Method for improving robustness of wireless sensor network based on hierarchical topology reconstruction

Abstract

The invention discloses a method for improving robustness of a wireless sensor network based on hierarchical topology reconstruction, which belongs to the field of wireless sensor networks and comprises the following steps of: initializing a topological structure; nodes are divided into three layers, namely a core layer, a middle layer and a peripheral layer; selecting a node set in a communication range from the wireless sensor network to perform edge reconnection; establishing a convergence state monitoring mechanism based on a moving average method, and starting a multi-strategy collaborative optimization mechanism when detecting that the random edge reconnection process is in a stagnation state; and analyzing the optimized wireless sensor network, and judging whether the wireless sensor network is completely converged or not. According to the method, three strategies are provided, starting from the characteristics of an onion-shaped network structure, local convergence limitation of a traditional random edge reconnection algorithm is effectively broken through through a layered topology reconstruction mechanism, and on the premise that network degree distribution is not changed, a network topology structure is driven to evolve to the onion-shaped structure with the high-robustness characteristic.

Description

Technical Field

[0001] The invention relates to the field of wireless sensor networks, and in particular to a method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction. Background Art

[0002] Wireless sensor networks (WSNs) are networks composed of a large number of micro, low-power, distributed sensor nodes. Therefore, optimizing the network topology to improve its robustness has become an important research direction.

[0003] A lot of research has been conducted on the topology optimization of wireless sensor networks at home and abroad, and a variety of algorithms have been proposed, such as hill climbing algorithm, simulated annealing algorithm and genetic algorithm, etc. These algorithms have improved the robustness of the network to a certain extent, but there are significant shortcomings: first, the optimization effect is limited and it is difficult to meet actual needs; second, as the scale of the network increases, its robustness improvement effect decreases significantly, showing strong scale sensitivity. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a method for improving the robustness of a wireless sensor network by hierarchical topology reconstruction, which has a simple algorithm and is easy to implement.

[0005] The technical solution of the present invention to solve the above technical problem is: a method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, comprising the following steps: S1, topology initialization: based on the initial topology of the wireless sensor network, obtain the location information of all nodes and their corresponding neighbor node lists; S2, node stratification: Based on the acquired node information, the importance of each node in the wireless sensor network is calculated, and the nodes are divided into three layers according to their importance, namely the core layer, the middle layer and the peripheral layer; S3, edge reconnection evaluation: select a set of nodes within the communication range from the wireless sensor network for edge reconnection, evaluate the impact of reconnection on the robustness of the wireless sensor network, and decide whether to accept the reconnection operation based on the evaluation results; S4, topology optimization: establish a convergence status monitoring mechanism based on the moving average method. When it is detected that the random edge reconnection process is stagnant, start the multi-strategy collaborative optimization mechanism, including the core layer topology enhancement strategy, the inter-layer connection optimization strategy, and the peripheral layer structure reorganization strategy; S5, effect analysis: analyze the optimized wireless sensor network to determine whether it has fully converged and verify whether the goal of enhancing the robustness of the wireless sensor network has been achieved.

[0006] In the above-mentioned method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, in step S2, the importance of each node in the wireless sensor network is calculated by calculating three indicators of each node, including degree centrality, betweenness centrality and proximity centrality. Degree centrality is defined as the number of direct connections of a node, which directly reflects the influence of the node in the local range. The degree centrality calculation formula is as follows: ; Where: represents the degree centrality of node i; is the number of connections of node i, that is, the number of neighbor nodes of node i; Represents the total number of nodes in the wireless sensor network.

[0007] In the above-mentioned method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, in step S2, betweenness centrality is defined as the frequency of a node being located on the shortest path between other pairs of nodes in the wireless sensor network, and is used to identify nodes that play a key bridging role in the wireless sensor network. The betweenness centrality calculation formula is as follows: ; Where: represents the betweenness centrality of node i; represents the number of shortest paths connecting node s and node t and passing through node i; Represents the number of shortest paths connecting node s and node t.

