Method and system for evaluating the resilience of large-scale low earth orbit satellite networks based on graph theory and entropy theory

Abstract

The application discloses a large-scale low-orbit satellite network elasticity evaluation method and system based on graph theory and entropy theory, and integrates dynamic attributes of ISL and satellite nodes into a snapshot topology structure obtained from periodicity and predictability of a satellite network by using a time snapshot-based space-time expansion graph model according to a low-orbit satellite network service scene model and constellation model, to obtain a low-orbit satellite constellation time-varying network topology based on a space-time expansion graph, and further construct a satellite communication model and a satellite state updating mechanism, an elasticity analysis model and an elasticity evaluation index of the LEO satellite network; finally, an optimization problem of network elasticity recovery of the low-orbit satellite communication network under a damaged condition is established, and then network elasticity of the low-orbit satellite communication network under the damaged condition is obtained. The application can ensure that the network can quickly recover service capability after being damaged, and effectively improves adaptive recovery capability and service guarantee level of the LEO satellite network.

Description

Technical Field

[0001] This invention relates to a method and system for evaluating the resilience of large-scale low-Earth orbit satellite networks based on graph theory and entropy theory, belonging to the field of communication network technology. Background Technology

[0002] Low Earth Orbit (LEO) satellite networks, with their significant advantages of low latency, wide coverage, and high speed, occupy a key position in 6G networks, especially in remote areas where terrestrial networks are difficult to cover, providing efficient and stable connectivity to users worldwide. As a crucial component of the future integrated 6G air-space-ground-sea network, LEO networks play a central role in supporting ubiquitous global connectivity and diverse information services, and hold strategic value in multiple fields such as communication, navigation, and remote sensing. With the increasing demand for 6G networks, LEO satellite constellations are exhibiting a trend towards larger scale, higher density, and multi-layered development, significantly enhancing the information transmission capabilities of terrestrial networks by constructing a comprehensive three-dimensional coverage space.

[0003] The LEO satellite network faces numerous challenges due to its complex space environment. First, its low orbital altitude makes it susceptible to natural factors such as space debris, high-energy particles, and electromagnetic radiation. As the constellation size and satellite density increase, the network structure becomes more complex, exhibiting greater uncertainty and vulnerability. Furthermore, the LEO network is also vulnerable to human interference, such as cyberattacks. Especially in information warfare, satellites are prime targets, necessitating robust resilience and recovery capabilities. Simultaneously, the complex inter-node relationships within the satellite network mean that a failure in one node can lead to cascading failures, impacting network stability and overall service quality.

[0004] Current research on LEO satellite networks primarily focuses on network communication performance (such as latency and throughput), while research on resilience analysis and optimization in complex environments such as human interference and natural disasters remains insufficient, lacking a systematic and comprehensive resilience assessment framework. Furthermore, existing network assessment methods struggle to fully reflect the time-varying characteristics of LEO networks, making it difficult to assess and optimize network resilience in real time under complex environments, thus limiting the network's recovery capabilities under extreme conditions. This deficiency urgently necessitates a more in-depth resilience analysis and optimization scheme to ensure the LEO network's resilience and service capability in harsh environments. Summary of the Invention

[0005] Purpose of the invention: In order to solve the problem that traditional network recovery methods cannot effectively adapt to the dynamic topology characteristics of LEO networks, this invention provides a large-scale low-Earth orbit satellite network resilience assessment method based on graph theory and entropy theory.

[0006] Technical solution: To achieve the above objectives, the technical solution adopted by this invention is as follows:

[0007] A method for evaluating the resilience of large-scale low-Earth orbit satellite networks based on graph theory and entropy theory includes the following steps:

[0008] Step 1: Establish a low-Earth orbit satellite network service scenario model and constellation model.

[0009] Step 2: Based on the low-Earth orbit satellite network service scenario model and constellation model, the dynamic attributes of ISL and satellite nodes are integrated into the snapshot topology obtained from the periodicity and predictability of the satellite network using a time-snapshot-based spatiotemporal extended graph model to obtain the time-varying network topology of the low-Earth orbit satellite constellation.

[0010] Step 3: Construct a satellite communication model and satellite status update mechanism based on the time-varying network topology of the low-Earth orbit satellite constellation based on the spatiotemporal extension map.

[0011] Step 4: Construct a resilience analysis model and resilience evaluation index for the LEO satellite network based on the time-varying network topology of the LEO satellite constellation based on the spatiotemporal spread map, the satellite communication model, and the satellite state update mechanism.

[0012] Step 5: Based on the satellite communication model, the elasticity analysis model of the LEO satellite network, and the elasticity evaluation index, construct the network elasticity recovery optimization problem of the LEO satellite communication network under damage conditions, and thus obtain the network elasticity of the LEO satellite communication network under damage conditions.

[0013] The preferred optimization problem for the resilience recovery of low-Earth orbit satellite communication networks under damage conditions is as follows:

[0014]

[0015] Where Re represents network resilience, Re dam It is the resilience of damaged networks, Re opt It is the optimized network resilience, A t It is an adjacency matrix, N u I represents the number of arriving data packets, and I represents the amount of data relayed in the route. It is an optimized inter-satellite link, con opt Degree represents the full connectivity of the optimized network. S Indicates node degree. This represents the amount of unprocessed data at both ends of the optimized link, where ρ represents the congestion coefficient. Indicates the satellite's buffer capacity. Indicates optimizing the satellites at both ends of the link, T d Indicates the duration of the link. Dist represents the duration threshold, and Dist represents the inter-satellite link distance. χ SNR represents the maximum link distance, and SNR represents the link signal-to-noise ratio. χ This represents the signal-to-noise ratio threshold.

[0016] The preferred optimization method for the network resilience recovery optimization problem of low-Earth orbit satellite communication networks under damage conditions is as follows: First, the minimum cut algorithm is applied to identify bottleneck links in the network, and edges are added to these links first to ensure that critical links have redundancy and sufficient bandwidth, enhancing resilience and connectivity. Next, potential new links in the current network are evaluated. Based on two core indicators—load balancing and path optimization—each new link is scored, and the links with the highest scores are selected for edge addition. A comprehensive scoring mechanism is introduced during the scoring process, mainly measuring the impact of link changes on the network through changes in load variance and hop count before and after the introduction of new links.

