Large-scale low earth orbit satellite network elasticity evaluation method and system based on graph theory and entropy theory

Abstract

The invention discloses a large-scale low earth orbit satellite network elasticity evaluation method and system based on a graph theory and an entropy theory. According to a low-orbit satellite network service scene model and a constellation model, dynamic attributes of ISL and satellite nodes are integrated into a snapshot topological structure obtained from periodicity and predictability of a satellite network by utilizing a time-space expansion graph model based on time snapshots, and low-orbit satellite constellation time-varying network topology based on a time-space expansion graph is obtained. Constructing a satellite communication model, a satellite state updating mechanism, an elastic analysis model of the LEO satellite network and an elastic evaluation index; and finally, establishing a network elasticity recovery optimization problem of the low-orbit satellite communication network under the damaged condition, thereby obtaining the network elasticity of the low-orbit satellite communication network under the damaged condition. According to the method, the service capability can be quickly recovered after the network is damaged, and the adaptive recovery capability and the service guarantee level of the LEO satellite network are effectively improved.

Description

Technical Field

[0001] The present invention relates to a large-scale low-orbit satellite network resilience assessment method and system based on graph theory and entropy theory, belonging to the technical field of communication networks. Background Art

[0002] Low Earth Orbit (LEO) satellite networks play a key role in 6G networks with their significant advantages of low latency, wide coverage and high speed, especially in remote areas that are difficult to cover with ground networks, and can provide efficient and stable connections for users around the world. As an important part of the future 6G integrated network of air, space, land and sea, LEO networks play a core role in supporting global ubiquitous connectivity and diversified information services, and have strategic value in multiple fields such as communications, navigation and remote sensing. With the increasing demand for 6G networks, LEO satellite constellations are showing a trend of large-scale, high-density and multi-level development. By building a full-domain three-dimensional coverage space, the information transmission capacity of the ground network has been significantly improved.

[0003] LEO satellite networks face many challenges due to their complex space environment. First, due to the low altitude characteristics of their orbits, LEO satellite networks are susceptible to natural factors such as space debris, high-energy particles, and electromagnetic radiation. With the increase in constellation size and satellite density, the network structure has become more complex, showing higher uncertainty and vulnerability. In addition, LEO networks may also be subject to human interference, such as cyber attacks. Especially in information warfare, satellites have become important targets of attack and urgently need to have strong anti-destruction and recovery capabilities. At the same time, the interactive relationship between nodes in the satellite network is complex. Once a node fails, it may cause cascading failures, affecting the stability of the network and the overall service quality.

[0004] Current research on LEO satellite networks mainly focuses on the communication performance of the network (such as latency and throughput), while research on resilience analysis and optimization in complex environments such as human interference and natural disasters is still insufficient, lacking a systematic and comprehensive resilience assessment framework. At the same time, existing network assessment methods are difficult to fully reflect the time-varying characteristics of LEO networks, and it is difficult to evaluate and optimize network resilience in real time in complex environments, thus limiting the network's ability to recover under extreme conditions. This deficiency urgently requires a more in-depth resilience analysis and optimization solution to ensure the anti-destruction and service capabilities of LEO networks 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 topological characteristics of LEO networks, the present invention provides a large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory.

[0006] Technical solution: To achieve the above purpose, the technical solution adopted by the present invention is:

[0007] A large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory includes the following steps:

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

[0009] Step 2: According to the low-orbit satellite network service scenario model and constellation model, the dynamic properties of ISL and satellite nodes are integrated into the snapshot topology structure obtained from the periodicity and predictability of the satellite network using the time-snapshot-based spatiotemporal extension graph model, and the time-varying network topology of the low-orbit satellite constellation is obtained based on the spatiotemporal extension graph.

[0010] Step 3: construct a satellite communication model and satellite status update mechanism based on the time-varying network topology of the low-orbit satellite constellation based on the spatio-temporal expansion graph.

[0011] Step 4: Construct a resilience analysis model and resilience evaluation index for the LEO satellite network based on the time-space expansion diagram of the time-varying network topology of the LEO satellite constellation, the satellite communication model, and the satellite status 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, the network elasticity recovery optimization problem of the low-orbit satellite communication network under damage is constructed, and then the network elasticity of the low-orbit satellite communication network under damage is obtained.

[0013] Optimization problem of network resilience recovery of low-orbit satellite communication network in case of damage is:

[0014]

[0015] Among them, Re represents network elasticity, Re dam is the resilience of the damaged network, Re opt is the optimized network elasticity, A t is the adjacency matrix, N u is the number of packets arriving, I is the amount of data relayed by the router, is an optimized intersatellite link, con opt Denotes the full connectivity of the optimized network, Degree S represents the node degree, represents the amount of unprocessed data at the satellite nodes at both ends of the optimization link, ρ represents the congestion coefficient, represents the buffer capacity of the satellite, represents the satellites at both ends of the optimized link, T d Indicates the link duration, represents the duration threshold, Dist represents the intersatellite link distance, Dist χ Indicates the maximum link distance, SNR indicates the link signal-to-noise ratio, SNR χ Represents the signal-to-noise ratio threshold.

