Method and device for evaluating survivability of low-altitude airline network

Abstract

The invention discloses a low-altitude flight route network survivability evaluation method and device, and relates to the technical field of low-altitude flight safety, and the method comprises the steps: obtaining a low-altitude flight route network survivability evaluation index; constructing a low-altitude route complex network model; and based on a low-altitude route network survivability evaluation index, removing important nodes in the low-altitude route complex network model, and carrying out simulation analysis on the network survivability through a complex network theory. By adopting the technical scheme of the invention, the survivability of the low-altitude airline network under the weather influence can be better evaluated.

Description

Technical Field

[0001] The present invention relates to the field of low-altitude flight safety technology, and in particular to a method and device for evaluating the survivability of a low-altitude flight route network. Background Art

[0002] Low-altitude logistics and delivery is a new mode of transportation that aims to improve the efficiency of future urban logistics and delivery. It is currently experiencing rapid growth, with numerous cities both domestically and internationally having established or planning drone routes. For example, LI Shan published a method for constructing a network of urban low-altitude logistics drone routes based on cellular automata, while ZHANG Honghai et al. published a method for establishing initial paths and optimizing logistics route networks based on obstacle Voronoi diagrams.

[0003] Research on drone operational risks has shown that drones are susceptible to factors such as battery thermal management, flight control system failure, and illegal interference, with weather having a significant impact on drone safety. Station meteorological data alone is insufficient to determine whether route weather conditions are suitable for flight. Interpolation methods can be used to improve meteorological data accuracy. LIN Qiushuang et al. have published a method for reconstructing wind speed data based on kriging combined with probability distribution correction. Meanwhile, many scholars have conducted safety assessment research on route networks, constructing an indicator system based on resilience, robustness, vulnerability, and survivability to assess the safety of routes, airports, and other factors. Survivability is particularly suitable for assessing the safety of low-altitude logistics route networks under weather influences. However, current research on survivability indicators for low-altitude logistics route networks is limited, and it is necessary to combine weather and complex network theory to analyze the survivability of low-altitude route networks. Summary of the Invention

[0004] In order to solve the technical problems existing in the above-mentioned prior art, the present invention proposes a method and device for evaluating the invulnerability of a low-altitude route network to better evaluate the invulnerability of a low-altitude route network.

[0005] In one aspect, to achieve the above-mentioned objectives, the present invention provides a method for evaluating the invulnerability of a low-altitude route network, comprising:

[0006] Obtain low-altitude route network invulnerability evaluation indicators;

[0007] Construct a complex network model of low-altitude air routes;

[0008] Based on the low-altitude route network indestructibility evaluation index, important nodes in the low-altitude route complex network model are removed, and the network indestructibility is analyzed through complex network theory simulation.

[0009] Preferably, the low-altitude route network invulnerability evaluation indicators include: route meteorological risk, network efficiency, network density, relative size of the largest connected subgraph, entropy weighted node importance, node degree value, betweenness centrality, closeness centrality, structural entropy and comprehensive invulnerability index;

[0010] Among them, the index of node importance of the entropy weight method is constructed by weighting the degree value of the node, the betweenness centrality and the proximity centrality based on the entropy weight-TOPSIS method, and the comprehensive indestructibility index is constructed by weighting the network efficiency, the relative size of the largest connected subgraph and the network density in a preset ratio.

[0011] Preferably, obtaining the route weather risk includes:

[0012] Obtaining original meteorological data of the route, and performing pre-interpolation processing on the original meteorological data to obtain pre-processed meteorological difference data;

[0013] The pre-processed meteorological difference data is spatially interpolated based on the local thin disk smoothing spline method and combined with the DEM elevation data, longitude and latitude to obtain complete meteorological data;

[0014] The meteorological risk of the route is calculated using the complete meteorological data.

[0015] Preferably, obtaining pre-processed meteorological difference data includes:

[0016] Screening out outliers in the original meteorological data, reconstructing the data and encoding it into ASCII format, selecting an interpolation model and performing interpolation, comparing data sets of different interpolation models and performing generalized cross-validation;

[0017] The best interpolation model was determined by comparing the generalized cross-validation results, the smoothness RHO in the run log, and the signal degrees of freedom.