[0017] The specific definition of load variance variation is as follows:

[0018]

[0019] The comprehensive scoring formula is:

[0020]

[0021] in, Indicates the load variance. This represents the overall score, where ΔH is the reduction in global hop count after adding the edge. It represents the reduction in load variance before and after the introduction of the new link. ΔH max It is the maximum possible change in the global hop count. ω represents the maximum possible change in load variance. H and ω L ω is the weight parameter for hop count optimization and load optimization. H +ω L =1.

[0022] Preferred: The resilience analysis model and resilience evaluation index of the LEO satellite network in step 4 are as follows:

[0023] The absolute flow betweenness based on inter-satellite link quality is:

[0024]

[0025] in, This represents the absolute flow betweenness based on the quality of the inter-satellite link. Let W represent the set of satellites excluding node k. t Let represent the maximum flow matrix between all pairs of nodes in the network at time t. kW t Indicates from matrix W t Remove the k-th row and k-th column from the middle. *k W t This represents the maximum flow matrix recalculated after removing the k-th row and k-th column from the original network matrix.

[0026] Considering that edge capacity is related to link quality, edge capacity changes over time, as defined below:

[0027]

[0028] in, Represents edge capacity, Represents the elements of the adjacency matrix. The signal-to-noise ratio of the link between nodes i and j. This refers to the link bandwidth.

[0029] Let t be the node function measure of node k in the network based on satellite computing power and location criticality, taking into account the target satellite S. k For all relevant satellites within the two-hop range, the specific definitions are as follows:

[0030]

[0031] in, Satellite node S at time t k The set of adjacent nodes, It is node S k and node S m The smaller value of the node function index in the snapshot at time t. The node functionality metrics at time t are described and defined as follows:

[0032]

[0033] in, Let K be the K-shell value of node k at time t. For node computing power, It is node S k and node S m The weight value of the inter-satellite link at time t is defined as follows:

[0034]

[0035] p mk (t) is the interruption probability affected by the link signal-to-noise ratio, where ω S It is the weighting of the signal-to-noise ratio, ω F It is the weight allocation of node computing power, and ω S +ωF =1,F eff This represents the efficiency function, which indicates the actual processing capacity. This indicates the amount of unprocessed data.

[0036] The importance of node k in the network is defined as follows:

[0037]

[0038] in, This indicates the importance of node k in the network. Represents the absolute flow betweenness, Let ψ1 + ψ2 = 1, 0 ≤ ψ1, ψ2 ≤ 1, where ψ1 and ψ2 are the weights of the absolute flow measure and the node function measure, respectively.

[0039] The relative importance of node k in the network structure at time t is defined as follows:

[0040]

[0041] in, This indicates the relative importance of node k in the network structure at time t.

[0042] The absolute flow measure and satellite state measure of an edge are equally important for determining the importance of nodes in a network, i.e., ψ1 / ψ2 = 1, therefore:

[0043]

[0044] Define the resilience entropy of a time-varying network as:

[0045]

[0046] The corresponding time-varying network resilience evaluation index is defined as:

[0047]

[0048] Among them, Ent t N represents the resilience entropy of a time-varying network. t This represents the total number of network nodes at the current moment. Represents node importance. t G represents the resilience evaluation index of time-varying networks. t G represents the snapshot subgraph observed at time t. t ∈{G1,G2,…,G M}, N t The corresponding graph G at time t t The number of nodes below, It is G t The number of nodes currently in the running state.

[0049] Preferred method in step 3:

[0050] The signal transmission process is modeled as follows:

[0051]

[0052] In the formula, X is the emission intensity, l ij Y is the link loss factor. ij For the final signal, N ij P is additive white Gaussian noise independent of the signal. t For transmission power, L ij Let be the distance between satellite i and satellite j.

[0053] When the tracking error angle is θ ate For a Gaussian beam with a beam divergence half-width of ω0, the link loss factor l ij Represented as:

[0054]

[0055] At any time t, the signal-to-noise ratio (SNR) of the ISL between satellite i and satellite j is expressed as:

[0056]

[0057] in, N represents the signal-to-noise ratio (SNR) of the ISL between satellite i and satellite j, and N0 represents the variance.

[0058] During operation, the satellite continuously receives data from users and other satellites. The probability of user data arriving at the satellite is modeled as a Poisson process. For a time period Δt, the total number of data packets arriving at satellite S from ground users is... k ∈S is a parameter with λ u The probability of a data packet arriving is calculated using a Poisson process as follows:

[0059]

[0060] Wherein, P(N) u (Δt) = k) represents the probability of a data packet arriving, where ground user u's data arrives at satellite S. k The average speed is λ u N u (Δt) represents the number of data packets arriving within time Δt. Satellite S k The amount of data received from ground users is calculated as follows:

[0061]

[0062] in, Indicates satellite Sk The amount of data received from ground users Indicates satellite S k The area served within time Δt, and the size of each data packet is...

[0063] In addition, satellite S k Data from other satellites needs to be relayed, which depends on the source and destination satellites accessed by both communicating parties, and is calculated as follows:

[0064]

[0065] in, Indicates satellite S k The amount of data that needs to be relayed from other satellites, S t It is the source satellite, S d It is the destination satellite. via relay path from S t To S d The data being transmitted.

[0066] Satellite S k The total amount of data to be processed within Δt is calculated as follows:

[0067]

[0068] in, Indicates satellite S k The total amount of data to be processed within Δt, where Δt' is the time period preceding Δt. It is the unprocessed data stored in the buffer of the previous time period, calculated using the following formula:

[0069]

[0070] Here Indicates satellite S k The actual amount of data that can be processed within the time interval Δt' is defined as follows:

[0071]

[0072] in For maximum computing power, F eff The efficiency function for actual computing power is defined as follows:

[0073]

[0074] Where χ is the congestion coefficient, β is the computing power factor, ρ is the congestion coefficient, and the satellite's buffer capacity is... The calculation is as follows:

[0075]

[0076] Where γ > 0 is the capacity factor, used to describe the different buffer resources possessed by the satellite. For the satellite to pass through in orbit Time in the North Latitude It is the highest latitude that a satellite can actually reach.