[0008] In the above-mentioned method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, in step S2, the proximity centrality is defined as the inverse of the average shortest path length from the node to all other nodes in the wireless sensor network, reflecting the central position of the node in the global network. The calculation formula of the proximity centrality is as follows: ; Where: represents the proximity centrality of node i; Represents the distance from node i to node j.

[0009] In the above-mentioned method for improving the robustness of wireless sensor networks with hierarchical topology reconstruction, in step S2, a K-means clustering algorithm is used to perform cluster analysis on the wireless sensor network nodes with the degree centrality, betweenness centrality and proximity centrality of the nodes as characteristic indicators; the number of clusters K is set, and the maximum-minimum method is used to select the initial centroid, and iterative calculation is performed until the sum of squared errors within the cluster converges, and finally the wireless sensor network nodes are divided into three layers: a core layer, an intermediate layer and a peripheral layer.

[0010] The above-mentioned method for improving the robustness of a wireless sensor network by hierarchical topology reconstruction, the specific steps of step S3 are as follows: S31, select the conditions that the reconnected edge must meet: randomly select an edge from the wireless sensor network during each reconnection process, then traverse all edges within the node communication distance, and select an edge to reconnect with the selected edge; there is no additional connection between the edges selected for reconnection, that is, the reconnected edges are independent of each other; the four end nodes of the reconnected edge are within the same communication range, that is, they can communicate with each other, which is the basis for reconnection; S32, setting two reconnection strategies: assuming that two edges are selected, one reconnection strategy is to connect the head nodes of the two edges to the head nodes and the tail nodes to the tail nodes, and the other reconnection strategy is to cross-connect the head nodes and the tail nodes of the two edges, so that the degree of each node in the wireless sensor network will not change; Set a control factor It is used to measure the advantages and disadvantages of the two reconnection strategies, that is, to perform degree difference analysis. The specific formula of degree difference analysis is as follows: ; in, The range is 0.1-1, , , , are the degrees of nodes i, j, k and l respectively, and the numerator Represents the maximum degree difference of the new connection after the exchange; the denominator Represents the maximum degree difference of the original connection; the entire ratio represents the relative size of the maximum degree difference of the new connection relative to the original connection, and the entire ratio must be less than ; If the reconnection strategy does not meet the formula conditions, the reconnection operation will not be performed; S33, make a final decision: if the robustness of the wireless sensor network is improved after the reconnection, accept the reconnection; otherwise, abandon the reconnection and proceed to the next step of reconnection. The specific formula for evaluating the robustness R is as follows: ; in Represents the total number of nodes in the largest connected subgraph in the wireless sensor network after removing n nodes.

[0011] In the above-mentioned method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, in step S4, three strategies are used to optimize the topological structure of the wireless sensor network, so that the topological structure of the wireless sensor network evolves into an "onion-like" network structure, and the characteristics of the "onion-like" network structure are: high-degree nodes form the core of the onion; nodes with the same degree are interconnected and form a ring; low-degree nodes are located outside the ring, serving as a protective layer to protect high-degree core nodes; The core layer topology enhancement strategy is as follows: traverse the core layer node set, sort based on the degree difference of the edges, select the two edges with the largest degree difference and the second largest degree difference as candidate edges, then reconnect the two candidate edges, analyze the degree difference of the results after the two reconnection methods, retain the results that meet the constraints and have the smallest degree difference, and then calculate their robustness. If the robustness is improved, accept the reconnection, otherwise retain the original network structure; mark the reconnected edges and prohibit repeated operations in subsequent iterations.

[0012] In the above-mentioned method for improving the robustness of a wireless sensor network by hierarchical topology reconstruction, in step S4, the inter-layer connection optimization strategy is: There are two methods. The first one is core layer-middle layer edge reconnection. It traverses the core layer and the middle layer node set, and filters the edges that meet the cross-layer connection constraints, that is, one end of the edge is a core layer node, and the other end is a middle layer node. The second one is middle layer-peripheral layer edge reconnection. It traverses the middle layer and the peripheral layer node set, and filters the edges that meet the cross-layer connection constraints, that is, one end of the edge is a middle layer node, and the other end is a peripheral layer node. In both methods, two edges with the largest edge degree difference and the second largest edge degree difference are selected as candidate edges, and the selected edges are reconnected. The degree difference analysis is performed on the results after the two reconnection methods, and the results that meet the constraints and have the smallest degree difference are retained, and then their robustness is calculated. If the robustness is improved, the reconnection is accepted, otherwise the original network structure is retained; the reconnected edges are marked to prohibit repeated operations in subsequent iterations.