[0016] Preferred: The optimization method for the optimization problem of network resilience recovery of low-orbit satellite communication networks in the event of damage 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 key links of the network have redundancy and sufficient bandwidth, and enhance anti-destruction 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 mainly measures the impact of link changes on the network by the load variance and hop count changes before and after the introduction of new links.

[0017] The load variance change is specifically defined as follows

[0018]

[0019] The comprehensive scoring formula is:

[0020]

[0021] in, represents the load variance, represents the comprehensive score, N represents, express, Indicates that ΔH is the reduction in the number of global hops after adding edges. is the reduction in load variance before and after the new link is introduced. ΔH max is the maximum possible change in the global hop count, is the maximum possible change in load variance, ω H and ω L is the weight parameter for hop optimization and load optimization, ω H +ω L =1.

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

[0023] The absolute flow betweenness based on the intersatellite link quality is:

[0024]

[0025] in, represents the absolute flow betweenness based on the intersatellite link quality, represents the set of satellites except node k, W trepresents the maximum flow matrix between all pairs of nodes in the network at time t, k W t Represents the matrix W t Remove the kth row and kth column from *k W t It represents the maximum flow matrix recalculated by removing the k-th row and k-th column from the original network matrix.

[0026] Considering that the edge capacity is related to the link quality, the edge capacity will change over time and is defined as follows:

[0027]

[0028] in, represents the edge capacity, represents the adjacency matrix element, is the link signal-to-noise ratio between nodes i and j, is the link bandwidth.

[0029] is the node function measure of node k in the network at time t based on satellite computing power and location criticality, considering the target satellite S k For all relevant satellites within two hops, the specific definitions are as follows:

[0030]

[0031] in, is the satellite node S at time t k The set of adjacent nodes of It is node S k and node S m The smaller value of the node function index of the two nodes in the snapshot graph at time t, Describes the node function indicators at time t, which are defined as follows:

[0032]

[0033] in, is the K-shell value of node k at time t, is the node computing power, It is node S k and node S m The weight value of the intersatellite link between the two at time t is specifically defined as follows:

[0034]

[0035] p mk (t) is the outage probability affected by the link signal-to-noise ratio, where ω S is the weight distribution of the signal-to-noise ratio, ω Fis the weight distribution of node computing power, and ω S +ω F =1, F eff represents the actual processing capacity efficiency function, Indicates the amount of unprocessed data.

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

[0037]

[0038] in, represents the node importance of node k in the network, represents the absolute flow betweenness, represents the node function, ψ1+ψ2=1,0≤ψ1,ψ2≤1, 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:

[0040]

[0041] in, represents the relative importance of node k in the network structure at time t, and N represents, express, express, express.

[0042] The absolute flow measure of the edge and the satellite state measure are equally important for judging the importance of nodes in the network, that is, ψ1 / ψ2=1, so:

[0043]

[0044] The time-varying network anti-destruction entropy is defined as:

[0045]

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

[0047]

[0048] Among them, Ent t represents the time-varying network anti-destruction entropy, N t Indicates the total number of network nodes at the current moment, Represents the importance of the node, t represents the time-varying network resilience index, G t represents the snapshot subgraph observed at time t, G t ∈{G1,G2,…,G M},N tis the graph G at time t t The number of nodes under It's G t The number of nodes in the running state.

[0049] Preferably, the method of step 3 is:

[0050] The signal transmission process is modeled as:

[0051]

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

[0053] When the tracking error angle is θ ate When the half width of the beam divergence is ω0, the link loss factor l ij It is expressed as:

[0054]

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

[0056]

[0057] in, represents the signal-to-noise ratio of the ISL between satellite i and satellite j, and Ν0 represents the variance.

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

[0059]

[0060] Among them, P(N u (Δt) = k) represents the probability of data packet arrival, and the data of ground user u reaches satellite S k The average rate is λ u , N u (Δt) is the number of data packets arriving within Δt. Satellite S k The amount of data received from ground users is calculated as follows:

[0061]

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

[0063] In addition, satellite S k It is necessary to relay data from other satellites, which is related to the source and destination satellites visited by both parties. The calculation is as follows:

[0064]

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

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

[0067]

[0068] in, Indicates satellite S k The total amount of data that needs to be processed within Δt, Δt' is the time period before Δt, and is the unprocessed data stored in the buffer of the previous time period, and the calculation formula is:

[0069]

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

[0071]

[0072] in is the maximum computing power, F eff is the actual computing power efficiency function, which is defined as follows

[0073]

[0074] Among them, χ is the congestion coefficient, β is the computing power factor, ρ is the congestion coefficient, and the buffer capacity of the satellite The calculation is as follows:

[0075]

[0076] Where γ>0 is the capacity factor, which is used to describe the different buffer resources owned by the satellite. For satellites passing in orbit Time in northern latitude, It is the highest latitude that a satellite can actually reach.

