A method for airspace operation risk assessment based on fuzzy matter-element analysis

Abstract

This invention provides a method for airspace operation risk assessment based on fuzzy matter-element analysis, comprising: summarizing airspace operation risk indicators into conflict risk indicators and operational status risk indicators to establish a comprehensive operation risk assessment indicator system; calculating the weights of each assessment indicator using an objective weighting method; analyzing the classical domain and section domain of the airspace operation risk matter-element model using a clustering algorithm; determining the risk level of the assessment object by combining fuzzy mathematics theory, using membership functions as an objective measure of fuzziness, and providing a method for calculating membership degrees; finally, based on the indicator weights obtained in the above steps and the membership degrees of the assessment object with respect to each risk level, determining the airspace operation risk level according to the principle of maximum membership degree. This method avoids the interference of subjective human factors in the determination of operation risk levels, and because parameters such as the assessment system and the total number of risk levels can be flexibly set, it ensures the practicality and scalability of the algorithm, and can provide a basis for risky airspace identification.

Description

Technical Field

[0001] This invention relates to a method for assessing airspace operation risks, and more particularly to a method for assessing airspace operation risks based on fuzzy matter-element analysis. Background Technology

[0002] With the continuous development of my country's air transport industry, the complexity of air traffic operations and potential operational risks are constantly increasing, highlighting the growing importance of real-time assessment of the comprehensive operational risks of airspace units. Comprehensive airspace operational risk assessment is a typical multivariate correlation analysis problem, related to multiple factors, including flight schedules and airspace structure. Objective and quantitative airspace operational risk assessment plays a crucial role in improving airspace operational safety, reducing controller workload, and effectively assisting management personnel in making decisions such as flight schedule adjustments, operational plan design, and airspace structure adjustments.

[0003] Currently, commonly used airspace integrated operation risk assessment methods include Bayesian network-based safety risk assessment (reference: Research on General Aviation Safety Risk Assessment Based on Bayesian Network [J]. Ship Electronic Engineering, 2021, 41(3): 4.), analytic hierarchy process (reference: Research on Terminal Area Weather Situation Emergency Response Risk Assessment Model Based on Analytic Hierarchy Process [J]. Air Traffic, 2017(1): 4.), fuzzy comprehensive evaluation method (reference: Research on Low-Altitude Airspace Flight Safety Risk Assessment Method [J]. Young Scientists: Teacher Edition, 2014, 35(5)), and traditional matter-element analysis evaluation method (Research on Airport Apron Risk Assessment Based on Matter-Element Extension Model [J]. Journal of Civil Aviation, 2018(5): 6). These methods often rely on empirical values ​​for weight analysis, indicator assignment, or risk level range division, making the accuracy of the assessment values ​​dependent on the experience of air traffic controllers, thus making it difficult to objectively assess airspace operation risks. Summary of the Invention

[0004] Purpose of the invention: The technical problem to be solved by the present invention is to provide a method for assessing airspace operation risk based on fuzzy matter-element analysis, which addresses the shortcomings of the existing technology.

[0005] To address the aforementioned technical problems, this invention discloses a spatial operation risk assessment method based on fuzzy matter-element analysis, comprising the following steps:

[0006] Step 1: Construct an indicator system for airspace operation risk assessment;

[0007] Step 2: Determine the weights of the indicator system;

[0008] Step 3: Perform classical domain analysis and section domain analysis on the index system;

[0009] Step 4: Analyze the fuzzy correlation degree of the indicator system;

[0010] Step 5: Conduct a comprehensive risk assessment of the airspace operation based on the aforementioned indicator system.

[0011] Beneficial effects:

[0012] This invention constructs a comprehensive airspace operation risk assessment system. It employs the entropy method to assign values ​​to each indicator, and combines clustering algorithms with historical operational data analysis of the classical and nodal domains of the matter-element model. Based on this, it provides a method for calculating the membership degree of risk assessment indicators with respect to each risk level. Finally, an objective assessment value of airspace operation risk can be obtained based on the aforementioned indicator weights and membership degree matrix. The resulting operational risk assessment value is objective and effective, providing a basis for risky airspace identification and airspace control. Attached Figure Description

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0014] Figure 1 This is a schematic diagram of the overall invention.

