Remote air-sea cross-domain communication network single node failure recovery method

Abstract

The invention discloses a single-node failure recovery method for a remote air-sea cross-domain communication network. The method comprises the following steps of air-sea cross-domain communication network topology modeling, node failure detection and classification, link quality prediction and node failure recovery. According to the method, the recovery efficiency and stability of the air-sea cross-domain communication network after the single node fails are remarkably improved, the prediction average absolute percentage error (MAPE) of the GM-WOA model for the link quality is only 3.46%, which is superior to the traditional ARIMA (8.20%) and ARGM (14.33%), the method adapts to the dynamic change of the network, and under different network moving speeds (2-10m / s), the method has the advantages that the recovery efficiency and stability of the air-sea cross-domain communication network are greatly improved. Compared with a traditional method (non-prediction and one-hop neighbor prediction), the time consumed for recovering link reselection is reduced by 40%-60%, the real-time requirement is met, after the load balancing algorithm is combined, the link load variance of the network is recovered to 0 from 0.675, local congestion is avoided, and the overall transmission efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of air-sea cross-domain communication, specifically a method for recovering from single-node failure in a long-range air-sea cross-domain communication network. Background Technology

[0002] With the development of 6G technology, the air-sea cross-domain communication network, as a key infrastructure connecting the air and the sea, is crucial for the reliability and stability of scenarios such as maritime rescue and marine resource development. The air-sea cross-domain communication network corresponds to various types of relay nodes such as drones, unmanned ships, and unmanned underwater vehicles in the air, on the surface, and underwater. The nodes communicate with each other through multi-mode links such as electromagnetic waves and underwater acoustics. The topology changes dynamically and is susceptible to environmental factors such as sea waves and electromagnetic radiation, or node failures such as hardware failure and energy depletion. Node failure will lead to a decrease in network connectivity, or even splitting into disconnected subsets, which will seriously affect the continuity of communication.

[0003] Currently, traditional methods for damage recovery of cross-domain air-sea communication networks do not fully consider the multi-media characteristics and node mobility of cross-domain communication, making it difficult to accurately describe dynamic changes in the topology. Communication network recovery often targets single node types or simple networks, failing to differentiate the impact of different failure types such as central nodes, critical nodes, and edge nodes, resulting in lower recovery efficiency. To address these issues, this application proposes a method for single-node failure recovery in remote cross-domain air-sea communication networks, which can effectively solve the aforementioned problems. Summary of the Invention

[0004] The purpose of this invention is to provide a method for recovering from single-node failure in a remote air-sea cross-domain communication network, so as to solve the connectivity problem caused by single-node failure in existing air-sea cross-domain networks.

[0005] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0006] This invention relates to a method for single-node failure recovery in a long-range air-sea cross-domain communication network, comprising the following steps;

[0007] Step 1: Topology modeling of the air-sea cross-domain communication network: Establish a model of the air-sea cross-domain communication network, map nodes as vertices and links as edges, and define the communication cost weight matrix;

[0008] Step 2, Node Failure Detection and Classification: Node failure is detected through a time-slice polling mechanism, and classified into central nodes, critical nodes, or edge nodes according to node degree and network role;

[0009] Step 3, Link Quality Prediction: A link quality prediction algorithm based on grey theory and whale optimization weights is used to predict the communication quality of adjacent links of failed nodes;

[0010] Step 4, Node Failure Recovery: Depending on the type of failed node, network connectivity is restored by replacing the central node, reselecting the path of the critical node, or rebuilding the link of the edge node.

[0011] In step 1, considering the multi-layered architecture, long distance, and time-varying topology of the air-sea cross-domain communication network, a topology model of the air-sea cross-domain communication network is established based on the communication connections between network nodes per unit time. The network is abstractly mapped to a graph G(V,E,W) using graph theory, where V represents the set of nodes, E represents the set of edges, W represents the communication weight matrix, eij represents the edge between node i and node j, and wij represents the communication weight between node i and node j. The communication cost weight is defined as being determined by signal stability and load.

[0012] Signal stability is defined as a weighted sum of power intensity and relative velocity between nodes. In short-range communication, underwater acoustic wave transmission loss is dominated by geometric diffusion, with received power attenuating approximately according to log10(d), and the curve shape resembling spatial propagation. Therefore, in subsequent derivations, the power between nodes can be approximated as spatial propagation or calculated separately. To more accurately calculate communication costs, the power intensity between nodes in electromagnetic wave communication is calculated using the formula... Calculate, for node u, the magnitude of the signal power received by node v is defined as follows: P UV, received power P uv is related to the transmit power Ps, antenna gain Gs and Gr, wavelength λ and distance d, where d is the only variable. P Since uv is inversely proportional to d2, shortening the node spacing can improve signal strength and link quality. The power intensity between nodes in acoustic communication utilizes... P The equation uv = Mk.10log10(d) is used for calculation, where M is a constant and k is the spread coefficient, satisfying M = Ps + Gs + Gr. Higher signal power between nodes indicates better link quality. Taking nodes using electromagnetic wave communication as an example, power interpolation between adjacent time points is used as a condition for solving the relative motion between nodes. Figure 1 As shown, at time t, the relative positions of nodes u and v are 1 and 2, respectively. After Δt, the relative positions of nodes u and v become 1 and 3, respectively, with relative velocities vuv. The power of node v at position 2 is Pv2, and its frequency is fv2; the power at position 3 is Pv3, and its frequency is fv3. When the node's received power is at its minimum (Pmin), the communication distance between the transmitting and receiving nodes reaches its maximum value (Rmax).

[0013] Reference manual attached Figure 1 The distances between node v and node u at points 2 and 3 are:

[0014]

[0015] Let f be the frequency at which all nodes in the network transmit power. Then Δt = 1 / f. Node v receives a carrier wave transmitted by node u at frequency f'. According to the Doppler effect, we have...