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

[0078] Preferably: the method for establishing the time-varying network topology of the low-orbit satellite constellation based on the time-space expansion diagram in step 2 includes: a period of the satellite orbit T = [t0, t M ] is divided into a series of snapshots, and the snapshot time interval set is represented as T = {τ1,τ2,…,τ k ,…,τ M}, where τ k =[t k-1 ,t k ], t0 represents the start time of the cycle, t M represents the periodic betweenness moment, τ k represents the kth time interval, τ M represents the Mth time interval; the satellite network is represented by G = (A, C, S, T), A represents the adjacency matrix, C represents the edge capacity matrix, S represents the satellite set, T represents the period, and the corresponding static topology subgraph within a period is represented by {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} is the adjacency matrix, C={C1,C2,…,C M} is the capacity set of edges, S={S1,S2,…,S N} represents the satellite set. Considering the connection between snapshot graphs at adjacent moments, we get the spatiotemporal expansion graph G, which has M+1 layers, each layer contains N satellites, and a total of N(M+1) nodes.

[0079] Preferably, the method of step 1 is as follows: each orbital plane shares the same inclination α, the spatial positioning of the orbital plane is defined by the right ascension Ω of the ascending node, and the difference of the ascending nodes of adjacent planes depends on the number of orbital planes, calculated as ΔΩ=2π / N P , N P Indicates 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 on an orbital plane. The phase difference between orbital planes is calculated by the phase factor F∈{0,1,…,N P -1} to ensure that the positions of satellites in different orbital planes are relatively staggered in their orbits to optimize the coverage of the earth's surface. The phase difference between adjacent satellites in adjacent orbital planes is Δω f =2πF / N, F represents the phase factor, and N represents the total number of satellites.

[0080] Each satellite establishes permanent inter-satellite links with four adjacent satellites, including two intra-orbit links and two inter-orbital plane links. The sub-satellite point is the intersection of the connecting line from the satellite to the center of the earth and the earth's surface. The latitude of the sub-satellite point in the geodetic coordinate system at time t is and longitude λ(t) are 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 from the satellite to the ascending node, u∈[-π,π] is the angular distance between the ascending node and the satellite at time t, and ω e 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 intersatellite link distance between S1 and S2 can be calculated from the geocentric angle of satellites S1 and S2. The calculation is as follows:

[0088]

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

[0090] The clearance between the intersatellite link and the earth's surface is denoted as I, and the maximum visible distance len between two satellites is as follows:

[0091]

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

[0093] Another object of the present invention is to provide a large-scale low-orbit satellite network resilience assessment system based on graph theory and entropy theory, which adopts the large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory, including a network resilience recovery optimization problem unit for the low-orbit satellite communication network when it is damaged, and the network resilience recovery optimization problem unit for the low-orbit satellite communication network when it is damaged is provided with a network resilience recovery optimization problem model for the low-orbit satellite communication network when it is damaged, and the network resilience of the low-orbit satellite communication network when it is damaged is obtained according to the network resilience recovery optimization problem model for the low-orbit satellite communication network when it is damaged.

[0094] Another object of the present invention is to provide an electronic device, comprising a processor and a memory, wherein the memory is used to store processor executable instructions, and the processor is configured to call the instructions stored in the memory to execute the large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory.

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

[0096] This paper constructs a new elasticity quantitative evaluation method based on graph theory and entropy theory. By analyzing the time-varying topological structure and satellite node status, it comprehensively and dynamically evaluates the elasticity of the LEO network, providing an effective tool for network elasticity analysis in harsh environments. In order to cope with complex environments or sudden failures, an edge addition strategy based on network elasticity bottleneck identification and a global optimization edge addition strategy are proposed. By optimizing the link configuration in real time, it ensures that the network can quickly restore its service capabilities after being damaged, effectively improving the adaptive recovery capability and service guarantee level of the LEO satellite network. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0099] Figure 3 A satellite network spatiotemporal expansion diagram based on a time snapshot is provided in the first embodiment of the present invention.

[0100] Figure 4 This is a satellite state transition diagram provided by Embodiment 1 of the present invention. DETAILED DESCRIPTION

[0101] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0102] Example 1

[0103] A large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory, such as Figure 1 As shown, the following steps are included:

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

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

[0106] like Figure 1 As shown in the figure, users can directly connect to the satellites in the field of view through mobile devices, satellite base stations or dedicated satellite terminals. When there are multiple satellites in the field of view, users will give priority to establishing a connection with the closest satellite, thereby achieving more stable and efficient data transmission. Specifically, users can use satellite-to-ground links and inter-satellite links to achieve long-distance data transmission.