[0018] Preferably, the theoretical model of the local thin disk smoothing spline method is:

[0019] Z k =f(x k )+b T y k +e k k=1,2,…,N,

[0020] Where Z k is the dependent variable located at point k in space, x k is the d-dimensional spline independent variable, f(x k ) is the value to be estimated about x k An unknown smooth function of y k is a p-dimensional independent covariate; e khas a expected value of 0 and a variance of w k σ 2 The random error of the independent variable; w k is the known local relative coefficient of variation as a weight, σ 2 is the error variance, b T y k The p-dimensional coefficient of , N is the total number of nodes in the network.

[0021] Preferably, the route weather risk is calculated as:

[0022]

[0023] Where Y is the route meteorological risk value, p and q are the weights of wind speed and rainfall respectively, and w k 、w m are the wind speed sampling value and wind speed threshold respectively, r k 、r m are the sampling value and threshold of rainfall respectively, K is the total number of data sampling nodes on the route, and k is the sequence number of the data sampling node.

[0024] Preferably, constructing the low-altitude flight path complex network model includes:

[0025] Based on the spectral clustering algorithm with flight distance restriction, the maximum flight distance and the minimum flight distance are used as constraints, and the take-off and landing points at different longitudes and latitudes are clustered and analyzed. The complex network model of the low-altitude route is constructed by using a cyclic traversal algorithm to screen the cluster classification method with the largest silhouette coefficient.

[0026] Preferably, the spectral clustering algorithm based on flight distance restriction includes:

[0027] Step 1: Get the latitude, longitude and number data and set the environment variables;

[0028] Step 2: Set a flight distance limit, calculate the actual distance between each pair of nodes, and construct an adjacency matrix of the similarity graph, where only point pairs that meet the distance limit will be marked as similar in the adjacency matrix;

[0029] Step 3: Define the range of cluster numbers, traverse the range of cluster numbers, perform clustering using the spectral clustering algorithm, calculate the silhouette coefficient, and select the number of clusters corresponding to the highest silhouette coefficient as the optimal number of clusters;

[0030] Step 4: Re-perform spectral clustering using the optimal number of clusters, and check the distance from the take-off and landing points to the cluster center in each cluster. If the distance within the cluster exceeds the maximum flight distance limit, the clustering result is discarded.

[0031] Step 5: Repeat step 3 and step 4 until the cluster center no longer changes.

[0032] Preferably, the network invulnerability is analyzed by complex network theory simulation, including:

[0033] Based on the node degree, betweenness centrality, entropy weight node importance index, and route meteorological risk value, the nodes are removed from large to small, and the changes in the network efficiency, network density, relative size of the largest connected subgraph, and comprehensive indestructibility index are analyzed to analyze the network indestructibility.

[0034] On the other hand, to achieve the above-mentioned object, the present invention further provides a low-altitude route network survivability evaluation device, comprising:

[0035] Index acquisition module: used to obtain low-altitude route network invulnerability evaluation indicators;

[0036] Model building module: used to build a complex network model of low-altitude flight routes;

[0037] Evaluation and analysis module: used to remove important nodes in the low-altitude route complex network model based on the low-altitude route network invulnerability evaluation index, and analyze the network invulnerability through complex network theory simulation.

[0038] Compared with the prior art, the present invention has the following advantages and technical effects:

[0039] The present invention adopts the local thin disk smooth spline method, spectral clustering algorithm, entropy weight-TOPSIS method and complex network theory to analyze the impact of different node removals on the indestructibility of low-altitude route networks, in order to achieve a safety assessment of the indestructibility of low-altitude route networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0041] Figure 1 This is a flow chart of a method for evaluating the survivability of a low-altitude route network according to an embodiment of the present invention;

[0042] Figure 2 This is a schematic structural diagram of a low-altitude route network survivability evaluation device according to an embodiment of the present invention;

[0043] Figure 3 Flowchart of a spectral clustering algorithm with flight distance restriction according to an embodiment of the present invention. DETAILED DESCRIPTION

[0044] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0045] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0046] The present invention proposes a method for evaluating the invulnerability of low-altitude route networks. Figure 1 ,include:

[0047] Obtain low-altitude route network invulnerability evaluation indicators;

[0048] Construct a complex network model of low-altitude air routes;

[0049] Based on the low-altitude route network indestructibility evaluation index, important nodes in the low-altitude route complex network model are removed, and the network indestructibility is analyzed through complex network theory simulation.

