_{14}& R_{15}\\ R_{21}& R_{22}& R_{23}& R_{24}& R_{25}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ R_{v1}& R_{v2}& R_{v3}& R_{v4}& R_{v5}\end{array}\right)\left(\begin{array}{c}1\\ {\tau }_1\\ {\tau }_2\\ {\tau }_3\\ \eta \end{array}\right)\hfill \\ & ={\displaystyle \sum _{k=1}^v{W}_k{R}_{k1}}+{\displaystyle \sum _{k=1}^v{W}_k{R}_{k2}}{\tau }_1+{\displaystyle \sum _{k=1}^v{W}_k{R}_{k3}}{\tau }_2+{\displaystyle \sum _{k=1}^v{W}_k{R}_{k4}}{\tau }_3+{\displaystyle \sum _{k=1}^v{w}_k{R}_{k5}\eta }\hfill \\ & =a+b_1{\tau }_1+b_2{\tau }_2+b_3{\tau }_3+c\eta \hfill \end{array}$$

(22)

where W is the comprehensive weight coefficients matrix, R is the identical-discrepancy-contrary matrix, and E^T is the identical-discrepancy-contrary coefficients vector. The meaning of the specific parameters is shown in

Table 4. Meaning of model parameters and the corresponding risk levels.

Parameters	Meanings	Risk Levels
$a={\displaystyle \sum _{k=1}^v{w}_k{R}_{k1}}$	Same degree measure component	Level I
$b_1={\displaystyle \sum _{k=1}^v{w}_k{R}_{k2}}$	Partial measure component	Level II
$b_2={\displaystyle \sum _{k=1}^v{w}_k{R}_{k3}}$	Neutral measure component	Level III
$b_3={\displaystyle \sum _{k=1}^v{w}_k{R}_{k4}}$	Biased measure component	Level IV
$c={\displaystyle \sum _{k=1}^v{w}_k{R}_{k5}}$	Opposite measure component	Level V

.

3.4. Set Pair Potential Analysis

To some extent, the set pair potential reflects the dynamic evolutionary trends of the two sets including the same, balanced, and contrary trends. The function is expressed by Equation (23).

$$SHI\left(\mu \right)=\frac{a}{c}$$

(23)

When the set pair potential value is greater than 1, it represents the “same trend”, indicating that the risk of the assessment indicator is low. When the set pair potential is 1, it represents the “balanced trend”, indicating that the risk of the assessment indicator is medium. When the set pair potential is less than 1, it represents the “contrary trend”, indicating that the risk of the assessment indicator is high. Furthermore, the airport managers must take certain risk control measures to transmit the set pair potential to the “balanced trend” in order to achieve the “same trend”.

Table 5. Classification of set pair potential.

Parameters Relationships	Potential Levels
a > c, a < b1, b1 > b2, b2 < b3, b3 > c	Same trend level 61
a > c, a < b1, b1 < b2, b2 > b3, b3 > c	Same trend level 73
a < c, a > b1, b1 > b2, b2 < b3, b3 > c	Contrary trend level 169
a < c, a < b1, b1 > b2, b2 < b3, b3 > c	Contrary trend level 223
a < c, a < b1, b1 < b2, b2 < b3, b3 > c	Contrary trend level 241

shows the classifications of set pair potentials derived from Reference [33], which are associated with the set pair potential analysis in this paper.

4. Case Study

Taking an airport in North China as an example, the airport managers coming from the flight area departments were invited to score the indicators. The airport is located in the northeastern part of the North China Plain and faces the Bohai Sea in the east. In addition, the airport is located in the East Asian–Australian Flyway, one of the word’s nine major bird migration routes, which is an important stopover for the north–south migration of birds in China. The surrounding environment of the airport is mainly composed of large urban areas, villages, and farmland. The habitats in the airport flight area are mainly grasslands, buildings, boundary areas, ponds, and drainage channels. Twenty selected complete surveys were used to build the identical-discrepancy-contrary airports bird strike risk assessment model, which is designed according to the indicators as shown in Figure 3. SPSS (Statistical Product Service Solutions) was used to test the reliability of the survey data. The corresponding Cromabach Alpha coefficient is 0.925, which indicates that the reliability of the data is high. Furthermore, it is demonstrated that the airport bird strike risk index system established in this paper is reasonable.