[0107] This patent mainly studies the satellite network constructed by the Walker-Delta constellation. Figure 2 As shown, each orbital plane shares the same inclination α, which determines the highest latitude that the satellite can cover, thus affecting the coverage range. The satellite's sub-satellite point trajectory will not reach areas with latitudes greater than its orbital inclination. The spatial positioning of the orbital plane is mainly defined by the ascending node right ascension Ω, which is the geographical location of the satellite when it crosses the equator to the north. The ascending node right ascension RAAN of different orbital planes is usually different to ensure that the satellite can evenly cover the entire earth. The difference in the ascending nodes of adjacent planes depends on the number of orbital planes, calculated as ΔΩ=2π / N P , N P Indicates the number of satellite constellation orbits. The phase difference between adjacent satellites depends on the number of satellites in the plane, and the calculation formula is ΔΦ=2π / N Q , NQ represents the number of satellites in an orbital plane. The phase difference between orbital planes is calculated by the phase factor F∈{0,1,…,N P -1} to ensure that the positions of satellites in different orbital planes are relatively staggered in their orbits to optimize the coverage of the earth's surface. The phase difference between adjacent satellites in adjacent orbital planes is Δω f =2πF / N, F represents the phase factor, and N represents the total number of satellites.

[0108] Each satellite establishes permanent inter-satellite links with four adjacent satellites, including two intra-orbit links and two inter-orbital plane links. The sub-satellite point is the intersection of the connecting line from the satellite to the center of the earth and the earth's surface. The latitude of the sub-satellite point in the geodetic coordinate system at time t is and longitude λ(t) are 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 position in the orbital plane, ζ(u) is the longitude difference from the satellite to the ascending node, and u∈[-π,π] is the angular distance between the ascending node and the satellite at time t, which is used to determine the position of the satellite in orbit. The satellite is in the ascending phase and moving toward the northeast. Otherwise, the satellite is in the descending phase and moving toward the southeast. e is the angular velocity of the earth's rotation. The angle between the two satellites and the center of the earth can be calculated by the longitude and latitude of the satellites. The geocentric angle between satellite S1 and satellite S2 is calculated as follows:

[0113]

[0114] The instantaneous intersatellite link distance between S1 and S2 can be calculated from the geocentric angle of satellites S1 and S2. The calculation is as follows:

[0115]

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

[0117] Since the intersatellite link will cause signal attenuation when passing through the atmosphere, a minimum protection gap is set, that is, the gap between the intersatellite link and the earth's surface is recorded as I. The longest visible distance len between two satellites is as follows:

[0118]

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

[0120] Step 2: According to the low-orbit satellite network service scenario model and constellation model, the dynamic properties of ISL and satellite nodes are integrated into the snapshot topology structure obtained from the periodicity and predictability of the satellite network using the time-snapshot-based spatiotemporal extension graph model, and the time-varying network topology of the low-orbit satellite constellation is obtained based on the spatiotemporal extension graph.

[0121] The edge relationships and node states between nodes in satellite networks are time-varying. In order to construct a time-varying topological model of low-Earth orbit satellite networks, we use a spatiotemporal extended graph model based on time snapshots, such as Figure 3 As shown, the dynamic properties of ISLs and satellite nodes are integrated into a snapshot topology obtained from the periodicity and predictability of the satellite network.

[0122] Thanks to the periodicity and predictability of satellite networks, the following content models and analyzes the low-orbit satellite network within a cycle. A period of satellite orbit T = [t0,t M ] can be divided into a series of snapshots, and the snapshot time interval set is represented as T = {τ1,τ2,…,τ k ,…,τ M}, where τ k =[t k-1 ,t k ], t0 represents the start time of the cycle, t M represents the periodic intermediate moment, τk represents the kth time interval, τ M represents the Mth time interval; the satellite network is represented by G = (A, C, S, T), A represents the adjacency matrix, C represents the edge capacity matrix, and S represents the satellite set. Time t k The topological snapshot is represented as G k ={A k ,C k ,S k}, where A={A1,A2,…,A M} is the adjacency matrix, C={C1,C2,…,C M} is the capacity set of edges, S={S1,S2,…,S N} represents the satellite set. Considering the connection between snapshot graphs at adjacent moments, we get the spatiotemporal expansion graph G, which has M+1 layers, each layer contains N satellites, and 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-orbit satellite constellation based on the spatio-temporal expansion graph.