[0015] Figure 2 A schematic diagram illustrating the specific implementation steps of this invention. Detailed Implementation

[0016] like Figure 1 As shown, a method for assessing airspace operational risks based on fuzzy matter-element analysis includes the following steps:

[0017] Step 1: Construct an indicator system for airspace operation risk assessment;

[0018] Step 2: Determine the weights of the indicator system;

[0019] Step 3: Perform classical domain analysis and section domain analysis on the index system;

[0020] Step 4: Analyze the fuzzy correlation degree of the indicator system;

[0021] Step 5: Conduct a comprehensive risk assessment of the airspace operation based on the aforementioned indicator system.

[0022] like Figure 2 As shown, this method specifically includes the following steps:

[0023] Step 1: Construct an airspace operation risk assessment indicator system

[0024] In a certain airspace to be evaluated, based on the airspace operation characteristics, the airspace operation risk indicator Ind is summarized as the conflict risk indicator Ind. Cand operational status risk indicators Ind M That is, Ind = {Ind} C Ind M The detailed information about the indicator system is as follows:

[0025] Conflict Risk Indicator Ind C Including the number of flight conflicts C num Conflict incidence rate C rate Conflict duration C time Severity of the conflict (C) degree , represented as Ind C ={C num C rate C time C degree}

[0026] Conflict number C num The number of events where the distance between flights was less than the safe distance during the assessment period T;

[0027] Conflict incidence rate C rat Conflict number C num The ratio of C to the total number of flights n rate =C num / n;

[0028] Conflict duration C time : The time taken for all aircraft to complete the resolution of an operational conflict within the assessment period T;

[0029] Severity of conflict C degree : Measures the severity of conflict among all aircraft within the assessment period T; let the start and end times of period T be t. start t end Aircraft with operational conflicts f i f j The distance between them is a function D of time t. ij (t), the required safety interval distance is Ds, η represents the proportional gain coefficient, and the parameter CS ij (t) characterizes the degree of dangerous proximity between aircraft. Then aircraft f i f j The severity of the conflict between them is expressed as Let U = {F1, F2, ..., F} be the set of aircraft with operational conflicts during the evaluation period T. num}, F pair If (pair = 1, 2, ..., num) represents a pair of aircraft with operational conflicts, then the severity of the conflict is...

[0030] Operational risk indicator Ind M Including heading number M DirNum Mean heading change M DirAvg Adjust the height M HeightNum Average height change M HeightAv Speed ​​adjustment number M SpdNum Average velocity change M SpdAvg , represented as Ind M ={M DirNum M DirAvg M HeightNum M HeightAvg M SpdNum M SpdAvg}

[0031] Adjusting heading number M DirNum The number of heading adjustment events that occurred within the assessment period T;

[0032] Mean heading change M DirAvg Suppose that when a heading adjustment event occurs, the heading change is Dir. d (d = 1, 2, ..., M) DirNum If the evaluation period is T, then...

[0033] Adjust height M HeightNum : Assess the number of altitude adjustment events that occurred within the time period T;

[0034] Average height change M HeightAvg Suppose that when a height adjustment event occurs, the height change is Hgt. h (h = 1, 2, ..., M) HeightNu If the evaluation period is T, then...

[0035] Speed ​​adjustment number M SpdNum The number of speed adjustment events that occurred within the assessment period T;

[0036] Average velocity change M SpdAvg Let Spd be the speed change when a speed adjustment event occurs. s (s = 1, 2, ..., M) SpdNum If the evaluation period is T, then...

[0037] Step 2: Determining the weights of the indicator system

[0038] By combining historical operational data, the entropy method is used to assign weights to operational risk assessment indicators. The main steps include:

[0039] Step 2-1, Normalization of Indicators

[0040] Take m historical operational data points of the airspace to be evaluated as samples, and let the sample set D = {Ind1, Ind2, ..., Ind...} m}, This represents the indicator system for the row-th sample in the sample set, where,

[0041] (row = 1, 2, ..., m) represents the sample Ind row The index value; represented by the code. col (col = 1, 2, ..., n) represents the col-th indicator in the risk assessment indicator system, and the sample index is Ind. row The index value is denoted as Ind row ={x row1 , ..., x row，col , ..., x row，n}, x row，col Indicating sample Ind row The Chinese code is coded. col Indicator value, n=10 represents the number of indicators in the indicator system.