[0013] In the above-mentioned method for improving the robustness of wireless sensor networks by hierarchical topology reconstruction, in step S4, the strategy for reorganizing the structure of the peripheral layer is: Traverse the peripheral layer node set, sort based on the edge degree difference, select the two edges with the largest edge degree difference and the second largest edge degree difference as candidate edges, then reconnect the two candidate edges, analyze the degree difference of the results after the two reconnection methods, retain the result that meets the constraints and has the smallest degree difference, and then calculate its robustness. If the robustness is improved, accept the reconnection, otherwise retain the original network structure; mark the reconnected edges and prohibit repeated operations in subsequent iterations.

[0014] In the above-mentioned method for improving the robustness of wireless sensor networks with hierarchical topology reconstruction, in step S5, a moving average method is used to determine whether the global edge reconnection has fallen into a local solution. The local optimal solution refers to the optimization process converging to a suboptimal state at a certain stage. The formula is as follows: ; in Indicates the number of iterations of the current algorithm, that is, the number of edge reconnections; Indicates The robustness index of the current wireless sensor network in the iteration; Indicates the size of the calculation window, that is, the calculation of the nearest The average value of the robustness of the wireless sensor network in iterations; Indicates The moving average of iterations reflects the trend within the window; ; Indicates the change in adjacent moving averages; Indicates the set threshold value. is the convergence factor, when continuous If the number of times is less than the set threshold, it means that the global edge reconnection optimization has stagnated.

[0015] The beneficial effects of the present invention are as follows: first, according to the importance of the nodes in the wireless sensor network, the present invention divides the nodes in the network wireless sensor network into three layers: the core layer, the middle layer and the peripheral layer, and then reconnects the edges of the node set within the communication range; then, a convergence state monitoring mechanism based on the moving average method is established, and when it is detected that the random edge reconnection process is stuck in a stagnant state, a multi-strategy collaborative optimization mechanism is started; finally, the optimized wireless sensor network is analyzed to determine whether it has fully converged. The present invention proposes three strategies based on the characteristics of the "onion-like" network structure, and effectively breaks through the local convergence limitations of the traditional random edge reconnection algorithm through a hierarchical topology reconstruction mechanism. Without changing the network degree distribution, the network topology structure is driven to evolve to an "onion-like" structure with high robustness characteristics. The present invention shows insensitivity to the scale of the network, that is, when processing wireless sensor networks of different scales, the improvement of its network robustness is more stable than other algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The overall flow chart provided by the present invention.

[0017] Figure 2 It is a schematic diagram of edge reconnection of the present invention.

[0018] Figure 3 Regulatory factor A schematic diagram showing the effect of the present invention.

[0019] Figure 4 This is a curve diagram of the change in robustness of the initial wireless sensor network under three attacks.

[0020] Figure 5 Curve diagram for improving the robustness of wireless sensor networks under three attacks.

[0021] Figure 6 The figure is a comparison chart of the improved robustness under malicious attacks between the method of the present invention and the existing method.

[0022] Figure 7 is the convergence factor Schematic diagram showing the impact of the value on network robustness and number of iterations. DETAILED DESCRIPTION

[0023] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0024] like Figure 1 As shown, a method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction includes the following steps: S1, topology initialization: Based on the initial topology of the wireless sensor network, obtain the location information of all nodes and their corresponding neighbor node lists.

[0025] S2, node stratification: Based on the acquired node information, the importance of each node in the wireless sensor network is calculated, and the nodes are divided into three layers according to their importance, namely the core layer, the middle layer and the peripheral layer.