[0050] Specifically, this embodiment adopts the local thin disk smooth spline method, spectral clustering algorithm, entropy weight-TOPSIS method and complex network theory to analyze the impact of different node removals on the indestructibility of the low-altitude route network, in order to achieve a safety assessment of the indestructibility of the low-altitude route network.

[0051] Furthermore, the low-altitude route network invulnerability evaluation indicators include: route meteorological risk, network efficiency, network density, relative size of the largest connected subgraph, entropy weighted node importance, node degree value, betweenness centrality, closeness centrality, structural entropy and comprehensive invulnerability index;

[0052] Among them, the index of node importance of the entropy weight method is constructed by weighting the degree value of the node, the betweenness centrality and the proximity centrality based on the entropy weight-TOPSIS method, and the comprehensive indestructibility index is constructed by weighting the network efficiency, the relative size of the largest connected subgraph and the network density in a preset ratio.

[0053] Specifically, after a node failure occurs, a comprehensive resilience indicator serves as an important criterion for evaluating network resilience. The construction of a resilience indicator should consider the network's absorption, resistance, and recovery capabilities. When a network is attacked, a network with strong absorptive capacity can absorb the impact and provide strong load balancing capabilities, preventing local failures from significantly decreasing global network efficiency. A network with strong resilience has good connectivity, slowing the decrease in the size of the connected subgraph when a node fails, enabling the network to continue operating. A network with strong recovery capabilities has high density, allowing for rapid recovery by increasing connections. Therefore, network efficiency, network density, and connected subgraph size can measure network resilience from different perspectives.

[0054] Therefore, in this embodiment, the comprehensive indestructibility index is constructed by weighting the network efficiency, the relative size of the largest connected subgraph, and the network density in a ratio of 2:2:1, reflecting the network's indestructibility from the three aspects of absorption, resistance, and recovery.

[0055] Specifically, the low-altitude route network invulnerability evaluation index of this embodiment is calculated as follows:

[0056] Network efficiency E: measures the ease of material and information transfer within a network and reflects the network's ability to absorb shocks. It is calculated by taking the shortest path between all pairs of nodes in the entire network. A higher network efficiency indicates better network resilience. It is calculated as follows:

[0057]

[0058] Where N is the total number of nodes in the network, d ij is the shortest path length from node i to node j,

[0059] Network density D: Defined as the ratio of the actual number of edges in the network to the upper limit of the number of edges that can be accommodated, it can be used to characterize the density of the interconnections between nodes in the network. The greater the network density, the better the network's invulnerability. It is calculated as follows:

[0060]

[0061] Where E' is the actual number of edges.

[0062] The relative size of the largest connected subgraph M: represents the ratio of the size of the largest connected subgraph in the network to the size of the entire network, reflecting the degree of connectivity of the network. It is calculated as follows:

[0063]

[0064] Where N max is the number of nodes in the maximum connected subgraph.

[0065] Furthermore, the node importance index of the entropy weight method is constructed by weighting the node's degree, betweenness centrality, and closeness centrality based on the entropy weight-TOPSIS method to reflect the comprehensive importance of the node.

[0066] Specifically, the entropy-weighted TOPSIS method is a multi-attribute decision-making method that comprehensively considers the objective weights of various indicators. It determines the optimal and worst options in a decision problem and then ranks the alternatives based on their proximity to the optimal and worst options. The entropy value of the evaluation indicator is calculated to determine the degree of dispersion of the evaluation indicator and thus determine the indicator weight.