[0042] All historical data were processed using linear dimensionless transformation; the airspace operation risk assessment index system described in step 1 was applied using the following formula:

[0043]

[0044] Perform normalization, min(x) col ) represents the sample set D with number Code. col The minimum value of the index, max(x) col ) indicates that the number is Code col The maximum value of the indicator, x′ row，col This represents the value after data normalization.

[0045] Step 2-2, Calculation of indicator weights

[0046] Step 2-2-1, Calculation of Sample Index Weights

[0047] Calculate the proportion p of the col-th indicator in the row-th sample to the total proportion of all samples for that indicator. row，col :

[0048] Step 2-2-2: Calculation of entropy value and information entropy redundancy.

[0049] The entropy value of the index col in Satisfy e col≥0; Indicator Code col Information entropy redundancy d col =1-e col ;

[0050] Step 2-2-3, evaluate the weight of the indicators

[0051] Use ω col Indicates the indicator Code col The weights of each risk assessment indicator are calculated using the following formula:

[0052] Step 3: Classical domain / section domain cluster analysis of the indicator system

[0053] Based on sample data D = {Ind1, Ind2, ..., Ind...} m}, combined with the fuzzy C-means algorithm (FCM) (Reference: Research on the improved K-means algorithm and new clustering effectiveness index combining density parameter and center replacement [J]. Computer Science, 2022, 49(1): 121-132.) to complete the classical domain and section domain analysis of the index system.

[0054] Step 3-1, Sectional Analysis of the Indicator System

[0055] In matter-element analysis theory, the domain refers to the range of values ​​for all levels of each characteristic of the object to be evaluated, combined with sample data D.

[0056] The index field can be represented as:

[0057]

[0058] In the formula, R fp N represents the matter-element model for airspace operation risk assessment. fp Indicates the level of airspace operational risk, X fpcol = fpcol b fpcol >, (col = 1, 2, ..., n) represents the indicator Code. col The range of values ​​for the node domain, a fpcol For the sample set D, the numbered Code col The minimum value of the index, b fpcol For the indicator Code col The maximum value, i.e., a fpcol =min(x col ), b fpcol =max(x col ).

[0059] Step 3-2, Classical Domain Analysis of the Indicator System

[0060] ​In matter-element analysis theory, the classical domain refers to the range of values ​​for each evaluation index across different evaluation levels. Based on usage requirements, the airspace operation risk assessment is divided into k levels. Using sample data D, the fuzzy C-means algorithm (FCM) is employed to analyze the sample data for each evaluation index. The specific steps are as follows:

[0061] Step 3-2-1: Initialize the parameters of the fuzzy C-means clustering algorithm.

[0062] The FCM clustering algorithm determines the degree to which an object belongs to a cluster based on its membership degree to each category. The membership matrix U is a k×m matrix, where k is the set number of categories and m is the total number of samples. The membership matrix U is initialized using data between (0, 1) and satisfies the following constraints. u mi，mj This represents the element in the mi-th row and mj-th column of the membership matrix.

[0063] The FCM clustering algorithm requires setting a fuzziness index ex∈[1,∞). The fuzziness index is a parameter that constrains the degree of fuzziness in classification. Unless otherwise specified, ex is usually set to 2.

[0064] The FCM clustering algorithm requires setting a stable classification threshold δ (0, 1). This threshold is used to determine whether the current classification result is stable. If the difference between the value function of the current classification result and the value function of the previous classification result is less than δ, then the current classification is considered stable compared to the previous classification. Otherwise, it is considered unstable. This invention sets δ = 1 × 10⁻⁶. -4 .

[0065] The FCM clustering algorithm requires setting the number of classifications, iter ∈ [1, ∞). Since the fuzzy C-means algorithm is a fuzzy partitioning clustering algorithm, it is necessary to determine whether the classification result has reached a stable state by checking if iter classifications have been reached, thus ending the algorithm process. In this invention, iter = 20 is used.

[0066] Set the index variable col = 1, and retrieve the indicator Code. col Perform cluster analysis on the corresponding historical operating data, and execute step 3-2-2.