[0016] According to the Law of Cosines, cos...

[0017] Substituting equations (3-3), (3-4), and (3-6) into equation (3-5) yields...

[0018] Since the time interval Δt is very short, the velocity vuv can be approximated as constant. Therefore, d23 ≈ vuv.Δt, and vuv can then be solved as...

[0019] To prevent nodes from selecting links with very short lifespans, the received power corresponding to the maximum communication radius of edge nodes in the network is set as a power threshold.

[0020] Where tdelay is the communication delay.

[0021] Similarly, the inter-node vuv for acoustic communication can be obtained as follows:

[0022]

[0023] Its power threshold is:

[0024] Pthreshold_water=M-10klog10(Rmax-2vmaxtdelay)(3-11)

[0025] Therefore, the signal stability between nodes u and v is defined as:

[0026]

[0027] Pthreshold∈{Pthreshold_air,Pthreshold_water}

[0028] in, P uv is the signal power intensity between node u and node v; vuv is the relative velocity between node u and node v; Ps is the transmit power; vmax is the maximum velocity of the node; p and q are the weighting coefficients of power and velocity, satisfying the condition p+q=1.

[0029] Define the load between node u and node v as

[0030] Here, Mu and Mv represent the message queue lengths of nodes u and v at the current moment, respectively. The lower the load on the nodes at both ends of the link, the smoother and faster the communication between nodes, and the lower the communication cost between nodes.

[0031] Under normal circumstances, the smaller the relative speed between two nodes, the stronger the signal and the lower the link load, resulting in simpler communication and lower communication cost. Conversely, the greater the relative speed, the higher the signal strength and the lower the link load. It can be seen that signal strength and link load are inversely proportional. Therefore, the ratio of link load to signal stability can be defined as the communication cost.

[0032] Where kL is the weight of the link load; kS is the weight of the signal stability. After calculating the communication cost of the air-sea cross-domain communication network, the network model can be obtained by combining the theory of undirected weighted graphs as follows;

[0033]

[0034] Where W represents the network communication cost weight matrix, which is an n×n matrix. When wuv is a real number, it means that a link can be established between node u and node v, and the larger wuv is, the greater the communication cost and the later it is selected. When wuv is infinite, it means that a link cannot be established between node u and node v because the maximum communication distance is exceeded. The communication cost weight matrix is ​​calculated by combining signal stability and link load.

[0035] In step 2, node failure detection includes communication sending and communication reply phases. A time-slice polling mechanism is adopted, which divides the time into several time slices of equal length. At the beginning of each time slice, all nodes in the network need to access the channel and communicate status messages to neighboring nodes to indicate that they are in normal working condition. If no communication message is received from a neighboring node, it is determined to be a failure.

[0036] For any node i, if one of the following conditions occurs within a consecutive number of time slices, then its neighbor node j is determined to be invalid:

[0037] 1. No reply message received: Node i did not receive an "online" reply message from node j within the preset time window;

[0038] 2. Packet loss rate exceeds threshold: If the packet loss rate of “online” messages of node j exceeds the set threshold η, it indicates that the link quality has seriously degraded, and node j may have failed or been out of communication range.

[0039] Assume that data packets sent by node i can be received by all nodes within its communication range. When node i detects that its neighbor node j has failed, it immediately broadcasts a "node failure notice" to the entire network to synchronize the network outage status. This mechanism ensures that all relevant nodes can update topology information in a timely manner and adaptively trigger network recovery mechanisms to maintain overall network connectivity.

[0040] The causes of node failures in air-sea cross-domain communication networks can be summarized into four main categories: environmental factors, hardware failures, network attacks, and human factors. Environmental factors include the influence of natural conditions such as extreme weather, underwater communication interference, and electromagnetic interference; hardware failures involve equipment problems such as energy depletion, sensor damage, or propulsion system malfunctions; network attacks mainly include malicious acts such as denial-of-service attacks, spoofing attacks, and data tampering; and human factors encompass subjective factors such as operational errors and task adjustments. These causes of failure may act individually or in combination, leading to node communication interruptions.

[0041] For air links, factors causing node failure include weather conditions, frequency interference, hardware malfunctions, insufficient power, and human attacks. For underwater links, factors causing node failure include the underwater environment (turbulence, temperature, etc.), multipath attenuation, and human attacks. In underwater links, when sound waves reach the sound shadow zone, their intensity significantly decreases or even disappears, leading to network outages. The sound shadow zone refers to the area where sound waves cannot directly reach due to the uneven distribution of sound speed in seawater, causing sound rays to bend towards the direction of lower sound speed.

[0042] In step 2, the node with the highest degree in the network is defined as the central node.

[0043] kV_center=max(ki),i∈Vair / Vsurface / Vwater(4-1)

[0044] Where kV_center is the degree of the central node; ki is the degree of node i; Vair, Vsurface, and Vwater represent the sets of air, surface, and underwater nodes in the air-sea cross-domain communication network, respectively; / refers to or.

[0045] In the distributed architecture of air-sea cross-domain communication networks, according to the above definition, the central node connects most nodes and plays a crucial role in coordination and control. However, the central node may fail due to hardware malfunctions, power depletion, human attacks, or other reasons, leading to network paralysis, communication interruptions, and task failures. This makes establishing a reliable central node failure recovery mechanism a critical issue that urgently needs to be addressed. When a central node fails, a suitable replacement node must be selected within the affected area according to a predetermined recovery plan to assume the functions of the central node, thereby maintaining normal network operation and the continuity of communication connections.