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

[0125]

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

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

[0128]

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

[0130]

[0131] During the operation phase, 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 time period Δt, the total number of data packets from ground users arriving at the satellite S k ∈S is a parameter λ u The Poisson process, the probability of data packet arrival can be calculated as:

[0132]

[0133] The ground user u data arrives at the satellite S k The average rate is λ u , N u (Δt) is the number of data packets arriving within 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 Δt time, the size of each data packet is In addition, satellite S k It is necessary to relay data from other satellites, which is related to the source and destination satellites visited by both parties. The calculation is as follows:

[0136]

[0137] Where S t is the source satellite, S d is the destination satellite, is through the relay path from S t To S d The relay path of the transmitted data is related to the specific routing algorithm.

[0138] Satellite S k The total amount of data that needs to be processed within Δt is calculated as:

[0139]

[0140] where Δt' is the time period before Δt, and is the unprocessed data stored in the buffer of the previous time period, and the calculation formula is:

[0141]

[0142] Here Indicates satellite S k The data that can actually be processed within the time interval Δt' is defined as follows

[0143]

[0144] in is the maximum computing power, F eff is the actual computing power efficiency function, which is defined as follows

[0145]

[0146]

[0147] Where χ is the congestion coefficient, which indicates the difficulty of the satellite to reach the congestion. The buffer capacity of the satellite The calculation is as follows:

[0148]

[0149] Where γ>0 is the capacity factor, which is used to describe the different buffer resources owned by the satellite. For satellites passing in orbit Time in northern latitude, This is the highest latitude that a satellite can actually reach.

[0150] Figure 4 The satellite state transition mechanism is shown. When the satellite buffer is overcrowded, the satellite will enter the congestion state, i.e. Satellites that enter a congested state require additional computing resources for buffer management and prioritize forwarding order based on packet size, destination, or other factors. This situation will significantly reduce the satellite's processing efficiency per unit time, resulting in a decrease in processing capacity, which may cause the satellite to further enter an overload state, i.e. Of course, it may return to normal.

[0151] Step 4: construct a resilience analysis model and resilience evaluation index of the LEO satellite network based on the time-space expansion graph for the time-varying network topology of the LEO satellite constellation, the satellite communication model, and the satellite status update mechanism. 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 LEO satellite networks is constructed, and a new resilience quantification index is proposed. The importance of nodes is evaluated from two aspects:

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

[0154]

[0155] in, represents the absolute flow betweenness based on the intersatellite link quality, represents the set of satellites except node k, W t represents the maximum flow matrix between all pairs of nodes in the network at time t, k W t Represents the matrix W t Remove the k-th row and k-th column from . *k W t It means removing the k-th row and the k-th column from the original network matrix and recalculating the maximum flow matrix.

[0156] This patent considers that the edge capacity is related to the link quality, and the edge capacity will change over time, which is defined as follows

[0157]

[0158] in, represents the edge capacity, represents the adjacency matrix element, is the link signal-to-noise ratio between nodes i and j, is the link bandwidth.

[0159] is the node function measure of node k in the network at time t based on satellite computing power and location criticality, considering the target satellite S k For all relevant satellites within two hops, the specific definitions are as follows:

[0160]

[0161] is the 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 function index of the two nodes in the snapshot graph at time t. Describes the node function index at time t, defined as follows

[0162]

[0163] in is the K-shell value of node k at time t, is the node computing power, It is node S k and node S m The weight value of the intersatellite link between the two at time t is defined as follows:

[0164]

[0165] p mk (t) is the outage probability affected by the link signal-to-noise ratio, where ω S is the weight distribution of the signal-to-noise ratio, ω F is the weight distribution of node computing power, and ω S +ω F =1, F eff represents the actual processing capacity efficiency function, Represents the amount of unprocessed data. Define the node importance of node k in the network as:

[0166]

[0167] in, represents the node importance of node k in the network, represents the absolute flow betweenness, represents the node function, ψ1+ψ2=1,0≤ψ1,ψ2≤1, ψ1 and ψ2 are the weights of the absolute flow measure and the node function measure respectively.

[0168] Furthermore, the relative importance of node k in the network structure at time t can be defined as:

[0169]

[0170] in, represents the relative importance of node k in the network structure at time t, N represents the number of network nodes, represents the set of satellites except node k, Represents a set of adjacent nodes.

[0171] At the same time, we believe that the absolute flow measure of the edge and the satellite function measure are equally important for judging the importance of nodes in the network, that is, ψ1 / ψ2=1, so:

[0172]

[0173] The time-varying network anti-destruction entropy is defined as:

[0174]

[0175] The corresponding time-varying network resilience indicator is defined as:

[0176]

[0177] Among them, Ent t represents the time-varying network anti-destruction entropy, N t Indicates the total number of network nodes at the current moment, Represents the importance of the node, t represents the time-varying network resilience index, G t represents the snapshot subgraph observed at time t, G t ∈{G1,G2,…,G M},N t is the graph G at time t t The number of nodes under It's G t The specific elasticity characterization algorithm is shown in Table 1.