[0026] The importance of each node in the wireless sensor network is calculated by calculating three indicators of each node, including degree centrality, betweenness centrality and closeness centrality. Degree centrality is defined as the number of direct connections of a node, which directly reflects the influence of the node in the local area. The degree centrality calculation formula is as follows: ; Where: represents the degree centrality of node i; is the number of connections of node i, that is, the number of neighbor nodes of node i; Represents the total number of nodes in the wireless sensor network.

[0027] Betweenness centrality is defined as the frequency of a node being located on the shortest path between other pairs of nodes in a wireless sensor network. It is used to identify nodes that play a key bridging role in a wireless sensor network. The betweenness centrality calculation formula is as follows: ; Where: represents the betweenness centrality of node i; represents the number of shortest paths connecting node s and node t and passing through node i; Represents the number of shortest paths connecting node s and node t.

[0028] Proximity centrality is defined as the inverse of the average shortest path length from a node to all other nodes in the wireless sensor network, reflecting the central position of the node in the global network. The calculation formula for proximity centrality is as follows: ; Where: represents the proximity centrality of node i; Represents the distance from node i to node j.

[0029] By combining these three indicators, the importance of nodes can be comprehensively evaluated from multiple dimensions such as local influence, bridging role, and global centrality, thereby providing more comprehensive and accurate results for network stratification.

[0030] The K-means clustering algorithm is used to cluster the nodes of wireless sensor networks with the degree centrality, betweenness centrality and proximity centrality of nodes as characteristic indicators; the number of clusters K is set to 3, and the initial centroid is selected using the maximum-minimum method. The wireless sensor network nodes are finally divided into three layers: core layer, middle layer and peripheral layer through iterative calculation until the sum of square errors within the cluster converges. In this way, the optimal stratification boundary can be automatically determined, while ensuring that the nodes within the layer have a high similarity, while the nodes between the layers maintain significant differences, thereby achieving scientific stratification of the network structure.

[0031] S3, edge reconnection evaluation: select a set of nodes within the communication range of the wireless sensor network for edge reconnection, evaluate the impact of reconnection on the robustness of the wireless sensor network, and decide whether to accept the reconnection operation based on the evaluation results.

[0032] The specific steps of step S3 are as follows: S31, select the conditions that the reconnected edge must meet: randomly select an edge from the wireless sensor network during each reconnection process, then traverse all edges within the node communication distance, and select an edge to reconnect with the selected edge; there is no additional connection between the edges selected for reconnection, that is, the reconnected edges are independent of each other; the four end nodes of the reconnected edge are within the same communication range, that is, they can communicate with each other, which is the basis for reconnection; S32, setting two reconnection strategies: assuming that two edges are selected, one reconnection strategy is to connect the head nodes of the two edges to the head nodes and the tail nodes to the tail nodes, and the other reconnection strategy is to cross-connect the head nodes and the tail nodes of the two edges, so that the degree of each node in the wireless sensor network will not change; The ultimate goal of optimizing the network is to increase the robustness of the network. Existing theories have proven that the "onion-like" network structure has good resistance to attacks. Therefore, the purpose of the algorithm is to make the initial wireless sensor network structure evolve into an "onion-like" network structure. The characteristic of the "onion-like" network structure is that nodes with similar degrees are connected to each other. In view of this characteristic, a control factor is set It is used to measure the advantages and disadvantages of the two reconnection strategies, that is, to perform degree difference analysis. The specific formula of degree difference analysis is as follows: ; in, The range is 0.1-1, , , , are the degrees of nodes i, j, k and l respectively, and the numerator Represents the maximum degree difference of the new connection after the exchange; the denominator Represents the maximum degree difference of the original connection; the entire ratio represents the relative size of the maximum degree difference of the new connection relative to the original connection, and the entire ratio must be less than By comparing different The impact on network robustness is obtained only when When is equal to 0.9, the robustness of the network is the largest, so The value of is set to 0.9. By comparing the relative degree difference between the new connection and the original connection, a dimensionless measurement method is provided to evaluate and compare different reconnection strategies. By adopting the above formula, the computational complexity can be effectively reduced. There is no need to calculate the robustness of the network after each edge reconnection. The advantages and disadvantages of the two reconnection strategies can be quickly evaluated, the computational overhead can be reduced, and the edge reconnection strategy with the best reconnection effect can be selected. If the reconnection strategy does not meet the formula conditions, the reconnection operation is not performed, thereby optimizing the computational efficiency; S33, make the final decision: In step S32, by analyzing the structure of the wireless sensor network, an edge reconnection strategy that is beneficial to the evolution of the network into an "onion-like" structure is selected. However, the final decision still needs to be judged based on the robustness of the wireless sensor network after reconnection. If the robustness of the wireless sensor network is improved after reconnection, the reconnection is accepted; otherwise, the reconnection is abandoned and the next reconnection is performed. The specific formula for evaluating robustness R is as follows: ; in It represents the total number of nodes in the largest connected subgraph in the wireless sensor network after removing n nodes. This formula quantifies the network robustness of the wireless sensor network under malicious attacks targeting degree (that is, deleting the node with the largest degree in the wireless sensor network and its edges each time) as an evaluation of robustness.