4.1. Weights of Evaluation Indicators Calculation

Taking the criterion layer indicators C₁, C₂, C₃, C₄, and C₅ as examples, the scores of five experts are listed first. The objective weights U are calculated by Equations (10) and (11), while the subjective weights V are calculated by Equations (12)–(14). The linear coefficients’ α and β values can be obtained by Equations (19) and (20), and the results are listed in Equation (24).

Table 6. Scoring and weights calculation results of criterion layers.

Criterion Layer	Expert A	Expert B	Expert C	Expert D	Expert E	Objective Weight U	Subjective Weight V	Comprehensive Weight W
C1	1	2	2	1	2	0.2641	0.1321	0.1927
C2	7	5	4	4	4	0.1659	0.2527	0.2119
C3	3	2	3	3	3	0.1101	0.2094	0.1629
C4	5	5	4	5	6	0.1925	0.2621	0.2292
C5	2	3	2	3	1	0.2674	0.1489	0.2033

shows the results of the scoring of criterion layers and the weights calculation.

$$\alpha =0.6536,\beta =0.7568$$

(24)

The weight values, as shown in Table 6, are plotted in Figure 4. Figure 4 shows that the values of comprehensive weights W are located between the objective weights U and the subjective weights V. This indicates that the designed combined weighting method weakens the deviation degree of some indicators of the entropy weight method. Furthermore, it reduces the subjective influence of the AHP method, so that the calculation results have better accuracy.

Similarly, the weights of each indicator are determined, and the results are shown in

Table 7. Weights for each indicator.

Criterion Layer	Indicator Layer	Objective Weight U	Subjective Weight V	Comprehensive Weight W
C1 (0.1927)	C11	0.5770	0.1153	0.3292
	C12	0.2400	0.1735	0.2043
	C13	0.0729	0.3284	0.2100
	C14	0.1102	0.3828	0.2565
C2 (0.2119)	C21	0.1854	0.1728	0.1786
	C22	0.1879	0.1821	0.1848
	C23	0.1975	0.1368	0.1649
	C24	0.1104	0.1942	0.1554
	C25	0.2007	0.1579	0.1777
	C26	0.1181	0.1562	0.1385
C3 (0.1629)	C31	0.2561	0.1873	0.2192
	C32	0.2782	0.2087	0.2409
	C33	0.3316	0.2826	0.3053
	C34	0.1341	0.3215	0.2346
C4 (0.2292)	C41	0.2982	0.2549	0.2750
	C42	0.1975	0.2847	0.2443
	C43	0.1455	0.2414	0.1970
	C44	0.3588	0.2189	0.2838
C5 (0.2033)	C51	0.3604	0.2109	0.2802
	C52	0.2058	0.2318	0.2198
	C53	0.2352	0.2070	0.2201
	C54	0.1986	0.3503	0.2800

.

4.2. Risk Situations and Trends Analysis

The identical-discrepancy-contrary airports bird strike risk assessment model is constructed from Equation (22), with the weights of each indicator calculated above. The partial connection numbers for different orders are calculated by Equations (4)–(7). The set pair potential analysis results are shown in

Table 8. Five-element connection numbers and first-order partial connection numbers.