[0067] The specific steps of the entropy weight-TOPSIS method are as follows:

[0068] 1) Data forward processing:

[0069] For all indicators, before comprehensive calculation, all indicators are unified and the evaluation indicator matrix X of the positive indicator set consisting of N' evaluation objects and M' evaluation indicators is obtained as follows:

[0070]

[0071] Where x nm It represents the value of the evaluation index data of each evaluation object after being positively converted, and X represents the value of x. nm The evaluation index matrix of the positive indicator set is constructed.

[0072] 2) Matrix normalization:

[0073] The matrix after matrix normalization is recorded as Z, and the matrix forward normalization formula is as follows:

[0074]

[0075]

[0076] In the formula, max(x nm ) and min(x nm ) represent the maximum and minimum values ​​of each evaluation index, Z nm The evaluation index data of each evaluation object is the value after positive normalization, and Z represents the value of Z. nm A standardized evaluation index matrix is ​​constructed, where m is the number of indicators and n is the number of samples.

[0077] 3) Matrix normalization processing:

[0078] Calculate the value Z after forward normalization nm The proportion of B nm ,in:

[0079]

[0080] Where B nm It indicates the proportion of the nth sample value under the mth indicator to the indicator.

[0081] 4) Calculate the information entropy value C of the mth indicator m and the coefficient of variation d m ,in:

[0082]

[0083] d m =1-C m ,

[0084] Among them, C m represents the information entropy value of the mth indicator; d m represents the difference coefficient of the mth indicator, d m The larger the value, the smaller the row matrix Z m The greater the degree of influence in the comprehensive evaluation, the greater the degree of influence. The sum of each column of the matrix Z is the row matrix Z m .

[0085] 5) Calculate the row matrix Z m The weight W m , the importance of each indicator is evaluated based on the size of the information entropy. The smaller the information entropy, the greater the amount of information in the indicator and the greater its weight. The calculated difference coefficients are normalized so that their sum is 1. The calculation formula is:

[0086]

[0087] Among them, W m Represents the normalized weight value of the mth indicator.

[0088] 6) Calculate the evaluation value R n , the calculation formula is:

[0089]

[0090] Where R n Indicates the evaluation value of the nth evaluation object.

[0091] Because Z nm are all positive indicators, so R n The larger the value is, the better the corresponding evaluation object is.

[0092] 7) Construct the weighted standard evaluation matrix U as follows:

[0093]

[0094] In the formula, U is represented by Z nm With W m The weighted standard evaluation matrix obtained by multiplication.

[0095] 8) Determine the positive ideal solution U + and negative ideal solution U - :

[0096]

[0097] In the formula, the positive ideal solution U + and negative ideal solution U - are the sets of corresponding maximum and minimum values ​​in the weighted standard evaluation matrix U respectively.

[0098] 9) Calculate the Euclidean distance between each evaluation object and the ideal solution. The calculation formulas are:

[0099]

[0100] Where, and Respectively represent the Euclidean distance of each evaluation object to the positive ideal solution and the negative ideal solution, U nm It represents the weighted normalized value of the nth evaluation object on the mth indicator.

[0101] 10) Calculate the correlation closeness T n , for the relative closeness T n After normalization, the calculation is as follows:

[0102]

[0103] Where, T n Indicates the relative closeness of the nth evaluation object, P n is the normalized value of the relative closeness of each evaluation object; according to the normalized P n , each evaluation object can be ranked, P n The larger the value, the better the evaluation object.

[0104] Specifically, structural entropy is a concept in network science and information theory that measures the uncertainty or randomness of a network's structure. A higher structural entropy indicates a more random network's connectivity patterns and more concentrated connections between nodes. It is calculated as follows:

[0105]

[0106] Where p ij is the probability of node i and node j being connected, is the structural entropy.

[0107] Betweenness centrality CB (v) refers to the intermediary capacity of a node in the network, that is, the number of pairs of nodes on which the node appears on the shortest path. The greater the betweenness centrality, the more important the node. It is calculated as follows:

[0108]

[0109] Where σ(s,t) represents the number of shortest paths from node s to node t, and σ(s,t|v) represents the number of shortest paths passing through node v.