[0178] Table 1 Time-varying network resilience algorithms

[0179]

[0180]

[0181] Step 5: Based on the satellite communication model, the elasticity analysis model of the LEO satellite network and the elasticity evaluation index, the network elasticity recovery optimization problem of the low-orbit satellite communication network under damage is constructed, and then the network elasticity of the low-orbit satellite communication network under damage is obtained.

[0182] The network resilience recovery problem is modeled as a multi-attribute decision-making problem:

[0183]

[0184] Among them, Re represents network elasticity, Re dam is the resilience of the damaged network, Re opt is the optimized network elasticity, A t is the adjacency matrix, N u is the number of packets arriving, I is the amount of data relayed by the router, is an optimized intersatellite link, con opt Denotes the full connectivity of the optimized network, Degree S represents the node degree, represents the amount of unprocessed data at the satellite nodes at both ends of the optimization link, ρ represents the congestion coefficient, represents the buffer capacity of the satellite, represents the satellites at both ends of the optimized link, T d Indicates the link duration, represents the duration threshold, Dist represents the intersatellite link distance, Dist χ Indicates the maximum link distance, SNR indicates the link signal-to-noise ratio, SNR χ Represents the signal-to-noise ratio threshold.

[0185] Step 6: An optimization method for the optimization problem of network resilience recovery of low-orbit satellite communication networks under damaged conditions is proposed.

[0186] A network elastic bottleneck identification and global optimization edge addition strategy is proposed. By introducing the collaborative optimization of two edge addition strategies, this strategy can effectively identify bottleneck links in the network and optimize the load balancing and transmission efficiency of the network at the global level. 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 usually carry a large amount of traffic and connect key nodes. Especially in the case of high network load or failure, these links are prone to become weak links that affect network performance. By adding redundant edges to bottleneck links, the network's survivability and connectivity can be significantly improved.

[0187] The global optimization strategy based on potential intersatellite link quality assessment aims to optimize the overall load distribution and routing efficiency of the network by introducing new intersatellite links. To evaluate the impact of potential intersatellite links, the strategy introduces a comprehensive scoring mechanism, which mainly measures the impact of link changes on the network by the load variance and hop count changes before and after the introduction of new links.

[0188] The load variance change is specifically defined as follows

[0189]

[0190] The comprehensive scoring formula is:

[0191]

[0192] Among them, ΔH is the reduction of the global hop count after adding the edge, is the reduction in load variance before and after the new link is introduced. ΔH max is the maximum possible change in the global hop count, is the maximum possible change in load variance, ω H and ω L is the weight parameter for hop optimization and load optimization, ω H +ω L =1.

[0193] We combine 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 the key links of the network have redundancy and sufficient bandwidth, and enhance anti-destruction and connectivity. Next, potential new links in the current network are evaluated. According to 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. This process can significantly improve the global load distribution and prevent high-load nodes in the network from becoming bottlenecks. At the same time, it optimizes the transmission path by reducing the number of hops, further improving the transmission efficiency of the network. The optimization process is implemented step by step in an iterative manner, and each round of iteration contains multiple time steps of the entire satellite cycle. The specific elastic optimization algorithm is shown in Table 2.

[0194] Table 2 Network elasticity bottleneck identification and global optimization edge addition strategy

[0195]

[0196]

[0197] Example 2

[0198] The present embodiment provides a large-scale low-orbit satellite network resilience assessment system based on graph theory and entropy theory, which adopts the large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory, including a network resilience recovery optimization problem unit for the low-orbit satellite communication network when it is damaged, wherein the network resilience recovery optimization problem unit for the low-orbit satellite communication network when it is damaged is provided with a network resilience recovery optimization problem model for the low-orbit satellite communication network when it is damaged, and the network resilience of the low-orbit satellite communication network when it is damaged is obtained according to the network resilience recovery optimization problem model for the low-orbit satellite communication network when it is damaged.

[0199] Example 3

[0200] This embodiment provides an electronic device, including a processor and a memory, wherein the memory is used to store processor executable instructions, and the processor is configured to call the instructions stored in the memory to execute the large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory.

[0201] This invention considers building a new elasticity quantitative evaluation method based on graph theory and entropy theory. By analyzing the time-varying topological structure and satellite node status, the elasticity of the LEO network is comprehensively and dynamically evaluated, providing an effective tool for network elasticity analysis in harsh environments. In order to cope with complex environments or sudden failures, an edge addition strategy based on network elasticity bottleneck identification and a global optimization edge addition strategy are proposed. By optimizing the link configuration in real time, the network is ensured to quickly restore service capabilities after being damaged, effectively improving the adaptive recovery capability and service guarantee level of the LEO satellite network.