[0077] Preferred: Satellite state transition mechanism, when the satellite's buffer zone becomes overcrowded, the satellite will enter a congestion state, i.e. Satellites entering a congested state require additional computing resources for buffer management, prioritizing forwarding order based on packet size, destination, or other factors.

[0078] Preferred method: The method for establishing the time-varying network topology of the low-Earth orbit satellite constellation based on the spatiotemporal spread graph in step 2 includes: one period of the satellite orbit T = [t0, t... M The topology within the area is divided into a series of snapshots, with the set of snapshot time intervals represented as T = {τ1, τ2, ..., τ}. k ,…,τ M}, where τ k =[t k-1 ,t k ], t0 represents the start time of the period, t M τ represents the end of the period. k τ represents the k-th time interval. M This represents the Mth time interval; the satellite network is represented as G = (A, C, S, T), where A represents the adjacency matrix, C represents the edge capacity matrix, S represents the satellite set, and T represents the period. Correspondingly, the static topological subgraph within one period is represented as {G1, G2, ..., G...}. M}, G M Indicates time t. k The topological snapshot is represented as G k ={A k C k ,S k}, where A = {A1, A2, ..., A M Let C be an adjacency matrix, where C = {C1, C2, ..., C}. M Let S be the capacity set of the edges, where S = {S1, S2, ..., S} N} represents the set of satellites. Considering the relationship between snapshots at adjacent times, we obtain a spatiotemporal extended graph, G, which has M+1 layers, each containing N satellites, for a total of N(M+1) nodes.

[0079] Preferred method: Step 1 is as follows: Each orbital plane shares the same inclination angle α. The spatial positioning of the orbital plane is defined by the right ascension Ω of the ascending node. The difference in the ascending node of adjacent planes depends on the number of orbital planes, and the calculation formula is ΔΩ = 2π / N P N P This represents the number of orbits in a satellite constellation. The phase difference between adjacent satellites depends on the number of satellites in the plane, and is calculated using the formula ΔΦ = 2π / N. Q N Q This represents the number of satellites in an orbital plane, and the phase difference between orbital planes is expressed by the phase factor F∈{0,1,…,N} of the Walker constellation. P The phase difference between adjacent satellites in adjacent orbital planes is adjusted to ensure that their positions in their orbits are relatively staggered, thus optimizing the coverage of the Earth's surface. The phase difference between adjacent satellites in adjacent orbital planes is denoted as Δω. f = 2πF / N, where F represents the phase factor and N represents the number of network nodes.

[0080] Each satellite establishes permanent inter-satellite links with four neighboring satellites, including two intra-orbital links and two inter-plane orbital links. A subsatellite point is the intersection of the line connecting the satellite to the Earth's center and the Earth's surface. The latitude of the subsatellite point in the geodetic coordinate system at time t is... The longitude λ(t) is calculated as follows:

[0081]

[0082] λ(t)=Lon0-ω e t+ζ(u)

[0083]

[0084] Where Lon0 is the initial ascending node longitude used to determine the orbital plane position, ζ(u) is the longitude difference between the satellite and the ascending node, u∈[-π,π] is the angular distance between the ascending node and the satellite at time t, and ω e It is the angular velocity of the Earth's rotation.

[0085] The geocentric angle between satellite S1 and satellite S2 is calculated as follows:

[0086]

[0087] The instantaneous inter-satellite link distance between satellites S1 and S2 can be calculated from their geocentric angles. The calculation is as follows:

[0088]

[0089] in, This represents the geocentric angle between satellite S1 and satellite S2. Indicates the latitude of satellite S1. λ1 represents the latitude of satellite S2, λ2 represents the longitude of satellite S1, and R represents the orbital radius of satellite S2.

[0090] The clearance between the inter-satellite link and the Earth's surface is denoted as I. The longest visible distance len between two satellites is shown below:

[0091]

[0092] Where r e is the radius of the Earth, and h is the altitude of the satellite.

[0093] Another objective of this invention is to provide a large-scale low-Earth orbit (LEO) satellite network resilience assessment system based on graph theory and entropy theory. The system employs the aforementioned large-scale LEO satellite network resilience assessment method based on graph theory and entropy theory, including a network resilience recovery optimization problem unit for LEO satellite communication networks under damaged conditions. This unit is equipped with a network resilience recovery optimization problem model for LEO satellite communication networks under damaged conditions, and the network resilience of the LEO satellite communication network under damaged conditions is obtained based on the network resilience recovery optimization problem model.

[0094] Another object of the present invention is to provide an electronic device including a processor and a memory, the memory being used to store processor-executable instructions, the processor being configured to invoke the instructions stored in the memory to execute the aforementioned method for evaluating the resilience of large-scale low-Earth orbit satellite networks based on graph theory and entropy theory.

[0095] Compared with the prior art, the present invention has the following advantages:

[0096] This invention constructs a novel elasticity quantification assessment method based on graph theory and entropy theory. By analyzing time-varying topology and satellite node states, it comprehensively and dynamically assesses the elasticity of LEO networks, providing an effective tool for network elasticity analysis in harsh environments. To address complex environments or sudden failures, it proposes an edge-addition strategy based on network elasticity bottleneck identification and a globally optimized edge-addition strategy. By optimizing link configuration in real time, it ensures that the network can quickly restore service capabilities after damage, effectively improving the adaptive recovery capability and service assurance level of LEO satellite networks. Attached Figure Description

[0097] Figure 1 This is a schematic diagram of a low-orbit satellite service scenario provided in Embodiment 1 of the present invention.

[0098] Figure 2 This is a schematic diagram of constellation parameters provided in Embodiment 1 of the present invention.

[0099] Figure 3 This is a spatiotemporal extension map of a satellite network based on a time snapshot, provided in Embodiment 1 of the present invention.