[0046] There is another type of node in the network that does not have the same degree as the central node, but its failure still significantly impacts the connectivity of the entire network, potentially leading to network partitioning. Critical nodes are defined using degree centrality, a graph theory term representing node importance, as follows:

[0047]

[0048] Where Cid is the degree centrality of node i; ki is the degree of node i; p, q, m, and n are the number of nodes on the water, on the surface, underwater, and the total number of nodes in the air-sea cross-domain communication network, respectively; there are corresponding relationships in the formula. An air-sea cross-domain communication network has a special characteristic: information propagates across different media, making nodes on the water surface act as relays. Regardless of the number of nodes connected to a surface node, the network will be paralyzed if a surface node is lost. Therefore, nodes on the water surface and those connected to both surface and underwater nodes are artificially classified as critical nodes; nodes located at the network edge, whose failure has a limited impact on the overall network connectivity, are defined as edge nodes. Edge nodes satisfy:

[0049]

[0050] Where ei is the path of node i (the maximum distance between any node and all nodes in the network); d(u,i) is the shortest distance between nodes u and i.

[0051] The central node is the node with the highest degree; the critical node is the relay node connecting the air and underwater subnets; and the edge node is the node with a lower degree and far from the core.

[0052] In step 3, considering the uncertainties of cross-domain communication networks between air and sea, a grey prediction system is adopted. This system is an efficient algorithm for observation and estimation, with high prediction accuracy and simple model verification and estimation methods, suitable for scenarios with small samples and limited information. However, its accuracy is slightly insufficient for nonlinear data. Therefore, this paper proposes a link quality prediction algorithm based on grey theory and whale-optimized weights, incorporating optimization algorithms to add new information to the grey prediction model.

[0053] As a modeling technique for systems with limited information, grey prediction can accurately predict the evolution trend of uncertain systems under conditions of limited and incomplete data. The initial stage of the prediction algorithm requires preprocessing the original data, using an accumulation generation operation to make the sequence distribution approximate an exponential law, thus laying the foundation for establishing the grey prediction model.

[0054] To eliminate random fluctuations and uncertainties in the original data, this study first performs cumulative processing on the initial data sequence to generate a more regular data sequence. A prediction model is then constructed based on the processed sequence, and the time response function is obtained by solving for it. Finally, the prediction result is obtained by reconstructing the original data using inverse cumulative subtraction operations. This process achieves a complete transformation from original data to prediction results.

[0055] Let the original sequence be W(0)={w(0)(1),w(0)(2),...,w(0)(k),...,w(0)(n)}, where w(0)(k) refers to the link quality data between nodes at time k. It is obtained by a single accumulation process.

[0056] w(1)(1)=w(0)(1)

[0057] w(1)(2)=w(0)(1)+w(0)(2)

[0058] w(1)(3)=w(0)(1)+w(0)(2)+w(0)(3)(4-4)w(1)(n)=w(0)(1)+w(0)(2)+...+w(0)(n)

[0059] Right now,

[0060]

[0061] After accumulating W(0), we get W(1).

[0062] W(1)={w(1)(1),w(1)(2),...,w(1)(n)}(4-6)

[0063] The mean-generating sequence is z(1)={z(1)(2),z(1)(3),...,z(1)(n)}, where,

[0064] The first-order differential equation obtained from the preprocessed cumulative generation sequence is as follows:

[0065]

[0066] Integrating both sides of the above equation simultaneously, we get:

[0067]

[0068] The right side of the equation is b, and the two terms on the left side are:

[0069]

[0070] At this point, the first-order differential equation becomes:

[0071] w(0)(k)+az(1)(k)=b,k=2,3,...,n(4-12)

[0072] Where a and b are the development coefficient and the grey effect, respectively. Solving for these values ​​yields the predicted link quality for future times. Substituting W(0)={w(0)(1),w(0)(2),...,w(0)(n)} and W(1)={w(1)(1),w(1)(2),...,w(1)(n)} into the equation, we obtain:

[0073] w(0)(2)+az(1)(2)=b

[0074] w(0)(3)+az(1)(3)=b

[0075] (4-13) ...

[0077] w(0)(n)+az(1)(n)=b

[0078] Transforming it and representing it as a vector, we get:

[0079] Where B is the coefficient matrix of a and b. This first-order differential equation is then transformed into a system of linear equations, which can be estimated using least squares:

[0080]

[0081] Therefore, the predicted sequence of this model is:

[0082]

[0083] To address the problem that traditional grey prediction models have a fixed time response function structure and struggle to adapt to dynamic data changes, this paper proposes an improved method based on the whale optimization algorithm. By introducing a variable weighting coefficient mechanism, the model's adaptability is enhanced, thereby effectively improving prediction accuracy.

[0084] Let the initial condition of the time response function be w(1)(β), then after weighting, we get:

[0085] w(1)(β)=αn-1w(1)(1)+αn-2w(1)(2)+...+α0w(1)(n),0<α<1; 1≤β≤n(4-17)

[0086] Right now

[0087] Where αn-k are the dynamic weighting coefficients; β is the time input coefficient. Therefore, the optimized time response function is:

[0088]

[0089] The optimal values ​​of α and β can be calculated by minimizing the mean absolute percentage error between the predicted and actual values. Based on this principle, an optimized objective function can be constructed.

[0090]

[0091] in, w(0)(k) and w(k) represent the fitted value and the actual value, respectively; n is the number of input data. Then, the whale optimization algorithm is used to obtain an approximate optimal solution. The whale optimization algorithm achieves optimization by simulating the hunting process of humpback whales. In summary, the steps of this prediction model are as follows, and the flowchart is shown below. Figure 2 As shown.