[0067] Step 3-2-2, Fuzzy C-means Clustering

[0068] Based on the membership matrix U, from the equation The k-th cluster center of this classification is obtained, and the distance d from each of the m data samples to each cluster center is calculated using the Euclidean distance formula. mi.mj (mi = 1, 2...k; mj = 1, 2...m); based on this, the value function J is calculated, and the formula is: In the formula, c center Let (center = 1, 2, ..., k) represent the cluster centers. If the difference between the value function of the current classification result and the value function of the previous classification result is greater than the stable classification threshold δ, then the current clustering operation has improved the classification result and has room for further improvement. The number of consecutive stable clustering iterations cnt is reset to 0, the membership matrix U is updated, and clustering is performed again. The update formula for the membership matrix is: If cnt = iter, then the FCM clustering algorithm ends, and the index Code is considered to be correct. col The corresponding historical operational data has been divided into k different clusters. The data of each cluster is arranged in ascending order and denoted as follows:

[0069] Let the index variable col = col + 1. If col ≤ n at this point, then take the index Code. col Perform cluster analysis on the corresponding historical operating data, and continue to step 3-2-2 to perform cluster analysis on the historical operating data of the evaluation indicators; if col > n, then the FCM data analysis based on the sample data is completed, and proceed to step 3-2-3.

[0070] Step 3-2-3, Calculation of the Classical Domain of the Indicator System

[0071] Let col be the index variable of the evaluation index system, for the index Code col Step 3-2-2 has yielded k distinct clusters of historical running data. Then the indicator Code col The classical field can be represented as:

[0072]

[0073] In the formula, R fcol，ui Indicates the indicator Code col In the classic domain object-element model of hierarchical UI, N fcol，ui Indicates the indicator Code col The uith risk level, X fuiα (α = 1, 2, ..., n) is the index Code col The range of values ​​at the risk level ui. For clusters The minimum value in, For clusters The maximum value in, i.e. n represents the number of risk assessment indicators, and k represents the number of airspace operation risk levels.

[0074] Step 4, Fuzzy Relationship Analysis of the Indicator System

[0075] To address the fuzziness and uncertainty inherent in operational risk level assessment, fuzzy mathematics theory is used to determine the risk level of the assessed object. In fuzzy correlation analysis, membership functions are employed as an objective measure of fuzziness. This invention uses a "half-trapezoidal" form of membership function, and the specific index system and fuzzy correlation degree analysis method are as follows:

[0076] Step 4-1, Membership Function Settings

[0077] Evaluation Metric Code col The membership degree of (col = 1, 2, ..., n) with respect to risk level ui, (i = 1, 2, ..., k) is represented by the variable Let x represent the code obtained from step 1 for the airspace to be evaluated. col Statistical value; Combining the index system domain and classical domain obtained in step 3, the membership function of the spatial domain to be evaluated with respect to risk level ui=1 is expressed as:

[0078]

[0079] The membership function of the airspace with respect to risk level ui, (1 < ui < k) is expressed as:

[0080]

[0081] The membership function of the airspace with respect to the risk level ui = k is expressed as:

[0082]

[0083] Step 4-2, Calculation of membership degree of evaluation index

[0084] Let R be the membership matrix of risk assessment indicators for the airspace to be assessed of order n×k, col be the index variable of the assessment indicator system (col = 1, 2, ..., n), and ui be the index variable of the risk assessment level (ui = 1, 2, ..., k), where n is the number of risk assessment indicators and k is the total number of risk levels, and the initial values ​​of col and ui are both 1.

[0085] Step 4-2-1: Based on the membership degree calculation formula in Step 4-1, solve for the risk assessment index Code. col The membership degree of risk level i is denoted as Let the values ​​of the matrix col row and ui column be...

[0086] Step 4-2-2: Let ui = ui + 1. If ui ≤ k, then repeat step 4-2-1; if ui > k, execute step 4-2-3.

[0087] Step 4-2-3: Let col = col + 1. If col ≤ n, then let ui = 1 and execute step 4-2-1. If col > n, then the membership degree of n risk assessment indicators with respect to k risk levels is calculated.