[0110] Furthermore, obtaining the route weather risk includes:

[0111] Obtain the original meteorological data of the route and perform pre-interpolation processing on the original meteorological data to obtain pre-processed meteorological difference data;

[0112] The pre-processed meteorological difference data is spatially interpolated based on the local thin disk smoothing spline method and combined with DEM elevation data, longitude and latitude to obtain complete meteorological data;

[0113] The weather risk of the route is calculated using complete weather data.

[0114] Furthermore, the pre-processed meteorological difference data is obtained, including:

[0115] The outliers in the original meteorological data were screened out, the data were reconstructed and encoded into ASCII format, an interpolation model was selected, the SPLINA script of ANUSPLIN was run, and the data sets of different interpolation models were compared and generalized cross-validation was performed;

[0116] The best interpolation model was determined by comparing the generalized cross-validation results, the smoothness RHO in the run log, and the signal degrees of freedom.

[0117] Specifically, it includes:

[0118] 1) Raw data processing: First, the outliers of the raw meteorological data (including wind speed and rainfall) were screened out, the elevation data and meteorological data were projected into the "WGS_1984_Albers" coordinate system, and the data were reconstructed and encoded into ASCII format.

[0119] 2) Interpolation model selection: run the SPLINA script of ANUSPLIN to perform pre-interpolation and compare the data sets of different interpolation models for generalized cross-validation.

[0120] For the prediction or interpolation dataset, first calculate the residual r for each data sampling point k k :

[0121]

[0122] Where y k is the actual observed value, is the model predicted value.

[0123] First, construct an n1×n1 hat matrix H, where n1 is the number of samples.

[0124] The elements of the hat matrix H are defined as:

[0125]

[0126] Where H ab is the element in row a and column b of matrix H.

[0127] For linear models, the hat matrix H can be simplified as:

[0128] H=X(X T +λI),

[0129] Where X is the design matrix, λ is the regularization parameter (for ridge regression), I is the identity matrix, and X T is the transposed matrix of X.

[0130] The generalized cross validation GCV score is given by the following formula:

[0131]

[0132] Where tr(H) is the trace of the hat matrix H, and k is the data sampling node number.

[0133] Finally, the generalized cross validation results GCV, the smoothness RHO in the running log, and the signal degrees of freedom are compared to determine the optimal interpolation model.

[0134] In this embodiment, the criteria for determining the optimal interpolation model are: small GCV, large RHO, small signal-to-noise ratio, signal degrees of freedom less than half the number of sites, and no "*" appears in the model success rate determination.

[0135] 3) Meteorological data interpolation: Based on the local thin disk smoothing spline method, the meteorological data are spatially interpolated in combination with DEM elevation data, longitude and latitude.

[0136] The theoretical model of the local thin disk smoothing spline method can be expressed as:

[0137] Z k =f(x k )+b T y k +e k k=1,2,…,N,

[0138] Where Z kis the dependent variable located at point k in space, x k is the d-dimensional spline independent variable, f(x k ) is the value to be estimated about x k An unknown smooth function of y k is a p-dimensional independent covariate; e k has a expected value of 0 and a variance of w k σ 2 The random error of the independent variable; w k is the known local relative coefficient of variation as a weight, b T y k The p-dimensional coefficient, σ 2 is the error variance, which is constant across all data points but is usually unknown.

[0139] f and b are determined by least squares estimation:

[0140]

[0141] Where, J m (f) is the function f(x k ), is defined as the m-order partial derivative of f, where ρ is a positive smoothness parameter and is determined by minimizing the generalized cross validation (GCV).

[0142] Furthermore, the route weather risk is calculated as:

[0143]

[0144] Where Y is the route meteorological risk value, p and q are the weights of wind speed and rainfall respectively, and w k 、w m are the wind speed sampling value and wind speed threshold respectively, r k 、r m are the sampling value and threshold of rainfall respectively, K is the total number of data sampling nodes on the route, and k is the sequence number of the data sampling node.

[0145] Specifically, the route weather risk Y is the risk of the route due to weather conditions calculated based on wind speed and rainfall. The larger the risk, the more likely it is to be affected by weather conditions. In this embodiment, both p and q are set to 1.