[0092] Step 1: Preprocess the raw data W(0) of the air-sea cross-domain communication network link quality to obtain the accumulated generation sequence; Step 2: Establish a first-order differential equation based on grey theory, determine the parameters through the least squares estimation method, and then solve for the time response function.

[0093] Step 3: Optimize the time response function: By introducing a dynamic weighting factor α and a time influence factor β, a corresponding objective function is constructed for optimization.

[0094] Step 4: Set the parameters of the whale algorithm, calculate the constraints, and determine the numerical range of parameters α and β;

[0095] Step 5: Calculate the cost value of each whale in the whale algorithm. Based on the concept of the fitness function, select the whale with the lowest cost value as the current optimal solution. The fitness function is:

[0096]

[0097] Step 6: Update the parameters of the whale algorithm, update the position of the individual whales according to the latest parameters, continue to calculate the cost value of the individual whales, and update the optimal solution;

[0098] Step 7: Update the whale's position iteratively until the maximum number of iterations is reached to obtain the optimal solution for α and β;

[0099] Step 8: Obtain the predicted sequence W(1), and perform a cumulative subtraction to obtain the predicted value.

[0100] In step 4, the central node recovery strategy is to select the node with the lowest communication cost among adjacent nodes in the failed region as the new central node. The critical node recovery strategy is to select the path with the lowest total communication cost in the failed region to rebuild the link. The edge node recovery strategy is to select the link with the lowest single-hop communication cost in the failed region to rebuild the link.

[0101] The failed central node and all nodes and combinations of links directly communicating with it are designated as network failure zones (Glapse). Within each zone, each node selects a new central node based on predicted link quality values ​​with other nodes to ensure network stability and connectivity. The selection rules are as follows:

[0102]

[0103] Where Wcenter_select is the metric for determining whether a node is selected as the new center node; ku is the degree of node u; This is the predicted communication cost between nodes u and v. When The smaller the value, the more suitable it is as a new central node. Parameters The value of is negatively correlated with the communication performance of node u. A smaller value indicates that the connection cost between node u and its neighboring nodes within the communication range is lower, reflecting that the node has more stable link quality and more reliable network connection characteristics. This advantage makes it an ideal candidate for a central node.

[0104] The network failure region Glapse is defined as the failed critical node and any nodes and combinations of links that have direct communication links with it. When a critical node fails, all its associated communication links also fail, eliminating it from the network and adaptively initiating a critical node reselection mechanism. The reselection method for any node in Glapse is as follows:

[0105]

[0106] Among them, Wkey_select_1 is the indicator 1 for measuring whether to select a new key node. It means that the neighbor node with the smallest predicted communication cost is selected in the failure area to establish a link. This represents the predicted communication cost for nodes u and v. In addition to this condition, the selection of new key nodes must also meet the requirements of overall network connectivity. Therefore, based on the above conditions, it is necessary to start from different nodes within the failure region, search and calculate reachable paths to other nodes, and calculate the communication cost. The minimum communication cost is recorded as Wkey_select_2.

[0107] Therefore, the critical node failure recovery method can be summarized as follows:

[0108] In the formula, node u is the set of one-hop neighbor nodes of v. By searching for candidate nodes within the failed region, the next-hop node that optimizes the link quality after repair is selected. This mechanism constitutes the network recovery strategy after the failure of a critical node.

[0109] The network failure region (Glapse) is defined as the failed edge node, nodes with direct communication links to that node, the next-hop node of that node with direct communication links, and the combination of links encompassed by these nodes. When an edge node fails, the impact on network connectivity is not significant; generally, other nodes act as relays to ensure normal transmission. However, due to node failure, when too much information needs to be transmitted through that node, network congestion and packet loss can easily occur, leading to a decrease in overall network performance and reliability. Therefore, in this situation, the remaining nodes in the Glapse adaptively select nodes to rebuild communication links. The selection criteria, i.e., the edge node failure recovery method, are as follows:

[0110]

[0111] The reason for selecting the node with the lowest predicted communication cost as the criterion for establishing a new link is that... The smaller the value, the more stable the link is, and the higher the success rate of establishing the link for communication.

[0112] Among the three different types of node failure recovery methods mentioned above, since the air-sea cross-domain communication network involves three types of nodes—air, surface, and underwater—a constraint is imposed when searching for replacement nodes: the replacement node must be of the same type as the original failed node to ensure that the connection status between different types of nodes in the network remains unchanged.

[0113] Compared with the prior art, the beneficial effects of the present invention are:

[0114] 1. This invention significantly improves the recovery efficiency and stability of single-node failures in air-sea cross-domain communication networks. The GM-WOA model's mean absolute percentage error (MAPE) for link quality prediction is only 3.46%, which is superior to traditional ARIMA (8.20%) and ARGM (14.33%), and adapts to dynamic network changes.

[0115] 2. In this invention, the time required to restore link reselection is reduced by 40%-60% compared with traditional methods (no prediction, one-hop neighbor prediction) under different network mobility speeds (2-10m / s), thus meeting the real-time requirements.

[0116] 3. In this invention, regarding connectivity, in a random failure scenario, when the proportion of failed nodes is ≤50%, the maximum connectivity ratio is ≥85% (for traditional algorithms, it is ≤70%).

[0117] In the case of deliberate attack, when the proportion of failed nodes is ≤40%, the average shortest path length ratio is ≤1.2 (≥1.5 for traditional algorithms), and the network resilience is significantly improved.