[0033] S4, topology optimization: A convergence status monitoring mechanism based on the moving average method is established. When it is detected that the random edge reconnection process is stagnant, a multi-strategy collaborative optimization mechanism is initiated, including the core layer topology enhancement strategy, the inter-layer connection optimization strategy, and the peripheral layer structure reorganization strategy.

[0034] In step S4, in order to solve the problem that the global edge reconnection strategy is prone to fall into a local solution, when its optimization process stagnates, three strategies are used to optimize the topological structure of the wireless sensor network, so that the topological structure of the wireless sensor network evolves to an "onion-like" network structure, thereby increasing the robustness of the wireless sensor network; the characteristics of the "onion-like" network structure are: high-degree nodes form the core of the onion; nodes with the same degree are interconnected and form a ring; low-degree nodes are located outside the ring, serving as a protective layer to protect high-degree core nodes; The core layer topology enhancement strategy is: traverse the core layer node set, sort based on the degree difference of the edge, select the two edges with the largest degree difference and the second largest degree difference as candidate edges, then reconnect the two candidate edges, analyze the degree difference of the results after the two reconnection methods, retain the result that meets the constraints and has the smallest degree difference, and then calculate its robustness. If the robustness is improved, accept the reconnection, otherwise retain the original network structure; mark the reconnected edges, prohibit repeated operations in subsequent iterations, and ensure the coverage efficiency of the search space. The core layer topology enhancement strategy enhances the connectivity within the core layer, so that the high-degree nodes form a tightly interconnected core subgraph, which conforms to the characteristics of the onion network "high-degree nodes form the core of the onion", and provides a robust central foundation for wireless sensor networks.

[0035] The inter-layer connection optimization strategy is as follows: it includes two methods. The first one is the core layer-middle layer edge reconnection, which traverses the core layer and the middle layer node set, and selects the edges that meet the cross-layer connection constraints, that is, one end of the edge is a core layer node and the other end is a middle layer node; the second one is the middle layer-peripheral layer edge reconnection, which traverses the middle layer and the peripheral layer node set, and selects the edges that meet the cross-layer connection constraints, that is, one end of the edge is a middle layer node and the other end is a peripheral layer node; in both methods, two edges with the largest edge degree difference and the second largest edge degree difference are selected as candidate edges, and the selected edges are reconnected. The degree difference analysis is performed on the results after the two reconnection methods, and the results that meet the constraints and have the smallest degree difference are retained, and then their robustness is calculated. If the robustness is improved, the reconnection is accepted, otherwise the original network structure is retained; the reconnected edges are marked, and repeated operations are prohibited in subsequent iterations to ensure the coverage efficiency of the search space. The inter-layer connection optimization strategy strengthens the hierarchical structure of the wireless sensor network by optimizing the connection between the core layer and the middle layer, ensuring that the middle layer effectively connects the core and the periphery, conforming to the characteristics of the onion network "nodes of the same degree are interconnected and form a ring", and promoting the formation of a hierarchical ring topology.