[0088] Step 5, Comprehensive Risk Assessment of Airspace Operations

[0089] Based on the weights ω of the risk assessment index system obtained in step 2 j The risk of the airspace to be evaluated is comprehensively assessed using the risk membership matrix R of the airspace to be evaluated (j = 1, 2, ..., n) and obtained in step 4. The specific steps are as follows:

[0090] Step 5-1, Calculation of the membership matrix of airspace operation risk

[0091] Let Co be a 1×k order spatial domain operation comprehensive risk membership matrix, and let the matrix element Co[i] be denoted as mem i , (i = 1, 2, ..., k), a 1×n order index weight matrix W, where W[1, j] = ω j If (j = 1, 2, ..., n), then the membership matrix of airspace operation risk takes the value Co = WR;

[0092] Step 5-2, Airspace Operation Risk Level

[0093] According to the principle of maximum membership, since the risk assessment index is a positive index and the classical domain of the matter-element model is arranged in ascending order, the risk level of spatial operation assessment is the risk level corresponding to the maximum membership value in the matrix Co. That is, if there exists an integer i and the maximum value of the membership matrix Co is max(Co)=Co[i], then the risk level LV=i, where Co[i] represents the element value of the matrix at position i.

[0094] The above method was used to conduct a comprehensive risk assessment of a certain operating segment in the terminal area of ​​an airport. The operational data was obtained through a simulation system, and the verification process is shown below:

[0095] 1. Establishment of the indicator system and analysis of operational data

[0096] Based on simulation data, the values ​​of each indicator in the risk assessment indicator system were calculated. Combined with some historical data, the entropy method was used to calculate the indicator weights, and the clustering method was used to analyze the value range and classical domain of each indicator. The specific results are shown in the table below.

[0097] Table 1: Analysis of Indicators and Operational Data

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] 2. Membership analysis

[0104] The membership degree of the evaluation index system with respect to each risk level is analyzed, and the calculation results are shown in the table below:

[0105] Table 2 Membership Degree Data

[0106]

[0107]

[0108] 3. Calculation of Comprehensive Airspace Operation Risk Assessment Value

[0109] Based on the risk indicator weights and membership data, the airspace operation risk assessment value was calculated, and the results are shown in the table below:

[0110] Table 3. Risk Level and Membership Degree in Comprehensive Airspace Operation Risk Assessment

[0111]

[0112] Based on the principle of maximum membership, it can be seen that the membership degree is the highest at risk level 3, so it can be concluded that the current operational risk level of the assessed airspace is level 3.

[0113] In its specific implementation, this application provides a computer storage medium and a corresponding data processing unit. The computer storage medium is capable of storing a computer program, which, when executed by the data processing unit, can run the invention's content regarding a spatial operation risk assessment method based on fuzzy matter-element analysis, as well as some or all of the steps in various embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0114] Those skilled in the art will clearly understand that the technical solutions in the embodiments of the present invention can be implemented using computer programs and their corresponding general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of computer programs, i.e., software products. These computer program software products can be stored in a storage medium and include several instructions to cause a device containing a data processing unit (which may be a personal computer, server, microcontroller, MUU, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