[0118] 4. In this invention, by combining the load balancing algorithm, the link load variance of the restored network is reduced from 0.675 to 0, avoiding local congestion and improving the overall transmission efficiency. Attached Figure Description

[0119] Figure 1 This is a schematic diagram of the relative motion between nodes in this invention;

[0120] Figure 2 This is a schematic diagram of the prediction algorithm flow of the present invention;

[0121] Figure 3 For the present invention Numerical distribution diagram;

[0122] Figure 4 This is a schematic diagram of the whale optimization algorithm of the present invention;

[0123] Figure 5 This is a schematic diagram illustrating the minimum communication cost algorithm of the present invention;

[0124] Figure 6 This is a schematic diagram illustrating the process of the present invention. Detailed Implementation

[0125] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0126] Please see Figure 1-6 The figure shows a method for single-node failure recovery in a remote air-sea cross-domain communication network according to the present invention.

[0127] Specifically, for air-sea cross-domain communication: air-sea cross-domain communication networks can realize data transmission on and under water, and enable efficient information exchange between devices.

[0128] Underwater environments, influenced by factors such as water flow, waves, and ocean currents, cause information carriers to face issues like absorption, scattering, and refraction. This leads to changes in environmental parameters and topology, affecting the position, movement speed, and other aspects of underwater nodes.

[0129] Maintaining stable transmission paths and other parameters is difficult. Energy harvesting and storage in various forms are extremely challenging underwater, leading to rapid power consumption and difficulties in battery replacement and recharging, resulting in frequent node failures. Node and link failures damage the network, disrupting connectivity, causing network fragmentation, and creating disconnected regions. Link damage increases the average path length between nodes and can even sever communication between some nodes. Furthermore, network damage alters topology parameters, such as changes in degree distribution, potentially forcing information to detour, increasing the network diameter (longest and shortest path), and reducing efficiency. Therefore, research on damage recovery methods for air-sea cross-domain communication networks is of significant importance, specifically in the following aspects:

[0130] (1) Air-sea cross-domain communication networks play an irreplaceable role in fields such as maritime rescue. When the network topology is damaged, the continuity and stability of communication will be severely affected, which may lead to serious consequences such as information transmission interruption and command failure. Researching effective topology damage recovery methods can quickly repair the network, ensure the continuity and stability of communication, and improve the reliability of the system.

[0131] (2) The working environment of air-sea cross-domain communication networks is complex and changeable, and they may face various threats such as natural disasters (such as typhoons and tsunamis) and human sabotage (such as network attacks). By studying topology damage recovery methods, we can enhance the resilience and fault tolerance of the network, enabling it to quickly restore communication and reduce losses in the face of various emergencies.

[0132] (3) Air-sea cross-domain communication networks serve as a bridge connecting air and sea platforms, involving the integrated application of various communication technologies (such as satellite communication, radio communication, and underwater acoustic communication). Researching topology damage recovery methods can not only solve technical problems in practical applications but also promote the development of related communication technologies and facilitate the overall progress of cross-domain communication networks.

[0133] In air-sea cross-domain communication networks, node failures exhibit randomness, meaning any node can fail at any time. However, the impact of different types of node failures on network performance varies significantly. For example, edge node failures have a relatively small impact on overall network performance because these nodes typically do not perform critical tasks; critical node failures, on the other hand, have a significant impact on overall network performance and can even cause the entire network to lose most of its functionality. As the number of failed nodes in the network increases, disconnected areas gradually emerge, essentially losing their original communication capabilities. Currently, no network recovery method has been found to address network impairment problems in the field of air-sea cross-domain communication networks. Therefore, this paper proposes a method suitable for impairment recovery in air-sea cross-domain communication networks to improve their reliability and stability.

[0134] Air-sea cross-domain communication networks have the following characteristics:

[0135] (1) Multi-domain integration: The air-sea cross-domain communication network can support two different communication environments, namely air and sea, and involves various types of communication nodes, such as drones, unmanned ships, and unmanned underwater vehicles.

[0136] (2) Wide coverage: The air-sea cross-domain communication network supports communication in both air and sea areas and can be combined with various communication platforms, such as high-altitude platforms and ground stations.

[0137] (3) Mobility and topology changes: The nodes of the air and sea cross-domain communication network are in motion, and the network topology will change frequently.

[0138] To enhance the robustness of air-sea cross-domain communication networks, this paper analyzes the network's topology characteristics and studies network topology damage recovery strategies. With the goal of constructing a stable air-sea cross-domain communication network, a link quality prediction algorithm can predict the network structure. Based on the prediction results, specific recovery strategies are formulated for different types of node failures. This approach can quickly respond to communication interruptions caused by missing or damaged nodes, effectively addressing the adaptive recovery challenges of node failures in air-sea cross-domain communication networks and ensuring network stability and reliability.

[0139] Air-sea trans-domain communication networks are becoming increasingly widespread and important in both civilian and commercial sectors. However, these networks, involving both air and underwater media environments, face complex propagation environments and wide coverage areas, making them susceptible to various factors such as natural disasters, human attacks, equipment failures, and energy depletion. The direct result of these impacts is node failure and network damage, severely affecting the continuity and reliability of communication and hindering the completion of specific network functions. Therefore, researching network damage methods is crucial for improving the performance and reliability of air-sea trans-domain communication networks. In the event of node failure, adaptive network topology restoration can ensure the stable operation of the air-sea trans-domain communication network.

[0140] Currently, research on damage recovery in air-sea cross-domain communication networks is limited. Therefore, referencing studies on topology recovery and reconstruction of underwater sensor networks, topology recovery and reconstruction of surface unmanned aerial vehicle (UAV) swarm networks, and the recoverability of complex networks, air-sea cross-domain communication networks are considered as an extension of underwater networks to surface networks. This section summarizes and outlines domestic and international literature from the perspective of network damage types.

[0141] Network impairments can be categorized by the number of failed nodes into single-node failure network impairments and multi-node failure network impairments; and by the importance of the nodes in the network's tasks into random failure network impairments and intentional attack network impairments. For network impairments caused by single-node failures, three recovery strategies currently exist: using optimization algorithms, network function reconstruction, and communication link-based prediction. For network impairments caused by multi-node failures, the network typically becomes multiple disconnected subsets, and recovery often employs topology reconstruction and swarm intelligence methods.