[0036] The strategy for reorganizing the peripheral layer structure is: traverse the peripheral layer node set, sort based on the degree difference of the edge, select the two edges with the largest edge degree difference and the second largest edge degree difference as candidate edges, then reconnect the two candidate edges, analyze the degree difference of the results after the two reconnection methods, retain the result that meets the constraints and has the smallest degree difference, and then calculate its robustness. If the robustness is improved, accept the reconnection, otherwise retain the original network structure; mark the reconnected edges, prohibit repeated operations in subsequent iterations, and ensure the coverage efficiency of the search space. The strategy for reorganizing the peripheral layer structure forms a sparse protection layer composed of low-degree nodes by reorganizing the peripheral layer structure, which enhances the robustness of the wireless sensor network, conforms to the characteristics of the onion network "low-degree nodes are located outside the ring, as a protection layer to protect the high-degree core nodes", and provides an effective external barrier for the core.

[0037] S5, effect analysis: analyze the optimized wireless sensor network to determine whether it has fully converged and verify whether the goal of enhancing the robustness of the wireless sensor network has been achieved.

[0038] The common goal of the core layer topology enhancement strategy, the inter-layer connection optimization strategy, and the peripheral layer structure reorganization strategy is to prevent the optimization process from falling into the local optimal solution (i.e., local solution), thereby breaking through the bottleneck of improving network robustness. In order to achieve this goal, the moving average method is used to determine whether the global edge reconnection has fallen into the local solution. The local optimal solution refers to the optimization process converging to a suboptimal state at a certain stage. The formula is as follows: ; in Indicates the number of iterations of the current algorithm, that is, the number of edge reconnections; Indicates The robustness index of the current wireless sensor network in the iteration; Indicates the size of the calculation window, that is, the calculation of the nearest The average value of the robustness of the wireless sensor network in iterations; Indicates The moving average of iterations reflects the trend within the window; ; Indicates the change in adjacent moving averages; Indicates the set threshold value. is the convergence factor, when continuous If the number of times is less than the set threshold, it means that the global edge reconnection optimization has stagnated. The goal of the present invention is to make the network evolve into an "onion-like" topology, but the improvement in robustness will weaken with iterations. Therefore, the objective function of the present invention is defined as robustness. In the optimization algorithm, the relative rate of change of the objective function is often used as a convergence criterion. Figure 7The results show that the optimal value of the convergence factor is 0.0001. This value can ensure the optimization accuracy of the robustness index while taking into account the computational efficiency of the algorithm, avoiding the risk of excessive iteration or premature convergence.

[0039] The use of the moving average method to detect whether the edge reconnection optimization is stagnant has the following advantages: Smoothness: The moving average method can effectively reduce the impact of random interference on the optimization trend judgment by smoothing short-term fluctuations, which can highlight the long-term change trend of network robustness and make the detection of optimization stagnation more stable and reliable. Accuracy: The moving average method can accurately determine whether the optimization process has reached a local solution by detecting the stagnant state of the robustness indicator trend, which can improve the accuracy of stagnation detection. Practicality: The parameters of the moving average method can be flexibly adjusted according to the network scale, ensuring that the method can effectively detect optimization stagnation in different scenarios.

[0040] Table 1 shows the values ​​of the parameters involved in the moving average method;

[0041] In order to verify the effect of the control algorithm proposed in the present invention for enhancing the robustness of wireless sensor networks through the edge reconnection mechanism, the BA (Barabási-Albert) network model is used to generate a network, where m=3, m represents the number of m edges connected to the nodes within the communication range after the new node is added; the network range is 500m×500m, and the node communication radius is 200m. In order to be closer to reality, the maximum degree of the node is limited to 30, and it is ensured that 50% of the nodes are within their respective communication ranges.

[0042] Figure 2 The initial BA network is shown ( Figure 2 Middle left figure) and the improved network structure obtained by optimizing the algorithm of the present invention ( Figure 2 The shape and size of the nodes reflect the classification of nodes in the network, that is, the nodes are divided into three layers: core layer nodes, middle layer nodes and peripheral layer nodes. The algorithm proposed in this invention reconnects the edges in the initial BA network, and without changing the node degree, the network structure gradually evolves into an "onion-like" network structure.