Criterion Layer	Indicator Layer	Five-Element Connection Number	Situation	First-Order Partial Connection Number	Trend
C1 (0.1927)	C11	0.30 + 0.25τ1 + 0.20τ2 + 0.20τ3 + 0.05η	Same	0.55 + 0.56τ1 + 0.50τ2 + 0.80τ3	Downward
	C12	0.25 + 0.20τ1 + 0.25τ2 + 0.15τ3 + 0.15η	Same	0.56 + 0.44τ1 + 0.63τ2 + 0.50τ3	Upward
	C13	0.10 + 0.25τ1 + 0.30τ2 + 0.20τ3 + 0.15η	Contrary	0.29 + 0.45τ1 + 0.60τ2 + 0.57τ3	Downward
	C14	0.00 + 0.25τ1 + 0.35τ2 + 0.30τ3 + 0.10η	Contrary	0.00 + 0.42τ1 + 0.54τ2 + 0.75τ3	Downward
	Add up	0.17 + 0.24τ1 + 0.27τ2 + 0.22τ3 + 0.10η	Same	0.41 + 0.47τ1 + 0.55τ2 + 0.69τ3	Downward
C2 (0.2119)	C21	0.00 + 0.10τ1 + 0.10τ2 + 0.35τ3 + 0.45η	Contrary	0.00 + 0.50τ1 + 0.22τ2 + 0.44τ3	Downward
	C22	0.10 + 0.20τ1 + 0.30τ2 + 0.20τ3 + 0.20η	Contrary	0.33 + 0.40τ1 + 0.60τ2 + 0.50τ3	Downward
	C23	0.00 + 0.15τ1 + 0.30τ2 + 0.30τ3 + 0.25η	Contrary	0.00 + 0.33τ1 + 0.50τ2 + 0.55τ3	Downward
	C24	0.15 + 0.25τ1 + 0.20τ2 + 0.30τ3 + 0.10η	Same	0.38 + 0.56τ1 + 0.40τ2 + 0.75τ3	Downward
	C25	0.15 + 0.30τ1 + 0.25τ2 + 0.15τ3 + 0.15η	Balanced	0.33 + 0.55τ1 + 0.63τ2 + 0.50τ3	Downward
	C26	0.20 + 0.30τ1 + 0.15τ2 + 0.20τ3 + 0.15η	Same	0.40 + 0.67τ1 + 0.43τ2 + 0.57τ3	Downward
	Add up	0.10 + 0.21τ1 + 0.22τ2 + 0.25τ3 + 0.22η	Contrary	0.32 + 0.49τ1 + 0.47τ2 + 0.53τ3	Downward
C3 (0.1629)	C31	0.25 + 0.30τ1 + 0.05τ2 + 0.25τ3 + 0.15η	Same	0.45 + 0.86τ1 + 0.17τ2 + 0.63τ3	Downward