[0142] Network topology restoration using optimization algorithms involves first abstracting the failed network topology restoration problem into a mathematical model, then providing the objective function and constraints based on the actual situation, transforming it into a problem of solving for the extremum of the objective function using mathematical methods. This solution, mapped to a practical engineering problem, is the network restoration solution. Single-objective optimization mainly includes linear programming and nonlinear programming. Sun et al. proposed a framework for robustness analysis of complex networks, analyzed network parameters affecting network robustness, and proposed an optimization method based on variable neighborhood search. They found that if the degree of nodes in a complex network tends to be consistent, the upper limit of the network robustness metric will increase. Chuanlong Wu et al. used...

[0143] Simulated annealing algorithm was used to optimize heterogeneous network topologies with the goal of maximizing system performance. Lian proposed a wireless communication network topology reorganization method using an improved ant colony algorithm, which has good output stability and low transmission error rate. Wu et al. proposed a node function model based on the Memetic algorithm and analyzed in depth the robustness of heterogeneous nodes in complex networks against deliberate attacks.

[0144] Besides exploring the role of single influencing factors in network robustness, some researchers have proposed multi-objective intelligent optimization methods to more comprehensively investigate the network robustness problem. The difference in these algorithms lies in finding the optimal solution by searching the parameter space. Li Zheng developed an algorithm that optimizes the robustness of network nodes and edges, and proposed a network robustness optimization algorithm based on minimum cost. Tang, from the perspective of topology optimization, studied the impact of different types of attacks on networks and designed a Memetic algorithm that not only efficiently optimizes network communication efficiency but also enhances the network's ability to resist malicious attacks, and verified the algorithm's effectiveness. Wenyan Fu et al. proposed a topology optimization algorithm for underwater acoustic sensor networks based on node dump energy, network load, and edge path optimization, extending the network's lifespan and reducing node energy consumption. X Li et al. proposed a routing protocol for underwater optical sensor networks based on multi-agent reinforcement learning. This protocol incorporates node remaining energy and link quality factors into the design of node rewards and q-value functions, achieving dynamic routing selection through information interaction between adjacent nodes. ZA Khan et al. proposed a scheme based on energy level and balanced load allocation. Ma et al. explored a method to restore the transmission path by replacing dead nodes with optimal nodes, and proposed a path optimization and restoration algorithm based on ant colony algorithm.

[0145] For network function recovery methods, the main goal is to restore the network's ability to transmit information normally, i.e., to restore information transmission functionality. Kang proposed an adaptive routing algorithm based on utility forwarding, dynamically calculating utility values ​​and utilizing utility forwarding technology to address the frequent movement of nodes in the network. By considering factors such as node latency, utility value, and hop count between nodes, the system can select only the optimal next-hop forwarding node, reducing latency and avoiding network resource waste. Xiao et al. addressed the problem of excessively long response times during network failures by applying Software-Defined Networking (SDN) architecture to network recovery methods, proposing an SDN-based fault recovery strategy. Results show that this method can reduce fault recovery time while ensuring bandwidth requirements and service quality.

[0146] The essence of communication link quality prediction and recovery methods lies in inferring the possibility of establishing links between nodes. Therefore, theoretically, they can be applied to the research on damage recovery in cross-domain communication networks between air and sea. Liu et al. introduced a spatiotemporal common neighbor index into their link prediction method to analyze the correlation between links between nodes in both spatiotemporal dimensions. Jian Chen et al. proposed a method to optimize route reselection by hop-by-hop decomposition and recombination of routes based on historical link information and channel state obtained through periodic detection to predict link and route interruptions in underwater sensor networks. Chuan et al. proposed a cooperative network link prediction metric based on content similarity and an algorithm based on topic modeling. Rafiee et al. proposed a link prediction algorithm that optimizes similarity calculation by introducing a penalty mechanism. This algorithm determines the similarity score based on the network structure, specific characteristics, and topological features. Shuaizong Si et al. proposed an energy-saving and fault-tolerant evolution model for large-scale wireless sensor networks based on link prediction. Li et al. proposed a deep dynamic network embedding method that uses historical information obtained from network snapshots with timestamps to learn the potential representation of the future network. This method can predict missing links. Liu Linfeng et al. applied the link prediction method to message propagation based on the characteristics of the underwater sensor network topology and specifically introduced a spatiotemporal common neighbor index to analyze potential links between nodes. Shu et al. proposed a link prediction scheme for UAV ad hoc networks based on depth graph embedding. This scheme utilizes long short-term memory networks to extract the temporal features of the network, thereby accurately predicting the future network connection status.

[0147] Network topology reconfiguration refers to improving network characteristics by redesigning the network structure, adjusting connections between nodes, or adding new nodes. When some nodes in the network fail or become ineffective, removing or replacing the faulty nodes restores normal network operation. Its essence lies in finding the shortest path between disconnected subsets of the network. Zhang et al. proposed a connectivity determination algorithm for polygonal networks using minimum link design based on algebraic graph theory, which has low complexity. They also proposed a communication topology reconfiguration method for multiple multi-agent systems with different functions after networking. Qin et al. proposed a method to solve the problem of poor fault tolerance in partition connectivity by constructing backbone polygons to restore the bi-connectivity of partitions. This reduces the algorithm's running time, thus quickly restoring network connectivity. Ma proposed a partition connectivity restoration method for wireless sensor networks based on obstacle avoidance. Kang et al., addressing the problem of optimal data acquisition device location and movement path, introduced virtual fragments and hierarchical chromosome structures, proposing a multi-objective optimization genetic algorithm with customized encoding and decoding.