[0100] Figure 4 This is a satellite state transition diagram provided in Embodiment 1 of the present invention. Detailed Implementation

[0101] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0102] Example 1

[0103] A method for assessing the resilience of large-scale low-Earth orbit satellite networks based on graph theory and entropy theory, such as Figure 1 As shown, it includes the following steps:

[0104] Step 1: Establish a low-Earth orbit satellite network service scenario model and constellation model.

[0105] 1. Establish a low-orbit satellite network service scenario model and constellation model.

[0106] like Figure 1 As shown, users can directly connect to satellites within their field of view via mobile devices, satellite base stations, or dedicated satellite terminals. When multiple satellites are within the field of view, users will prioritize establishing a connection with the nearest satellite, thereby achieving more stable and efficient data transmission. Specifically, users can utilize satellite-to-ground links and inter-satellite links to achieve long-distance data transmission.

[0107] This patent primarily focuses on satellite networks constructed using the Walker-Delta constellation. For example... Figure 2 As shown, each orbital plane shares the same inclination angle α. The inclination angle determines the highest latitude a satellite can cover, thus affecting the coverage area. The satellite's nadir trajectory will not reach regions with latitudes greater than its orbital inclination. Spatial positioning of an orbital plane is primarily defined by the right ascension Ω of its ascending node, which is the satellite's geographical location when it crosses the equator northward. The right ascension RAAN of the ascending node of different orbital planes typically differs to ensure that the satellite can uniformly cover the entire Earth. The difference in the ascending node between adjacent planes depends on the number of orbital planes, calculated using the formula ΔΩ = 2π / N. P N P This indicates the number of orbits in the satellite constellation. The phase difference between adjacent satellites depends on the number of satellites in the plane, and is calculated using the formula ΔΦ = 2π / N. Q N QThis represents the number of satellites in an orbital plane. The phase difference between orbital planes is determined by the phase factor F∈{0,1,…,N} of the Walker constellation. P The phase difference between adjacent satellites in adjacent orbital planes is adjusted to ensure that their positions in their orbits are relatively staggered, thus optimizing the coverage of the Earth's surface. The phase difference between adjacent satellites in adjacent orbital planes is denoted as Δω. f = 2πF / N, where F represents the phase factor and N represents the number of network nodes.

[0108] Each satellite establishes permanent inter-satellite links with four neighboring satellites, including two intra-orbital links and two inter-orbital-plane links. A subsatellite point is the intersection of the line connecting the satellite to the Earth's center and the Earth's surface; the latitude of the subsatellite point in the geodetic coordinate system at time t is... The longitude λ(t) is calculated as follows:

[0109]

[0110] λ(t)=Lon0-ω e t+ζ(u)

[0111]

[0112] Where Lon0 is the initial ascending node longitude used to determine the orbital plane position, ζ(u) is the longitude difference between the satellite and the ascending node, and u∈[-π,π] is the angular distance between the ascending node and the satellite at time t, used to determine the satellite's position in orbit. If The satellite is in its ascent phase and moving northeast. Otherwise, it is in its descent phase and moving southeast. ω e This is the angular velocity of Earth's rotation. The angle between the two satellites and the Earth's center can be calculated using the satellites' latitude and longitude positions. The geocentric angle between satellite S1 and satellite S2 is calculated as follows:

[0113]

[0114] The instantaneous inter-satellite link distance between satellites S1 and S2 can be calculated from their geocentric angles. The calculation is as follows:

[0115]

[0116] in, This represents the geocentric angle between satellite S1 and satellite S2. Indicates the latitude of satellite S1. λ1 represents the latitude of satellite S2, λ2 represents the longitude of satellite S1, and R represents the orbital radius of satellite S2.

[0117] Because inter-satellite links experience signal attenuation when passing through the atmosphere, a minimum protection margin is established; this margin between the inter-satellite link and the Earth's surface is denoted as I. The maximum visible distance len between the two satellites is shown below.

[0118]

[0119] Where r e is the radius of the Earth, and h is the altitude of the satellite.

[0120] Step 2: Based on the low-Earth orbit satellite network service scenario model and constellation model, the dynamic attributes of ISL and satellite nodes are integrated into the snapshot topology obtained from the periodicity and predictability of the satellite network using a time-snapshot-based spatiotemporal extended graph model to obtain the time-varying network topology of the low-Earth orbit satellite constellation.

[0121] In satellite networks, the connections between nodes and the node states are both time-varying. To construct a time-varying topology model for low Earth orbit satellite networks, we utilize a spatiotemporal extended graph model based on time snapshots, such as... Figure 3 As shown, the dynamic properties of ISL and satellite nodes are integrated into a snapshot topology obtained from the periodicity and predictability of the satellite network.

[0122] Benefiting from the periodicity and predictability of satellite networks, the following section models and analyzes low-Earth orbit satellite networks over a single period. One period of a satellite orbit is T = [t0, t...]. M The topology within a given area can be divided into a series of snapshots, with the set of snapshot time intervals represented as T = {τ1, τ2, ..., τ}. k ,…,τ M}, where τ k =[t k-1 ,t k ], t0 represents the start time of the period, t M τ represents the end of the period. k τ represents the k-th time interval. M Let t represent the Mth time interval; the satellite network is represented as G = (A, C, S, T), where A represents the adjacency matrix, C represents the edge capacity matrix, and S represents the satellite set. k The topological snapshot is represented as G k ={A k C k ,S k}, where A = {A1, A2, ..., A M Let C be an adjacency matrix, where C = {C1, C2, ..., C}. M Let S be the capacity set of the edges, where S = {S1, S2, ..., S} N} represents the set of satellites. Considering the relationship between snapshots at adjacent times, we obtain a spatiotemporal extended graph, G, which has M+1 layers, each containing N satellites, for a total of N(M+1) nodes.

[0123] Step 3: Construct a satellite communication model and satellite status update mechanism based on the time-varying network topology of the low-Earth orbit satellite constellation based on the spatiotemporal extension map.

[0124] The signal transmission process between satellites can be modeled as follows:

[0125]

[0126] In the formula, X is the emission intensity, l ij Y is the link loss factor. ij For the final signal, N ij For additive white Gaussian noise independent of the signal, the variance is... P t For transmission power, L ij Let ε be the distance between satellite i and satellite j, and ε be the path loss exponent. It can be seen that the statistical characteristics of laser transmission between satellites are reflected in the link loss factor l. ij superior.