	C32	0.25 + 0.15τ1 + 0.05τ2 + 0.30τ3 + 0.25η	Balanced	0.63 + 0.75τ1 + 0.14τ2 + 0.55τ3	Upward
	C33	0.20 + 0.10τ1 + 0.15τ2 + 0.30τ3 + 0.25η	Contrary	0.67 + 0.40τ1 + 0.33τ2 + 0.55τ3	Upward
	C34	0.05 + 0.15τ1 + 0.20τ2 + 0.30τ3 + 0.30η	Contrary	0.25 + 0.43τ1 + 0.40τ2 + 0.50τ3	Downward
	Add up	0.19 + 0.17τ1 + 0.12τ2 + 0.29τ3 + 0.24η	Contrary	0.53 + 0.59τ1 + 0.29τ2 + 0.55τ3	Downward
C4 (0.2292)	C41	0.00 + 0.55τ1 + 0.15τ2 + 0.20τ3 + 0.10η	Contrary	0.00 + 0.79τ1 + 0.43τ2 + 0.67τ3	Downward
	C42	0.00 + 0.25τ1 + 0.30τ2 + 0.35τ3 + 0.10η	Contrary	0.00 + 0.45τ1 + 0.46τ2 + 0.78τ3	Downward
	C43	0.20 + 0.30τ1 + 0.20τ2 + 0.10τ3 + 0.20η	Balanced	0.40 + 0.60τ1 + 0.67τ2 + 0.33τ3	Upward
	C44	0.30 + 0.30τ1 + 0.10τ2 + 0.20τ3 + 0.10η	Same	0.50 + 0.75τ1 + 0.33τ2 + 0.67τ3	Downward
	Add up	0.13 + 0.36τ1 + 0.18τ2 + 0.22τ3 + 0.12η	Same	0.27 + 0.67τ1 + 0.45τ2 + 0.65τ3	Downward
C5 (0.2033)	C51	0.30 + 0.25τ1 + 0.15τ2 + 0.05τ3 + 0.25η	Same	0.55 + 0.63τ1 + 0.75τ2 + 0.17τ3	Upward
	C52	0.10 + 0.30τ1 + 0.20τ2 + 0.30τ3 + 0.10η	Balanced	0.25 + 0.60τ1 + 0.40τ2 + 0.75τ3	Downward
	C53	0.20 + 0.35τ1 + 0.05τ2 + 0.25τ3 + 0.15η	Same	0.36 + 0.88τ1 + 0.17τ2 + 0.63τ3	Downward
	C54	0.00 + 0.05τ1 + 0.25τ2 + 0.45τ3 + 0.25η	Contrary	0.00 + 0.17τ1 + 0.36τ2 + 0.64τ3	Downward
	Add up	0.15 + 0.23τ1 + 0.17τ2 + 0.26τ3 + 0.20η	Contrary	0.39 + 0.58τ1 + 0.40τ2 + 0.57τ3	Downward
Add up in total		0.14 + 0.25τ1 + 0.19τ2 + 0.24τ3 + 0.17η	Contrary	0.37 + 0.56τ1 + 0.44τ2 + 0.59τ3	Downward