[0148] Swarm intelligence network recovery refers to using swarm intelligence methods to repair network faults or reorganize networks to restore normal network operation and optimize network performance. Swarm intelligence is a computational method that simulates and applies the behavior of natural groups. By simulating the interaction and information sharing among individuals in a group, it aims to achieve network repair, which is reflected in task planning. Zuo designed two topology reconstruction algorithms: one for node self-repair and the other for dynamic repair of redundant nodes. These two algorithms effectively improve the network's self-healing ability and stability. Chen et al. proposed a swarm intelligence-based damage recovery strategy for UAV swarm networks, which has good performance in terms of recovery capability, convergence time, and communication overhead. Cui et al. proposed a multi-UAV network topology optimization control algorithm based on improved particle swarm optimization, taking into account factors such as network connectivity, communication link quality, and network connection cost. Chouikhi et al. addressed network faults and network power...

[0149] To address the connection recovery problem, a distributed solution for multi-channel wireless sensor network connection recovery is proposed. This solution uses only neighborhood information when performing channel reallocation and does not consider the route followed by the data towards the sink. Based on this, a route-based connection recovery scheme for multi-channel wireless sensor networks is further proposed, utilizing routing trees and neighborhood information during the channel allocation / reallocation phase.

[0150] In summary, the following problems exist in the field of network damage recovery research:

[0151] (1) Network damage recovery schemes and technologies in different fields are relatively scattered, lacking standardized schemes and common solutions, which brings certain difficulties and uncertainties to research and application in air and sea cross-domain fields;

[0152] (2) There are many network damage recovery algorithms, but the efficiency and optimization of these algorithms still need further research and optimization to improve their practical application value.

[0153] (3) Research on network damage recovery requires abundant experimental data, but due to the complexity of real networks and issues such as data privacy, it is difficult to obtain and share experimental data.

[0154] The difference between air-sea cross-domain communication networks and other types of networks lies in the fact that cross-domain communication networks involve nodes in two transmission media and three operating environments. Their connections are not like those of UAV swarms and underwater sensor networks, but are geographically limited. That is, air nodes can only establish links with air nodes and surface nodes, underwater nodes can only establish links with underwater nodes and surface nodes, while surface nodes, as relays between air nodes and underwater nodes, can establish links with air, underwater and surface nodes.

[0155] Considering the multi-layered architecture, long distance, and time-varying topology of the air-sea cross-domain communication network, a topology model of the air-sea cross-domain communication network is established based on the communication connections between network nodes per unit time. The network is abstracted and mapped to a graph G(V,E,W) using graph theory, where V represents the set of nodes, E represents the set of edges, W represents the communication weight matrix, eij represents the edge between node i and node j, and wij represents the communication weight between node i and node j. The communication cost weight is defined as being determined by signal stability and load.

[0156] In some embodiments, such as the air-sea cross-domain communication network model, it is assumed that the network has 30 nodes, including 10 UAV nodes, 10 surface unmanned vessel nodes, and 10 underwater unmanned vehicle nodes. Surface unmanned vessel nodes serve as relay nodes, connecting surface and underwater nodes. All performance parameters are identical for each type of node. The movement speed of air nodes in the entire network is consistent with that of surface and underwater nodes. The entire network is based on a reference point group movement model, moving in a specific direction at a certain speed, with a maximum speed of 10 m / s. During the simulation, the network as a whole moves at a speed of vset, where the speed of each node is vset + vrand. The communication cost value wij is calculated based on the signal stability and load mentioned in the previously established model. Through multiple iterations, the sliding window contains historical data from multiple moments, and a communication cost prediction matrix is ​​obtained. like Figure 3 As shown, the closer the color is to yellow, the larger the value, representing the establishment of connections between nodes.

[0157] The more unstable the link, the closer the color is to blue, indicating a smaller value and thus a more stable link. Nodes 1-10 represent aerial drone nodes, nodes 11-20 represent surface unmanned vessel nodes, and nodes 21-30 represent underwater unmanned vehicle nodes. Aerial drone nodes and underwater unmanned vehicle nodes cannot establish links due to communication medium limitations, therefore their corresponding communication costs are infinite. The communication cost between nodes is reflected in signal stability and communication load. More unstable signals between nodes indicate greater distances, faster relative speeds, and higher loads, all contributing to higher communication costs. This indicates poor link stability. Therefore, this link was excluded from subsequent node selection.

[0158] The probability of selecting it as an alternative will decrease significantly. In W^, the value at the center node is one greater than that at other locations.

[0159] This is because the central node contains more communication links and therefore has a greater load.

[0160] In the air-sea cross-domain communication network model, it is assumed that the network has 30 nodes: 10 UAV nodes, 10 surface unmanned vessel nodes, and 10 underwater unmanned vehicle nodes. Surface unmanned vessel nodes serve as relay nodes, connecting surface and underwater nodes. The performance parameters of each type of node are identical. The movement speed of air nodes in the entire network is consistent with that of surface and underwater nodes. The entire network is based on a reference point group movement model, moving in a specific direction at a certain speed, with a maximum speed of 10 m / s. The maximum number of iterations for the whale algorithm is 50. Node failure states include random failure and deliberate attack failure.

[0161] A simulation experiment was conducted on the multi-node failure scenario of an air-sea cross-domain communication network. It was assumed that the set of failed nodes is Vlapse, and the set of affected nodes requiring recovery is Vrecover. When a network node fails, the affected node sends a link establishment request to its neighboring nodes. Through an information-sharing mechanism between nodes, the entire network can promptly obtain the set of nodes requiring recovery.