[0127] When the tracking error angle is θ ate For a Gaussian beam with a beam divergence half-width of ω0, the link loss factor l ij It can be represented as:

[0128]

[0129] At any time t, the signal-to-noise ratio (SNR) of the ISL between satellite i and satellite j can be expressed as:

[0130]

[0131] During operation, the satellite continuously receives data from users and other satellites. The probability of user data arriving at the satellite can be modeled as a Poisson process. For a time period Δt, the total number of data packets arriving at satellite S from ground users is... k ∈S is a parameter with λ u In a Poisson process, the probability of a data packet arriving can be calculated as:

[0132]

[0133] Ground user u data reaches satellite S k The average speed is λ u N u (Δt) represents the number of data packets arriving within time Δt. Satellite S k The amount of data received from ground users is calculated as follows:

[0134]

[0135] in Indicates satellite S k The area served within time Δt, and the size of each data packet is...

[0136] In addition, satellite S k Data from other satellites needs to be relayed, which depends on the source and destination satellites accessed by both communicating parties, and is calculated as follows:

[0137]

[0138] Where S t It is the source satellite, S d It is the destination satellite. via relay path from S t To S d The relay path for the transmitted data depends on the specific routing algorithm.

[0139] Satellite S k The total amount of data to be processed within Δt is calculated as follows:

[0140]

[0141] Where Δt' is the time interval preceding Δt, and It is the unprocessed data stored in the buffer of the previous time period, calculated using the following formula:

[0142]

[0143] Here Indicates satellite S k The actual amount of data that can be processed within the time interval Δt' is defined as follows:

[0144]

[0145] in For maximum computing power, F eff The efficiency function for actual computing power is defined as follows:

[0146]

[0147] Where χ is the congestion coefficient, representing the degree of difficulty in reaching the satellite due to congestion. The satellite's buffer capacity. The calculation is as follows:

[0148]

[0149] Where γ > 0 is the capacity factor, used to describe the different buffer resources possessed by the satellite. For the satellite to pass through in orbit Time in the North Latitude It is the highest latitude that a satellite can actually reach.

[0150] Figure 4 This demonstrates the satellite's state transition mechanism; when the satellite's buffer zone becomes overcrowded, the satellite enters a congestion state, i.e. Satellites entering a congested state require additional computing resources for buffer management, prioritizing forwarding orders based on packet size, destination, or other factors. This significantly reduces the satellite's processing efficiency per unit time, leading to a decrease in processing capacity and potentially causing the satellite to further enter an overload state. Of course, it's also possible to return to normal.

[0151] Step 4: Based on the time-varying network topology of the LEO satellite constellation based on the spatiotemporal spread map, the satellite communication model, and the satellite state update mechanism, a resilience analysis model and resilience evaluation index for the LEO satellite network are constructed. This embodiment constructs a resilience analysis model for the LEO satellite network and proposes a novel resilience evaluation index.

[0152] Based on graph theory and entropy theory, a resilience analysis model for the LEO satellite network is constructed, and a novel resilience quantification index is proposed. The importance of nodes is evaluated from two aspects:

[0153] definition Let be the absolute flow betweenness of network node k based on inter-satellite link quality at time t. It reflects the importance of node k in the network structure and measures the change in network traffic when a node is removed or its transmission is terminated.

[0154]

[0155] in, This represents the absolute flow betweenness based on the quality of the inter-satellite link. Let W represent the set of satellites excluding node k. t Let represent the maximum flow matrix between all pairs of nodes in the network at time t. k W t Indicates from matrix W t Remove the k-th row and k-th column from the middle. *k W t This represents the maximum flow matrix recalculated after removing the k-th row and k-th column from the original network matrix.

[0156] This patent considers that the edge capacity is related to the link quality, and the edge capacity changes over time, as defined below.

[0157]

[0158] in, Represents edge capacity, Represents the elements of the adjacency matrix. The signal-to-noise ratio of the link between nodes i and j. This refers to the link bandwidth.

[0159] Let t be the node function measure of node k in the network based on satellite computing power and location criticality, taking into account the target satellite S. k For all relevant satellites within the two-hop range, the specific definitions are as follows:

[0160] Satellite node S at time t k The set of adjacent nodes. It is node S k and node S m The smaller value of the node function index in the snapshot at time t. The node function index at time t is described and defined as follows:

[0161]

[0162] in Let K be the K-shell value of node k at time t. For node computing power, It is node S k and node S m The weight values ​​of the inter-satellite link at time t are defined as follows:

[0163]

[0164] p mk (t) is the interruption probability affected by the link signal-to-noise ratio, where ω S It is the weighting of the signal-to-noise ratio, ω F It is the weight allocation of node computing power, and ω S +ω F =1,F eff This represents the efficiency function, which indicates the actual processing capacity. This represents the amount of unprocessed data. The importance of node k in the network is defined as follows:

[0165]

[0166] in, This indicates the importance of node k in the network. Represents the absolute flow betweenness, Let ψ1 + ψ2 = 1, 0 ≤ ψ1, ψ2 ≤ 1, where ψ1 and ψ2 are the weights of the absolute flow measure and the node function measure, respectively.

[0167] Furthermore, the relative importance of node k in the network structure at time t can be defined as follows:

[0168]

[0169] in, This represents the relative importance of node k in the network structure at time t, where N represents the number of network nodes. This represents the set of satellites excluding node k. Represents the set of adjacent nodes.

[0170] We also believe that the absolute flow measure and satellite function measure of an edge are equally important for determining the importance of nodes in a network, i.e., ψ1 / ψ2 = 1, therefore:

[0171]

[0172] Define the resilience entropy of a time-varying network as:

[0173]

[0174] The corresponding time-varying network resilience evaluation index is defined as:

[0175]

[0176] Among them, Ent t N represents the resilience entropy of a time-varying network. t This represents the total number of network nodes at the current moment. Represents node importance. t G represents the resilience evaluation index of time-varying networks. t G represents the snapshot subgraph observed at time t. t ∈{G1,G2,…,G M}, N t The corresponding graph G at time t t The number of nodes below, It is G t The number of nodes currently in the running state. The specific elasticity representation algorithm is shown in Table 1.