[0115] This invention provides an approach and method for assessing airspace operational risks based on fuzzy matter-element analysis. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A method for assessing airspace operational risk based on fuzzy matter-element analysis, characterized in that, Includes the following steps: Step 1: Construct an indicator system for airspace operation risk assessment; Step 2: Determine the weights of the indicator system; Step 3: Perform classical domain analysis and section domain analysis on the index system; Step 4: Analyze the fuzzy correlation degree of the indicator system; Step 5: Conduct a comprehensive risk assessment of the airspace operation based on the aforementioned indicator system; The method for constructing an indicator system for airspace operation risk assessment as described in step 1 includes: In the airspace to be evaluated, the airspace operation risk indicators are combined with the aforementioned airspace operation characteristics. Summarized as conflict risk indicators and operational status risk indicators ,Right now The detailed information about the indicator system is as follows: Conflict risk indicators Including flight conflict numbers Conflict incidence rate Duration of the conflict and the severity of the conflict , is represented as: ; Number of conflicts Evaluation period Number of incidents where the distance between domestic flights was less than the safe distance; Conflict incidence rate Number of conflicts Total number of flights The ratio, ; Conflict duration Evaluation period The time taken for all aircraft within the country to resolve an operational conflict; Severity of the conflict : Measurement and evaluation period The severity of the conflict among all aircraft within the territory; setting time periods The start and end times are , Aircraft with operational conflicts and aircraft The distance between them is relative to time. function The required safe interval distance is , Represents the proportional gain coefficient, parameter Characterizing the degree of dangerous proximity between aircraft Then the aircraft The severity of the conflict between them is expressed as Set the evaluation period The set of aircraft with memory conflicts is , Let num represent the pair of aircraft with operational conflict, and num represent the total number of aircraft. Then, the severity of the conflict is... ; Operational status risk indicators Including heading number Average heading change Adjusting the height Change in average height Adjusting speed and the change in average velocity , is represented as: ; Adjusting heading number Evaluation period The number of times domestic aircraft undergo heading adjustment events; Mean heading change Suppose that when a heading adjustment event occurs, the heading change is denoted as . Then the evaluation period Inside ; Adjust height Evaluation period The number of altitude adjustment events that occurred on domestic aircraft; Average height change Suppose that when a height adjustment event occurs, the height change is... Then the evaluation period Inside ; Adjust speed number Evaluation period The number of speed adjustment events that occurred on the domestic aircraft; Change in average velocity Suppose that when a speed adjustment event occurs, the speed change is... Then the evaluation period Inside .

2. The airspace operation risk assessment method based on fuzzy matter-element analysis according to claim 1, characterized in that, Step 2 includes: Step 2-1, the normalization processing of the indicators in the indicator system, the specific method is as follows: Take the airspace to be evaluated Let historical operational data be used as a sample, and let the sample set be... , This represents the indicator system for the row-th sample in the sample set, where, ; , , indicating sample The index value; using the number This represents the col-th indicator in the risk assessment indicator system, and the sample size is... The index value is denoted as , Indicates sample The Chinese number is Indicator value, Indicates the number of indicators in the indicator system; All historical data were processed using linear dimensionless transformation; the airspace operation risk assessment index system described in step 1 was applied using the following formula: ； Normalization is performed. Represents the sample set The Chinese number is The minimum value of the indicator, Indicates the number is The maximum value of the indicator, This represents the value after data normalization.

3. The airspace operation risk assessment method based on fuzzy matter-element analysis according to claim 2, characterized in that, Step 2 includes: Step 2-2: Calculate the weights of the indicators in the indicator system: Step 2-2-1, Calculate the sample indicator weights; calculate the proportion of the col-th indicator in the row-th sample to the total weight of that indicator in all samples. : ; Step 2-2-2, Calculation of entropy value and information entropy redundancy; Indicators entropy value ,in ,satisfy ;index Information entropy redundancy ; Step 2-2-3, evaluate the weight of the indicators; use Indicators The weights of each risk assessment indicator are calculated using the following formula: , .

4. The airspace operation risk assessment method based on fuzzy matter-element analysis according to claim 3, characterized in that, Step 3 includes: Step 3-1, Index System Section Analysis; Based on Sample Set The classic domain and section domain analysis of the indicator system were completed by combining the fuzzy C-means algorithm (FCM). Combined sample set The indicator system is represented as follows: ； In the formula, This represents the matter-element model for airspace operation risk assessment. Indicates the level of airspace operational risk. Indicators The range of values ​​for the node domain, For sample set The Chinese number is The minimum value of the indicator, As an indicator The maximum value, i.e. , .