[0146] Furthermore, a complex network model of low-altitude air routes is constructed, including:

[0147] Based on the spectral clustering algorithm with flight distance restriction, the maximum flight distance and the minimum flight distance are used as constraints, and the take-off and landing points at different longitudes and latitudes are clustered and analyzed. The complex network model of the low-altitude route is constructed by using a cyclic traversal algorithm to screen the cluster classification method with the largest silhouette coefficient.

[0148] Specifically, if Figure 3 , based on a spectral clustering algorithm with flight distance constraints, including:

[0149] Step 1: Read the latitude, longitude and number data from Excel and set environment variables to avoid memory leaks;

[0150] Step 2: Set the flight distance limit, calculate the actual distance between each pair of nodes, and construct the adjacency matrix of the similarity graph. Only the point pairs that meet the distance limit will be marked as similar in the adjacency matrix.

[0151] Step 3: Define the range of cluster numbers, traverse the range of cluster numbers, use the spectral clustering algorithm to perform clustering, calculate the silhouette coefficient, and select the number of clusters corresponding to the highest silhouette coefficient as the optimal number of clusters;

[0152] Step 4: Re-perform spectral clustering using the optimal number of clusters and check the distance from the take-off and landing points to the cluster center in each cluster. If the distance within the cluster exceeds the maximum flight distance limit, the clustering result is discarded.

[0153] Step 5: Repeat step 3 and step 4 until the cluster center no longer changes.

[0154] Furthermore, the network's invulnerability is analyzed through complex network theory simulation, including:

[0155] Based on the node degree, betweenness centrality, entropy weight node importance index, and route meteorological risk value, the nodes are removed from large to small, and the changes in the network efficiency, network density, relative size of the largest connected subgraph, and comprehensive indestructibility index are analyzed to analyze the network indestructibility.

[0156] Specifically, based on complex network theory, low-altitude route network nodes are removed and an indestructibility simulation analysis is performed. Nodes are removed based on the degree, betweenness centrality, entropy weighted node importance index, and route meteorological risk value, sorted from large to small. The changes in complex network indicators such as network efficiency, network density, relative size of the largest connected subgraph, and comprehensive indestructibility index are analyzed to analyze the network's indestructibility.

[0157] This embodiment uses the local thin disk smoothing spline method, spectral clustering algorithm, entropy weight-TOPSIS method and complex network theory to analyze the impact of different node removals on the indestructibility of the low-altitude route network, in order to achieve a safety assessment of the indestructibility of the low-altitude route network.

[0158] This embodiment also provides a low-altitude route network invulnerability evaluation device, such as Figure 2 ,include:

[0159] Index acquisition module: used to obtain low-altitude route network invulnerability evaluation indicators;

[0160] Model building module: used to build a complex network model of low-altitude flight routes;

[0161] Evaluation and analysis module: used to remove important nodes in the low-altitude route complex network model based on the low-altitude route network invulnerability evaluation index, and analyze the network invulnerability through complex network theory simulation.

[0162] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for evaluating the invulnerability of a low-altitude flight path network, characterized in that: include: Obtain low-altitude route network invulnerability evaluation indicators; Construct a complex network model of low-altitude air routes; Based on the low-altitude route network indestructibility evaluation index, important nodes in the low-altitude route complex network model are removed, and the network indestructibility is analyzed through complex network theory simulation.

2. The low-altitude route network invulnerability evaluation method according to claim 1, characterized in that: The low-altitude route network invulnerability evaluation indicators include: route meteorological risk, network efficiency, network density, relative size of the largest connected subgraph, entropy weighted node importance, node degree value, betweenness centrality, closeness centrality, structural entropy and comprehensive invulnerability index; Among them, the index of node importance of the entropy weight method is constructed by weighting the degree value of the node, the betweenness centrality and the proximity centrality based on the entropy weight-TOPSIS method, and the comprehensive indestructibility index is constructed by weighting the network efficiency, the relative size of the largest connected subgraph and the network density in a preset ratio.