[0177] Table 1 Resilient Algorithm for Time-Varying Networks

[0178]

[0179]

[0180] Step 5: Based on the satellite communication model, the elasticity analysis model of the LEO satellite network, and the elasticity evaluation index, construct the network elasticity recovery optimization problem of the LEO satellite communication network under damage conditions, and thus obtain the network elasticity of the LEO satellite communication network under damage conditions.

[0181] The network resilience recovery problem is modeled as a multi-attribute decision problem:

[0182]

[0183] Where Re represents network resilience, Re dam It is the resilience of damaged networks, Re opt It is the optimized network resilience, A t It is an adjacency matrix, N u I represents the number of arriving data packets, and I represents the amount of data relayed in the route. It is an optimized inter-satellite link, con opt Degree represents the full connectivity of the optimized network. S Indicates node degree. This represents the amount of unprocessed data at both ends of the optimized link, where ρ represents the congestion coefficient. Indicates the satellite's buffer capacity. Indicates optimizing the satellites at both ends of the link, T d Indicates the duration of the link. Dist represents the duration threshold, and Dist represents the inter-satellite link distance. χ SNR represents the maximum link distance, and SNR represents the link signal-to-noise ratio. χ This represents the signal-to-noise ratio threshold.

[0184] Step 6: An optimization method is proposed for the network elastic recovery optimization problem of low-orbit satellite communication networks under damaged conditions.

[0185] A network resilient bottleneck identification and global optimization edge-addition strategy is proposed. This strategy effectively identifies bottleneck links in the network and optimizes network load balancing and transmission efficiency at the global level by introducing the synergistic optimization of two edge-addition strategies. The bottleneck link edge-addition strategy based on minimum cut relies on the minimum cut algorithm to identify bottleneck links in the network. These bottleneck links typically carry a large amount of traffic and connect critical nodes. Especially under high network load or failure conditions, these links can easily become weak links affecting network performance. By adding redundant edges to bottleneck links, the resilience and connectivity of the network can be significantly improved.

[0186] The global optimization strategy based on potential inter-satellite link quality assessment aims to optimize the overall load distribution and routing efficiency of the network by introducing new inter-satellite links. To evaluate the impact of potential inter-satellite links, the strategy introduces a comprehensive scoring mechanism, primarily measuring the impact of link changes on the network by the changes in load variance and hop count before and after the introduction of the new link.

[0187] The specific definition of load variance variation is as follows:

[0188]

[0189] The comprehensive scoring formula is:

[0190]

[0191] Where ΔH is the reduction in global hop count after adding the edge. It represents the reduction in load variance before and after the introduction of the new link. ΔH max It is the maximum possible change in the global hop count. ω represents the maximum possible change in load variance. H and ω L ω is the weight parameter for hop count optimization and load optimization. H +ω L =1.

[0192] We combined these two strategies to form a collaborative optimization process. First, the minimum cut algorithm is applied to identify bottleneck links in the network, and edges are added to these links first to ensure that critical links have redundancy and sufficient bandwidth, enhancing resilience and connectivity. Next, potential new links in the current network are evaluated. Based on two core indicators—load balancing and path optimization—each new link is scored, and the links with the highest scores are selected for edge addition. This process significantly improves the global load distribution, prevents high-load nodes from becoming bottlenecks, and further improves network transmission efficiency by optimizing transmission paths by reducing hop count. This optimization process is implemented iteratively, with each iteration containing multiple time steps throughout the entire satellite cycle. The specific resilient optimization algorithm is shown in Table 2.

[0193] Table 2. Identification of Network Resilience Bottlenecks and Global Optimization Edge-Adding Strategies

[0194]

[0195]

[0196] Example 2

[0197] This embodiment provides a large-scale low-Earth orbit (LEO) satellite network resilience assessment system based on graph theory and entropy theory. The system employs the aforementioned large-scale LEO satellite network resilience assessment method, which includes a network resilience recovery optimization problem unit under damaged conditions. This unit is equipped with a network resilience recovery optimization problem model under damaged conditions, and the network resilience of the LEO satellite communication network under damaged conditions is obtained based on the model.

[0198] Example 3

[0199] This embodiment provides an electronic device, including a processor and a memory. The memory is used to store processor-executable instructions, and the processor is configured to invoke the instructions stored in the memory to execute the large-scale low-Earth orbit satellite network resilience assessment method based on graph theory and entropy theory.

[0200] This invention proposes a novel elasticity quantification assessment method based on graph theory and entropy theory. By analyzing time-varying topology and satellite node states, it comprehensively and dynamically assesses the elasticity of LEO networks, providing an effective tool for network elasticity analysis in harsh environments. To address complex environments or sudden failures, it proposes an edge-addition strategy based on network elasticity bottleneck identification and a globally optimized edge-addition strategy. By optimizing link configuration in real time, it ensures that the network can quickly restore service capabilities after damage, effectively improving the adaptive recovery capability and service assurance level of LEO satellite networks.