[0202] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory, characterized in that: The following steps are involved: Step 1: Establish a low-orbit satellite network service scenario model and constellation model; Step 2: According to the low-orbit satellite network service scenario model and constellation model, the dynamic properties of ISL and satellite nodes are integrated into the snapshot topology structure obtained from the periodicity and predictability of the satellite network using the time-snapshot-based spatiotemporal expansion graph model, and the time-varying network topology of the low-orbit satellite constellation is obtained based on the spatiotemporal expansion graph; Step 3, constructing a satellite communication model and a satellite status update mechanism according to the time-varying network topology of the low-orbit satellite constellation based on the spatiotemporal expansion graph; Step 4, constructing a resilience analysis model and resilience evaluation index of the LEO satellite network based on the time-space expansion diagram for the time-varying network topology of the LEO satellite constellation, the satellite communication model, and the satellite status update mechanism; Step 5: Based on the satellite communication model, the elasticity analysis model of the LEO satellite network and the elasticity evaluation index, the network elasticity recovery optimization problem of the low-orbit satellite communication network under damage is constructed, and then the network elasticity of the low-orbit satellite communication network under damage is obtained.

2. The large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory according to claim 1 is characterized by: The optimization problem of network resilience recovery of low-orbit satellite communication network in the event of damage is: Among them, Re represents network elasticity, Re dam is the resilience of the damaged network, Re opt is the optimized network elasticity, A t is the adjacency matrix, N u is the number of packets arriving, I is the amount of data relayed by the router, is an optimized intersatellite link, con opt Denotes the full connectivity of the optimized network, Degree S represents the node degree, represents the amount of unprocessed data at the satellite nodes at both ends of the optimization link, ρ represents the congestion coefficient, represents the buffer capacity of the satellite, represents the satellites at both ends of the optimized link, T d Indicates the link duration, represents the duration threshold, Dist represents the intersatellite link distance, Dist χ Indicates the maximum link distance, SNR indicates the link signal-to-noise ratio, SNR χ Represents the signal-to-noise ratio threshold.

3. The large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory according to claim 1 is characterized in that: The optimization method for the optimization problem of network resilience recovery of low-orbit satellite communication networks in the event of damage 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 key links of the network have redundancy and sufficient bandwidth, and enhance anti-destruction 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 mainly measures the impact of link changes on the network through the load variance and hop count changes before and after the introduction of new links; The load variance change is specifically defined as follows The comprehensive scoring formula is: in, represents the load variance, represents the comprehensive score, N represents, express, Indicates that ΔH is the reduction in the number of global hops after adding edges. is the reduction in load variance before and after the introduction of the new link; ΔH max is the maximum possible change in the global hop count, is the maximum possible change in load variance, ω H and ω L is the weight parameter for hop optimization and load optimization, ω H +ω L =1.

4. The large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory according to claim 1 is characterized by: The elasticity analysis model and elasticity evaluation indicators of the LEO satellite network in step 4 are as follows: The absolute flow betweenness based on the intersatellite link quality is: in, represents the absolute flow betweenness based on the intersatellite link quality, represents the set of satellites except node k, W t represents the maximum flow matrix between all pairs of nodes in the network at time t, k W t Represents the matrix W t Remove the kth row and kth column from * k W t It means the maximum flow matrix recalculated by removing the kth row and kth column from the original network matrix; Considering that the edge capacity is related to the link quality, the edge capacity will change over time and is defined as follows: in, represents the edge capacity, represents the adjacency matrix element, is the link signal-to-noise ratio between nodes i and j, is the link bandwidth; is the node function measure of node k in the network at time t based on satellite computing power and location criticality, considering the target satellite S k For all relevant satellites within two hops, the specific definitions are as follows: in, is the satellite node S at time t k The set of adjacent nodes of It is node S k and node S m The smaller value of the node function index of the two nodes in the snapshot graph at time t, Describes the node function indicators at time t, which are defined as follows: in, is the K-shell value of node k at time t, is the node computing power, It is node S k and node S m The weight value of the intersatellite link between the two at time t is specifically defined as follows: p mk (t) is the outage probability affected by the link signal-to-noise ratio, where ω S is the weight distribution of the signal-to-noise ratio, ω F is the weight distribution of node computing power, and ω S +ω F =1, F eff represents the actual processing capacity efficiency function, Indicates the amount of unprocessed data; The node importance of node k in the network is defined as: in, represents the node importance of node k in the network, represents the absolute flow betweenness, represents the node function, ψ1+ψ2=1,0≤ψ1,ψ2≤1, 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: in, represents the relative importance of node k in the network structure at time t, N represents the number of network nodes, represents the set of satellites except node k, represents a set of adjacent nodes; The absolute flow measure of the edge and the satellite function measure are equally important for judging the importance of nodes in the network, that is, ψ1 / ψ2=1, so: The time-varying network anti-destruction entropy is defined as: The corresponding time-varying network resilience indicator is defined as: Among them, Ent t represents the time-varying network anti-destruction entropy, N t Indicates the total number of network nodes at the current moment, Represents the importance of the node, t represents the time-varying network resilience index, G t represents the snapshot subgraph observed at time t, G t ∈{G1,G2,…,G M },N t is the graph G at time t t The number of nodes under It's G t The number of nodes in the running state.