and

Table 9. Partial connection numbers of the second, third, and fourth orders.

Criterion Layer	Indicator Layer	Second- Order	Trend	Third- Order	Trend	Fourth- Order	Trend
C1 (0.1927)	C11	0.50 + 0.53τ1 + 0.38τ2	Downward	0.49 + 0.58τ1	Downward	0.46	Upward
	C12	0.56 + 0.42τ1 + 0.56τ2	Downward	0.57 + 0.43τ1	Upward	0.57	Upward
	C13	0.39 + 0.43τ1 + 0.51τ2	Downward	0.47 + 0.46τ1	Upward	0.51	Upward
	C14	0.00 + 0.44τ1 + 0.42τ2	Downward	0.00 + 0.51τ1	Downward	0.00	Constant
	Add up	0.47 + 0.46τ1 + 0.44τ2	Downward	0.50 + 0.51τ1	Downward	0.50	Upward
C2 (0.2119)	C21	0.00 + 0.69τ1 + 0.34τ2	Downward	0.00 + 0.67τ1	Downward	0.00	Constant
	C22	0.45 + 0.40τ1 + 0.55τ2	Downward	0.53 + 0.42τ1	Upward	0.56	Upward
	C23	0.00 + 0.40τ1 + 0.48τ2	Downward	0.00 + 0.46τ1	Downward	0.00	Constant
	C24	0.40 + 0.58τ1 + 0.35τ2	Downward	0.41 + 0.63τ1	Downward	0.40	Upward
	C25	0.38 + 0.47τ1 + 0.56τ2	Downward	0.45 + 0.46τ1	Downward	0.50	Upward
	C26	0.38 + 0.61τ1 + 0.43τ2	Downward	0.38 + 0.59τ1	Downward	0.40	Upward
	Add up	0.40 + 0.51τ1 + 0.47τ2	Downward	0.44 + 0.52τ1	Downward	0.47	Upward
C3 (0.1629)	C31	0.35 + 0.84τ1 + 0.21τ2	Downward	0.29 + 0.80τ1	Downward	0.27	Upward
	C32	0.45 + 0.84τ1 + 0.21τ2	Downward	0.35 + 0.80τ1	Downward	0.30	Upward
	C33	0.63 + 0.55τ1 + 0.38τ2	Downward	0.53 + 0.59τ1	Downward	0.48	Upward
	C34	0.37 + 0.52τ1 + 0.44τ2	Downward	0.42 + 0.54τ1	Downward	0.44	Upward
	Add up	0.47 + 0.67τ1 + 0.35τ2	Downward	0.42 + 0.66τ1	Downward	0.39	Upward
C4 (0.2292)	C41	0.00 + 0.65τ1 + 0.39τ2	Downward	0.00 + 0.62τ1	Downward	0.00	Constant
	C42	0.00 + 0.50τ1 + 0.37τ2	Downward	0.00 + 0.57τ1	Downward	0.00	Constant
	C43	0.40 + 0.47τ1 + 0.67τ2	Downward	0.46 + 0.42τ1	Upward	0.52	Upward
	C44	0.40 + 0.69τ1 + 0.33τ2	Downward	0.37 + 0.68τ1	Downward	0.35	Upward
	Add up	0.28 + 0.60τ1 + 0.41τ2	Downward	0.32 + 0.59τ1	Downward	0.35	Upward
C5 (0.2033)	C51	0.47 + 0.45τ1 + 0.82τ2	Downward	0.51 + 0.36τ1	Upward	0.59	Upward
	C52	0.29 + 0.60τ1 + 0.35τ2	Downward	0.33 + 0.63τ1	Downward	0.34	Upward
	C53	0.29 + 0.84τ1 + 0.21τ2	Downward	0.26 + 0.80τ1	Downward	0.24	Upward
	C54	0.00 + 0.32τ1 + 0.36τ2	Downward	0.00 + 0.47τ1	Downward	0.00	Constant
	Add up	0.41 + 0.59τ1 + 0.41τ2	Downward	0.41 + 0.59τ1	Downward	0.41	Upward
Add up in total		0.40 + 0.56τ1 + 0.43τ2	Downward	0.41 + 0.57τ1	Downward	0.42	Upward

.

4.3. Results Analysis

(1)

Table 7 shows that the indicators “bird factors C₂” and “environmental factors C₄” have greater weights among the criterion layers, which have a higher degree of impact on the airport bird strike risk. The indicator layer indicators “number of bird-repelling personnel C₁₁”, “types of birds at the airport C₂₂”, “maintenance of bird-repelling equipment C₃₃”, “weather and climate at the airport C₄₄”, and “daily inspection system C₅₁” have relatively large weights, indicating that these factors are important reasons for the occurrence of airport bird strike events.

(2)

Table 8 shows that the five-element connection number of airport bird strike risk is μ = 0.14 + 0.25τ₁ + 0.19τ₂ + 0.24τ₃ + 0.17η, and its set pair potential calculated by Equation (23) is 0.82. It locates at contrary trend level 223, indicating that the risk is high. In addition, the risk situations of each criterion layer indicator are shown as follows. “personnel factors C₁” locates at same trend level 73, “bird factors C₂” locates at contrary trend level 241, “equipment factors C₃” locates at contrary trend level 169, “environmental factors C₄” locates at same trend level 61, and “management factors C₅” locates at contrary trend level 223. Among the 22 indicator layer indicators, 8 factors have the same trend, 4 factors have the balanced trend, and 10 factors have the contrary trend. The number of the contrary trend factors is slightly more than that of the same trend factors.

(3)

Table 9 shows that the first, second, and third-order partial connection numbers all locate in a downward trend, indicating that the risk trend is increasing. The fourth-order partial connection number locates in an upward trend, indicating that the risk trend is decreasing. This demonstrates that the airport bird strike risk has a dynamic trend. Overall, the indicators can be divided into five types, as shown in

Table 10. Risk classification of each indicator.