[0201] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for evaluating the resilience of a large-scale low earth orbit satellite network based on graph theory and entropy theory, characterized in that, Includes the following steps: Step 1: Establish a low-Earth orbit satellite network service scenario model and constellation model; Step 2: Based on the low-Earth orbit satellite network service scenario model and constellation model, the dynamic attributes of ISL and satellite nodes are integrated into the snapshot topology obtained from the periodicity and predictability of the satellite network using a time-snapshot-based spatiotemporal extended graph model to obtain the time-varying network topology of the low-Earth orbit satellite constellation. Step 3: Construct a satellite communication model and satellite status update mechanism based on the time-varying network topology of the low-Earth orbit satellite constellation based on the spatiotemporal spread graph; Step 4: Construct a resilience analysis model and resilience evaluation index for the LEO satellite network based on the time-varying network topology of the LEO satellite constellation using a spatiotemporal spread map, the satellite communication model, and the satellite state update mechanism; wherein, in the construction of the resilience analysis model, the time-varying network resilience entropy is defined as: The corresponding time-varying network resilience evaluation index is defined as: where Ent t represents the time-varying network invulnerability entropy, N t represents the total number of network nodes at the current time, V k t represents the node importance, Re t represents the time-varying network resilience evaluation index, G t represents the snapshot subgraph observed at time t, G t ∈{G1,G2,…,G M},N t is the number of nodes under the graph G t at time t, is the number of nodes in the running state under G t ; Step 5: Based on the satellite communication model, the elasticity analysis model of the LEO satellite network, and the elasticity evaluation index, construct the network elasticity recovery optimization problem of the LEO satellite communication network under damage conditions, and then obtain the network elasticity of the LEO satellite communication network under damage conditions. The optimization method for the network resilience recovery optimization problem of low-Earth orbit satellite communication networks under damage conditions is as follows: First, the minimum cut algorithm is applied to identify bottleneck links in the network, and edges are added to these links first to ensure that the critical links of the network have redundancy and sufficient bandwidth, thereby enhancing resilience and connectivity. Next, potential new links in the current network are evaluated. Based on the two core indicators of load balancing and path optimization, each new link is scored, and the links with the highest scores are selected for edge addition. A comprehensive scoring mechanism is introduced in the scoring process, which measures the impact of link changes on the network by the changes in load variance and hop count before and after the introduction of new links.

2. The method of claim 1, wherein the method is characterized by: The optimization problem for the resilience recovery of low-Earth orbit satellite communication networks under damage conditions is as follows: where Re represents the network resilience, Re dam is the resilience of the damaged network, Re opt is the optimized network resilience, A t is the adjacency matrix, N u is the number of arrived data packets, I is the relay data amount in the route, is the optimized inter-satellite link, con opt represents the full connectivity of the optimized network, Degree S represents the node degree, represents the unprocessed data amount of the satellite nodes at both ends of the optimized link, and p represents the congestion coefficient, represents the buffer capacity of the satellite, represents the satellite at both ends of the optimized link, T d represents the link duration, represents the duration threshold, Dist represents the inter-satellite link distance, Dist χ represents the maximum link distance, and SNR represents the link signal-to-noise ratio, SNR χ represents the signal-to-noise ratio threshold.

3. The method of claim 2, wherein, The specific definition of load variance variation is as follows: The comprehensive scoring formula is: wherein, denotes the load variance, denotes the overall score, AH is the reduction in global hops after adding the edge, is the reduction of load variance before and after the new link is introduced; AH max is the maximum possible change of global hop count, is the maximum possible change of load variance, ω H and ω L are the weight parameters of hop count optimization and load optimization, ω H + ω L = 1.

4. The method of claim 3, wherein: The resilience analysis model and resilience evaluation indicators for the LEO satellite network in step 4 are as follows: The absolute flow betweenness based on inter-satellite link quality is: wherein, denotes the absolute flow conductance based on the inter-satellite link quality, denotes the set of satellites excluding node k, W t denotes the maximum flow matrix between all pairs of nodes in the network at time t, k W t denotes the matrix W t with the kth row and column removed, * k W t denotes the maximum flow matrix recomputed from the original network matrix with the kth row and column removed; Considering that edge capacity is related to link quality, edge capacity changes over time, as defined below: wherein, denotes an edge capacity, denotes an adjacency matrix element, is the link signal-to-noise ratio between nodes i and j, is the link bandwidth; is the node function measure based on satellite computing power and position criticality of node k at time t, which considers all relevant satellites within two-hop range of target satellite S k are all relevant satellites within two-hop range of target satellite S, which is defined as follows: wherein, is the set of neighboring nodes of satellite node S k at time t, is the smaller value of the node functionality index of node S k and node S m at time t in the snapshot graph, describes the node functionality index at time t, defined as follows: wherein, is the K-shell value of node k at time t, is the node computing power, is the node S k and node S m is the weight value of the interstellar link between the two nodes at time t, which is specifically defined as follows: p mk (t) is the interruption probability affected by the link signal-to-noise ratio, where ω S It is the weighting of the signal-to-noise ratio, ω F It is the weight allocation of node computing power, and ω S +ω F =1,F eff This represents the efficiency function, which indicates the actual processing capacity. This indicates the amount of unprocessed data; The importance of node k in the network is defined as follows: in, This indicates the importance of node k in the network. Let ψ1 + ψ2 = 1, 0 ≤ ψ1, ψ2 ≤ 1, where ψ1 and ψ2 are the weights of the absolute flow measure and the node function measure, respectively. The relative importance of node k in the network structure at time t is defined as follows: in, This represents the relative importance of node k in the network structure at time t, where N represents the number of network nodes. This represents the set of satellites excluding node k. Represents the set of adjacent nodes; The absolute flow measure and satellite function measure of an edge are equally important for determining the importance of nodes in a network, i.e., ψ1 / ψ2 = 1, therefore:

5. The method for evaluating the resilience of large-scale low-Earth orbit satellite networks based on graph theory and entropy theory according to claim 4, characterized in that: The method for step 3 is as follows: The signal transmission process is modeled as follows: where X is the transmitted intensity, l ij is the link loss factor, Y ij is the final signal, N ij is the additive white Gaussian noise independent of the signal, P t is the transmitted power, L ij is the distance between satellite i and satellite j; When the tracking error angle is θ ate For a Gaussian beam with a beam divergence half-width of ω0, the link loss factor l ij is expressed as: At any time t, the signal-to-noise ratio (SNR) of the ISL between satellite i and satellite j is expressed as: in, N represents the signal-to-noise ratio (SNR) of the ISL between satellite i and satellite j, and N0 represents the variance. In the operational phase, the satellite continuously receives data from users and other satellites, the probability of user data arriving at the satellite is modeled as a Poisson process; for a time period Δt, the total number of data packets from ground users arriving at satellite S k ∈S is a Poisson process with parameter λ u The probability of a data packet arriving is calculated as: where P(N u (Δt) = k) is the probability of data packet arrival, the average rate of data arrival from ground users u to satellite S k is λ u , N u (Δt) is the number of data packets arrived in Δt; the amount of data received by satellite S k from ground users is calculated as follows: in, Indicates satellite S k The amount of data received from ground users Indicates satellite S k The area served within time Δt, and the size of each data packet is... In addition, the satellite S k The need for relaying data from other satellites, which is related to the source satellite and the destination satellite accessed by the communicating parties, is calculated as follows: in, Indicates satellite S k The amount of data that needs to be relayed from other satellites, S t It is the source satellite, S d It is the destination satellite. via relay path from S t To S d The data being transmitted; Satellite S k The total amount of data that needs to be processed in Δt is calculated as: in, Indicates satellite S k The total amount of data to be processed within Δt, where Δt' is the time period preceding Δt. It is the unprocessed data stored in the buffer of the previous time period, calculated using the following formula: Here Indicates satellite S k The actual amount of data that can be processed within the time interval Δt' is defined as follows: in For maximum computing power, F eff The efficiency function for actual computing power is defined as follows: Where β is the computing power factor, ρ is the congestion coefficient, and the satellite's buffer capacity is... The calculation is as follows: Where γ > 0 is the capacity factor, used to describe the different buffer resources possessed by the satellite; For the satellite to pass through in orbit Time in the North Latitude It is the highest latitude that a satellite can actually reach.