5. The airspace operation risk assessment method based on fuzzy matter-element analysis according to claim 4, characterized in that, Step 3 includes: Step 3-2, Classical Domain Analysis of the Indicator System: Step 3-2-1, Initialize the parameters of the fuzzy C-means clustering algorithm: The airspace operation risk assessment is divided into several parts. Each level, combined with the sample set The fuzzy C-means algorithm (FCM) was used to analyze the sample data for each evaluation index. The FCM clustering algorithm determined the degree to which each object belonged to a particular cluster based on its membership degree to each category. The membership matrix... for 1-th order matrix The set number of categories, Total number of samples; membership matrix Initialize using data between (0, 1) and satisfy the constraints. ; This represents the element in the mi-th row and mj-th column of the membership matrix; Set fuzziness index The fuzziness index is a parameter that constrains the degree of fuzziness in classification. Set a stable classification threshold The stable classification threshold is used to determine whether the current classification result has reached stability. If the difference between the value function of the current classification result and the value function of the previous classification result is less than 1%, then the stable classification threshold is established. If the classification is stable compared to the previous classification, then the current classification is considered stable; otherwise, it is considered unstable. Set the number of categories By whether or not it is achieved Substable classification is used to determine whether the classification result has reached a stable state; Set index variable Take indicators Cluster analysis was performed on the corresponding historical operational data; Step 3-2-2, Fuzzy C-means clustering; based on the membership matrix , by formula , The first one obtained in this classification The cluster centers are obtained respectively using the Euclidean distance formula. Distance from each data sample to each cluster center , Based on this, the value function is calculated. The formula is: In the formula, Indicates the cluster center; If the difference between the value function of the current classification result and the value function of the previous classification result is greater than the stable classification threshold... This clustering operation improved the classification results and has room for further improvement, with a continuous and stable number of clustering operations. Reset to 0 and update the membership matrix. Then, clustering is performed again, and the formula for updating the membership matrix is: ;like Then the FCM clustering algorithm ends, and the index is considered to be... The corresponding historical operating data has been divided into There are three different clusters. The data for each cluster is arranged in ascending order and denoted as... ; Let index variable If at this time Then take the index Perform cluster analysis on the corresponding historical operating data, and continue with step 3-2-2 to perform cluster analysis on the historical operating data of the evaluation indicators; if Then the FCM data analysis based on the sample data is completed, and step 3-2-3 is executed; Step 3-2-3, Classical domain calculation of the indicator system; Let col be the index variable of the evaluation indicator system, and calculate the index for each indicator. Historical operation data has been obtained from step 3-2-2. Different clusters Then the indicator The classical field representation is: ； In the formula, Indicators In level The classic domain matter-element model, Indicators The Each risk level As an indicator In risk level The range of values ​​at that location, For clusters The minimum value in, For clusters The maximum value in, i.e. , , Indicates the number of risk assessment indicators. This indicates the risk level of airspace operations.

6. The airspace operation risk assessment method based on fuzzy matter-element analysis according to claim 5, characterized in that, Step 4 includes: Step 4-1, Membership Function Settings: Set the evaluation metrics Regarding risk levels Membership degree using variables express, This indicates that the airspace to be evaluated is based on the indicators obtained in step 1. Statistical values; combining the indicator system domain and classical domain obtained in step 3, the spatial domain to be evaluated relates to the risk level u. The membership function is expressed as: ； Assess airspace risk level The membership function is expressed as: ； Assess airspace risk level The membership function is expressed as: 。 7. The airspace operation risk assessment method based on fuzzy matter-element analysis according to claim 6, characterized in that, Step 4 includes: Step 4-2, Calculation of membership degree of evaluation index: Let Membership matrix of risk assessment indicators for the airspace to be assessed Evaluation index system index variables Risk assessment level index variable ,in The number of risk assessment indicators. The total number of risk levels. , The initial values ​​of all are 1; Step 4-2-1: Solve for the risk assessment index based on the membership degree calculation formula in Step 4-1. Regarding risk levels The degree of membership, denoted as Let the matrix OK Column values ; Step 4-2-2, let ,like If so, repeat step 4-2-1; Proceed to step 4-2-3; Step 4-2-3, let ,like Then let Execute step 4-2-1; if ,but Each risk assessment indicator is related to The membership degree of each risk level has been calculated.

8. The airspace operation risk assessment method based on fuzzy matter-element analysis according to claim 7, characterized in that, Step 5 includes: Step 5-1, Calculation of the airspace operation risk membership matrix; Let... Comprehensive Risk Membership Matrix of Space Domain Operation Matrix elements Represented as , Order index weight matrix ,in The membership matrix of airspace operation risk takes the value of .

9. The airspace operation risk assessment method based on fuzzy matter-element analysis according to claim 8, characterized in that, Step 5 includes: Step 5-2, assess the airspace operation risk level; based on the principle of maximum membership, the airspace operation risk level assessment is a matrix. The risk level corresponding to the maximum membership degree, i.e., if there exists a certain integer... And the membership matrix Maximum value The risk level is... ,in Indicates the position of the matrix The element value.

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