Type	Indicator	Partial Connection Number
		First Order	Second Order	Third Order	Fourth Order
1	C12, C43, C51	↑	↓	↑	↑
2	C32, C33	↑	↓	↓	↑
3	C13, C22	↓	↓	↑	↑
4	C1, C2, C3, C4, C5, C11, C24, C25, C26, C31, C34, C44, C52, C53	↓	↓	↓	↑
5	C14, C21, C23, C41, C42, C54	↓	↓	↓	-

, where “↑” indicates that the partial connection number locates in an upward trend, “↓” indicates that the partial connection number locates in a downward trend, and “—” indicates that the partial connection number locates in a constant state. It is worth noting that “competency level of bird-repelling personnel C₁₄”, “number of birds at the airport C₂₁”, “frequency of birds at the airport C₂₃”, “habitat at the airport C₄₁”, “water source at the airport C₄₂”, and “emergency management system C₅₄” are strong contrary factors. Therefore, when dealing with bird strike at the airports, we should first pay attention to indicators C₁₄, C₂₁, C₂₃, C₄₁, C₄₂, and C₅₄, then indicators C₁₁, C₂₄, C₂₅, C₂₆, C₃₁, C₃₄, C₄₄, C₅₂, and C₅₃, then indicators C₁₃, C₂₂, C₂₂, C₃₂, and C₃₃, and finally, indicators C₁₂, C₄₃, and C₅₁.

(4)

When considering the strong contrary factors mentioned above, the airport managers should build up the professional team, form a cooperation system between professional talents and experienced talents, set up a high-level bird strike prevention team, and carry out the bird-repelling work efficiently. In terms of equipment, the airport managers should strictly conduct regular inspections and maintenance of various types of bird-repelling equipment, and ensure the layout is prioritized in significant areas for bird strike prevention, such as runways, taxiways, and aircraft takeoff or landing directions. It is suggested that the linkage use of all kinds of bird-repelling equipment be strengthened, and that the bird-repelling work be carried out from multiple dimensions in terms of hearing, vision, smell, and physical interception. In addition, the airport managers should establish an emergency management system according to the characteristics of the local data and information on birds, and should also improve the other working mechanisms, such as airport bird information notifications, navigation notices, and flight dynamic adjustments. Furthermore, the airport managers ought to establish a coordination mechanism with the local governments and carry out management of the ecological environment around the airport, such as bird habitats, water sources, and farming land. Therefore, the number and frequency of birds flying around the airport can also be reduced. As a result, the threat of bird strike to flight safety is reduced to some extent. In the end, the airport managers should prepare to prevent danger and focus on the factors for the contrary trend, so as to minimize the risk of airport bird strike.

5. Conclusions

There are many factors that influence bird strike events, but few previous studies have focused on certain and uncertain factors of bird strike risk. This paper evaluates airport bird strike risk based on the SPA model, from a fresh perspective. Guided by the SPA theory, this study analyzes the risk factors of airport bird strike, constructs an airport bird strike risk assessment index system from the perspective of “personnel-bird-equipment-environment-management”, and establishes the identical-discrepancy-contrary airport bird strike risk assessment model. In addition, inspired by the maximum variance idea, an indicators’ weights determination method is designed by coupling subjective and objective factors in order to calculate the weights of each indicator.

Taking an airport in North China as an example, the results of the study indicate that the proposed model in this paper can, on one hand, evaluate the risk of bird strike; on the other hand, it can analyze the risk trend of bird strike. Finally, it can achieve static and dynamic assessments for the risk of bird strike at airports. Furthermore, the method developed in this paper will be able to provide a data reference for airport managers to reduce the airport bird strike risk, which is significant for airport personnel to carry out bird strike prevention works.

In this study, the airport bird strike risk assessment index system only considers five factors; however, all kinds of detailed factors should also be taken into consideration. This will be improved in future research. Aiming at promoting sustainable development of airport security, we do hope that our approach can be applied to different case study airports.