[0162] Using the time it takes for the network to reselect links after a network node fails as an indicator, the network recovery algorithm without prediction of the shortest path achieves network recovery by finding the shortest path without link prediction; the one-hop neighbor link prediction recovery algorithm predicts the communication cost of each node in the network and selects the node with the best weight for network recovery.

[0163] Network survivability and resilience are crucial characteristics that measure a communication network's ability to maintain its functionality and performance in the face of various threats and failures. In air-sea trans-domain communication networks, survivability and resilience are particularly critical because these networks typically face dynamic environments and diverse threat sources. Both network survivability and resilience refer to the ability of a network to continue operating and providing services after an attack or failure. To more effectively evaluate the performance of air-sea trans-domain communication networks under random failures and deliberate attacks, two key metrics are introduced: the network's maximum connectivity ratio and the average shortest path length ratio. These two metrics provide a comprehensive analysis of the network's performance.

[0164] Furthermore, the Whale Optimization Algorithm (WOA) is a metaheuristic optimization method inspired by the foraging behavior of whale groups. This algorithm effectively simulates the food-hunting process of humpback whales, particularly their unique search and encirclement mechanisms. Its core mechanism mainly comprises three interrelated stages: prey encirclement, bubble-net predation strategy, and global search. These stages collectively reflect the complex foraging behavior of humpback whales in the marine ecosystem. The Whale Optimization Algorithm can discover the optimal solution in the parameter space, providing a better parameter calculation and adjustment scheme for link quality prediction algorithms, thereby making the prediction results more accurate and reliable. In addition, the Whale Optimization Algorithm features strong global search capabilities and fast search speed, enabling it to quickly find the optimal parameters, improving algorithm performance and efficiency. Its basic process is as follows: Figure 4 As shown.

[0165] Finally, regarding the minimum communication cost algorithm, the flowchart is as follows: Figure 5 As shown;

[0166] Step 1: Input the starting node s, the target node j, and the communication cost prediction matrix W;

[0167] Step 2: Construct the set of labeled nodes as S, the set of unlabeled nodes as U, the communication cost matrix W*, and the shortest path vector p;

[0168] Step 3: Determine the starting point s and add it to set S. Search the set of unmarked nodes U and find node j such that the path from s to j satisfies all preset constraints and minimizes the communication cost of the path. Mark the node j that meets the conditions and add it to S.

[0169] Step 4: Using nodes in set S as intermediate nodes, iteratively update the communication cost matrix W* and the shortest path vector p;

[0170] Step 5: Search for new nodes in S. If the destination cannot be found, backtrack and update the communication cost matrix W* and the shortest path vector p, find the previous branch and start the search operation again.

[0171] Step 6: Continue searching the nodes in U, find the node j with the minimum communication cost to the starting point s, and add it to S; Step 7: Continue steps 5 and 6 until the destination is reached; otherwise, continue.

[0172] The above description, in conjunction with specific embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection defined by the claims submitted herein.

Claims

1. A method for single-node failure recovery in a long-range air-sea cross-domain communication network, characterized in that, Includes the following steps; Step 1: Topology modeling of the air-sea cross-domain communication network: Establish a model of the air-sea cross-domain communication network, map nodes as vertices and links as edges, and define the communication cost weight matrix; Step 2, Node Failure Detection and Classification: Node failure is detected through a time-slice polling mechanism, and classified into central nodes, critical nodes, or edge nodes according to node degree and network role; Step 3, Link Quality Prediction: A link quality prediction algorithm based on grey theory and whale optimization weights is used to predict the communication quality of adjacent links of failed nodes; Step 4, Node Failure Recovery: Depending on the type of failed node, network connectivity is restored by replacing the central node, reselecting the path of the critical node, or rebuilding the link of the edge node.

2. The method for single-node failure recovery in a long-range air-sea cross-domain communication network according to claim 1, characterized in that: In step 1, the communication cost weight matrix is ​​calculated by combining signal stability and link load.

3. The method for single-node failure recovery in a long-range air-sea cross-domain communication network according to claim 1, characterized in that: In step 2, node failure detection includes communication sending and communication reply phases. A time-slice polling mechanism is adopted, which divides the time into several time slices of equal length. At the beginning of each time slice, all nodes in the network need to access the channel and communicate status messages to neighboring nodes to indicate that they are in normal working condition. If no communication message is received from a neighboring node, it is determined to be a failure.

4. The method for single-node failure recovery in a long-range air-sea cross-domain communication network according to claim 1, characterized in that: In step 2, the central node is the node with the highest degree; the key node is the relay node connecting the air and underwater subnets; and the edge node is the node with a lower degree and far from the core.

5. The method for single-node failure recovery in a long-range air-sea cross-domain communication network according to claim 1, characterized in that: In step 3, the link quality prediction algorithm includes: Historical link quality data is accumulated and processed to generate the data. A grey prediction model is established based on first-order differential equations, and the parameters are solved by the least squares method. With the goal of minimizing prediction error, the whale optimization algorithm is used to optimize dynamic weights and time influence factors; Data is updated in real time through a sliding window to adapt to changes in network topology.

6. The method for single-node failure recovery in a long-range air-sea cross-domain communication network according to claim 1, characterized in that: In step 4, the central node recovery strategy is to select the node with the lowest communication cost among neighboring nodes in the failed region as the new central node.

7. The method for single-node failure recovery in a long-range air-sea cross-domain communication network according to claim 1, characterized in that: In step 4, the critical node recovery strategy is to select the path with the lowest total communication cost in the failed area to rebuild the link.

8. The method for single-node failure recovery in a long-range air-sea cross-domain communication network according to claim 1, characterized in that: In step 4, the edge node recovery strategy is to select the link with the lowest single-hop communication cost in the failed area for reconstruction.

Images