6. The method for evaluating the resilience of large-scale low-Earth orbit satellite networks based on graph theory and entropy theory according to claim 5, characterized in that: The satellite state transition mechanism involves the satellite entering a congestion state when its buffer zone becomes overcrowded. Satellites entering a congested state require additional computing resources for buffer management, prioritizing forwarding order based on packet size, destination, or other factors.

7. The method for evaluating the resilience of large-scale low-Earth orbit satellite networks based on graph theory and entropy theory according to claim 6, characterized in that: Step 2, the method for establishing the time-varying network topology of the low-Earth orbit satellite constellation based on the spatiotemporal spread graph, includes: one period of the satellite orbit T = [t0, t... M The topology within the area is divided into a series of snapshots, with the set of snapshot time intervals represented as T = {τ1, τ2, ..., τ}. k ,…,τ M }, where τ k =[t k-1 ,t k ], t0 represents the start time of the period, t M τ represents the end of the period. k τ represents the k-th time interval. M This represents the Mth time interval; the satellite network is represented as G = (A, C, S, T), where A represents the adjacency matrix, C represents the edge capacity matrix, S represents the satellite set, and T represents the period. Correspondingly, the static topological subgraph within one period is represented as {G1, G2, ..., G...}. M };Time t k The topological snapshot is represented as G k ={A k C k ,S k }, where A = {A1, A2, ..., A M Let C be an adjacency matrix, where C = {C1, C2, ..., C}. M Let S be the capacity set of the edges, where S = {S1, S2, ..., S} N } represents the set of satellites; considering the relationship between snapshots at adjacent times, a spatiotemporal extended graph is obtained. G has M+1 layers, each containing N satellites, for a total of N(M+1) nodes.

8. The method for evaluating the resilience of large-scale low-Earth orbit satellite networks based on graph theory and entropy theory according to claim 7, characterized in that: The method of step 1 is as follows: each orbital plane shares the same inclination a, the spatial positioning of the orbital planes is defined by the ascending node right ascension Ω, the difference of the ascending nodes of adjacent planes depends on the number of orbital planes, the calculation formula is ΔΩ = 2π / N P , N P represents the number of satellite constellation orbits, the phase difference between adjacent satellites depends on the number of satellites in the plane, the calculation formula is ΔΦ = 2π / N Q , N Q represents the number of satellites in an orbital plane, the phase difference between orbital planes is adjusted by the phase factor F of the Walker constellation ∈ {0, 1, …, N P -1}, which ensures that the positions of satellites on different orbital planes on their orbits are relatively staggered to optimize the coverage of the earth's surface, and the phase difference between adjacent satellites on adjacent orbital planes is denoted as Δω f = 2πF / N, F represents the phase factor, and N represents the number of network nodes; Each satellite establishes permanent inter-satellite links with four neighboring satellites, including two intra-orbital links and two inter-plane orbital links. A subsatellite point is the intersection of the line connecting the satellite to the Earth's center and the Earth's surface. The latitude of the subsatellite point in the geodetic coordinate system at time t is... The longitude λ(t) is calculated as follows: λ(t) = Lon0- ωt e t + ζ(u) where Lon0is the initial ascending node longitude used to determine the orbital plane position, ζ(u) is the longitude difference of the satellite to the ascending node, u ∈ [-π, π] is the angular distance of the ascending node and the satellite at time t, ω e is the angular velocity of the Earth rotation; The geocentric angle between satellite S1 and satellite S2 is calculated as follows: The instantaneous inter-satellite link distance between satellites S1 and S2 can be calculated from their geocentric angles. The calculation is as follows: in, This represents the geocentric angle between satellite S1 and satellite S2. Indicates the latitude of satellite S1. λ1 represents the latitude of satellite S2, λ2 represents the longitude of satellite S1, and R represents the orbital radius of satellite S2. The clearance between the inter-satellite link and the Earth's surface is denoted as I. The longest visible distance len between two satellites is shown below: where r e is the radius of the earth, and h is the altitude of the satellite.

9. A large-scale low-Earth orbit satellite network resilience assessment system based on graph theory and entropy theory, characterized in that, The large-scale low-Earth orbit satellite network resilience assessment method based on graph theory and entropy theory as described in claim 1 includes a network resilience recovery optimization problem unit for low-Earth orbit satellite communication networks under damaged conditions. The network resilience recovery optimization problem unit for low-Earth orbit satellite communication networks under damaged conditions is set with a network resilience recovery optimization problem model for low-Earth orbit satellite communication networks under damaged conditions. The network resilience of low-Earth orbit satellite communication networks under damaged conditions is obtained based on the network resilience recovery optimization problem model for low-Earth orbit satellite communication networks under damaged conditions.

10. An electronic device, characterized in that: It includes a processor and a memory, the memory being used to store processor-executable instructions, the processor being configured to invoke the instructions stored in the memory to execute the large-scale low-Earth orbit satellite network resilience assessment method based on graph theory and entropy theory as described in any one of claims 1-8.

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