5. The large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory according to claim 1 is characterized by: The method for step 3 is: The signal transmission process is modeled as: Where X is the emission intensity, l ij is the link loss factor, Y ij is the final signal, N ij is an additive Gaussian white noise that is independent of the signal, P t is the transmission power, L ij is the distance between satellite i and satellite j; When the tracking error angle is θ ate When the half width of the beam divergence is ω0, the link loss factor l ij It is expressed as: At any time t, the signal-to-noise ratio of the ISL between satellite i and satellite j is expressed as: in, represents the signal-to-noise ratio of the ISL between satellite i and satellite j, and Ν0 represents the variance; During the operation 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 the satellite S k ∈S is a parameter λ u The Poisson process, the probability of data packet arrival is calculated as: Among them, P(N u (Δt) = k) represents the probability of data packet arrival, and the data of ground user u reaches satellite S k The average rate is λ u , N u (Δt) is the number of data packets arriving within Δt; satellite S k The amount of data received 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 Δt time, the size of each data packet is In addition, satellite S k It is necessary to relay data from other satellites, which is related to the source and destination satellites visited by both parties. The calculation is as follows: in, Indicates satellite S k The amount of data that needs to be relayed from other satellites, S t is the source satellite, S d is the destination satellite, is through the relay path from S t To S d the data being passed; Satellite S k The total amount of data that needs to be processed within Δt is calculated as: in, Indicates satellite S k The total amount of data that needs to be processed within Δt, Δt' is the time period before Δt, and is the unprocessed data stored in the buffer of the previous time period, and the calculation formula is: Here Indicates satellite S k The data that can actually be processed within the time interval Δt' is defined as follows in is the maximum computing power, F eff is the actual computing power efficiency function, which is defined as follows Among them, χ is the congestion coefficient, β is the computing power factor, ρ is the congestion coefficient, and the buffer capacity of the satellite The calculation is as follows: Where γ>0 is the capacity factor, which is used to describe the different buffer resources owned by the satellite; For satellites passing in orbit Time in northern latitude, It is the highest latitude that a satellite can actually reach.

6. The large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory according to claim 1 is characterized by: Satellite state transition mechanism, when the satellite buffer is overcrowded, the satellite will enter the congested state, that is, Satellites entering a congested state require additional computing resources for buffer management and to prioritize forwarding order based on packet size, destination, or other factors.

7. The large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory according to claim 1 is characterized by: The method for establishing the time-varying network topology of the low-orbit satellite constellation based on the time-space expansion graph in step 2 includes: a period of the satellite orbit The topology in the system is divided into a series of snapshots, and the set of snapshot time intervals is denoted as T = {τ1,τ2,…,τ k ,…,τ M }, where τ k =[t k-1 ,t k ], t0 represents the start time of the cycle, t M represents the periodic betweenness moment, τ k represents the kth time interval, τ M represents the Mth time interval; the satellite network is represented by G = (A, C, S, T), A represents the adjacency matrix, C represents the edge capacity matrix, S represents the satellite set, T represents the period, and the corresponding static topology subgraph within a period is represented by {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 } is the adjacency matrix, C={C1,C2,…,C M } is the capacity set of edges, S={S1,S2,…,S N } represents the satellite set; considering the connection between snapshot graphs at adjacent moments, we get the spatiotemporal expansion graph, G has M+1 layers, each layer contains N satellites, and there are N(M+1) nodes in total.

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

9. A large-scale low-orbit satellite network resilience assessment system based on graph theory and entropy theory, characterized in that: The large-scale low-orbit satellite network resilience assessment method based on graph theory and entropy theory as described in claim 1 is adopted, including a network resilience recovery optimization problem unit for the low-orbit satellite communication network when it is damaged, and the network resilience recovery optimization problem unit for the low-orbit satellite communication network when it is damaged is provided with a network resilience recovery optimization problem model for the low-orbit satellite communication network when it is damaged, and the network resilience of the low-orbit satellite communication network when it is damaged is obtained according to the network resilience recovery optimization problem model for the low-orbit satellite communication network when it is damaged.

10. An electronic device, characterized in that: It includes a processor and a memory, wherein the memory is used to store processor executable instructions, and the processor is configured to call the instructions stored in the memory to execute the large-scale low-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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