3. The low-altitude route network invulnerability evaluation method according to claim 2, characterized in that: Obtaining the weather risk of the route includes: Obtaining original meteorological data of the route, and performing pre-interpolation processing on the original meteorological data to obtain pre-processed meteorological difference data; The pre-processed meteorological difference data is spatially interpolated based on the local thin disk smoothing spline method and combined with the DEM elevation data, longitude and latitude to obtain complete meteorological data; The meteorological risk of the route is calculated using the complete meteorological data.

4. The low-altitude route network invulnerability evaluation method according to claim 3, characterized in that: Obtain pre-processed meteorological difference data, including: Screening out outliers in the original meteorological data, reconstructing the data and encoding it into ASCII format, selecting an interpolation model and performing interpolation, comparing data sets of different interpolation models and performing generalized cross-validation; The best interpolation model was determined by comparing the generalized cross-validation results, the smoothness RHO in the run log, and the signal degrees of freedom.

5. The low-altitude route network invulnerability evaluation method according to claim 3, characterized in that: The theoretical model of the local thin disk smoothing spline method is: Z k =f(x k )+b T y k +e k k=1,2,…,N, Where Z k is the dependent variable located at point k in space, x k is the d-dimensional spline independent variable, f(x k ) is the value to be estimated about x k An unknown smooth function of y k is a p-dimensional independent covariate; e k has a expected value of 0 and a variance of w k σ 2 The random error of the independent variable; w k is the known local relative coefficient of variation as a weight, σ 2 is the error variance, b T y k The p-dimensional coefficient of , N is the total number of nodes in the network.

6. The low-altitude route network invulnerability evaluation method according to claim 3, characterized in that: The meteorological risk of the route is calculated as: Where Y is the route meteorological risk value, p and q are the weights of wind speed and rainfall respectively, and w k 、w m are the wind speed sampling value and wind speed threshold respectively, r k 、r m are the sampling value and threshold of rainfall respectively, K is the total number of data sampling nodes on the route, and k is the sequence number of the data sampling node.

7. The low-altitude route network invulnerability evaluation method according to claim 1, characterized in that: Constructing the complex network model of the low-altitude flight routes includes: Based on the spectral clustering algorithm with flight distance restriction, the maximum flight distance and the minimum flight distance are used as constraints, and the take-off and landing points at different longitudes and latitudes are clustered and analyzed. The complex network model of the low-altitude route is constructed by using a cyclic traversal algorithm to screen the cluster classification method with the largest silhouette coefficient.

8. The low-altitude route network invulnerability evaluation method according to claim 7, characterized in that: The spectral clustering algorithm based on flight distance restriction includes: Step 1: Get the latitude, longitude and number data and set the environment variables; Step 2: Set a flight distance limit, calculate the actual distance between each pair of nodes, and construct an adjacency matrix of the similarity graph, where only point pairs that meet the distance limit will be marked as similar in the adjacency matrix; Step 3: Define the range of cluster numbers, traverse the range of cluster numbers, perform clustering using the spectral clustering algorithm, calculate the silhouette coefficient, and select the number of clusters corresponding to the highest silhouette coefficient as the optimal number of clusters; Step 4: Re-perform spectral clustering using the optimal number of clusters, and check the distance from the take-off and landing points to the cluster center in each cluster. If the distance within the cluster exceeds the maximum flight distance limit, the clustering result is discarded. Step 5: Repeat step 3 and step 4 until the cluster center no longer changes.

9. The low-altitude route network invulnerability evaluation method according to claim 1, characterized in that: Analyze network invulnerability through complex network theory simulation, including: Based on the node degree, betweenness centrality, entropy weight node importance index, and route meteorological risk value, the nodes are removed from large to small, and the changes in the network efficiency, network density, relative size of the largest connected subgraph, and comprehensive indestructibility index are analyzed to analyze the network indestructibility.

10. A low-altitude route network invulnerability evaluation device, characterized in that: include: Index acquisition module: used to obtain low-altitude route network invulnerability evaluation indicators; Model building module: used to build a complex network model of low-altitude flight routes; Evaluation and analysis module: used to remove important nodes in the low-altitude route complex network model based on the low-altitude route network invulnerability evaluation index, and analyze the network invulnerability through complex network theory simulation.

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