[0043] from Figure 2 It can be seen that the "onion-like" network structure has the following characteristics: nodes with larger degrees (high-order nodes) tend to be highly interconnected, forming the core of the network; nodes with similar degrees also have a certain degree of interconnection, forming the middle layer; and lower-degree nodes are distributed in the outer layer, presenting a peripheral structure. This structure is similar to the layered wrapping of an onion: the core is composed of high-order nodes, and the outer layer is gradually wrapped by lower-degree nodes, showing obvious hierarchy and symmetry as a whole.

[0044] This "onion-like" network structure significantly improves the robustness of the network, enabling it to effectively resist multiple types of attacks, including random attacks, malicious attacks, and destructive attacks. The improvement in network robustness comes from the interconnectivity of high-order nodes and the hierarchical protection mechanism, which together ensure the connectivity and stability of the network under attack.

[0045] Figure 3 Shows a network robustness R The curve of change, where the horizontal axis represents The value range is 0.1 to 1; the vertical axis represents the quantitative value of network robustness. Curve analysis shows that when When the network robustness increases from 0.1 to 0.9, The increase of When it reaches 1, the network robustness decreases. =0.9, which indicates that the optimal parameter value is =0.9.

[0046] Used to control the constraint strength of edge reconnection. When the value is large, the constraint conditions of edge reconnection are looser, allowing more edge reconnection operations to be executed; When the value is small, the constraint condition of edge reconnection tends to be strict, and the exchange operation is allowed only when the degree difference of the newly created connection is significantly smaller than that of the original connection. The changing trend of The optimal value of is used to achieve a balance between the convergence speed of the algorithm and the optimization performance.

[0047] In order to quantify the effect of the optimization algorithm on improving the robustness of the network, three attacks are applied to the initial BA network and the improved network respectively, and the evaluation is performed by analyzing the changes in the maximum connected subgraph size ratio (that is, the ratio of the number of nodes in the maximum connected subgraph to the total number of nodes). The three attack methods are defined as follows:

[0048] Random attack: Each attack randomly selects a node from the network and deletes the node and all its edges. Malicious attack: Each attack deletes the node with the largest degree in the current network and all its edges. The degree of the nodes in the network is updated before each attack to ensure that the node with the largest degree is always targeted. Destructive attack: Each attack randomly selects a node and deletes the node, all nodes connected to the node, and related edges. Since the nodes deleted each time are randomly selected, the attack range is uncertain.

[0049] By comparing the changes in the ratio of the maximum connected subgraph sizes between the initial BA network and the improved network under the above attacks, the degree of improvement in the robustness of the optimized network can be intuitively verified.

[0050] Figure 4 The changing trend of the maximum connected subgraph size of the initial network of 100 nodes under three attack modes (random attack, malicious attack and destructive attack) is shown. The data comes from the average of multiple experiments. The horizontal axis represents the number of attacks, that is, the number of nodes removed from the initial BA network; the vertical axis represents the ratio of the maximum connected subgraph of the network after the attack, which is used as a quantitative indicator of network robustness. The higher the value, the better the degree of connectivity preservation of the network, and thus the higher the robustness of the network.

[0051] Figure 4 It shows that as the number of attacks increases, the ratio of the maximum connected subgraph shows a gradual downward trend in the three attack modes until the network is completely disconnected. The number of attacks required for the network to be completely disconnected is: destructive attack (24 times), malicious attack (43 times), and random attack (96 times). It can be seen that the robustness of the initial BA network to different attack modes is from high to low: random attack > malicious attack > destructive attack.

[0052] This difference in robustness stems from the topological structure characteristics of the BA network. The node degree distribution of the BA network follows a power law characteristic, which is manifested in that a few nodes (i.e., hub nodes) have significantly higher degree values, while most nodes have lower degree values. In a random attack, nodes are removed with equal probability, the probability of hub nodes being attacked is low, and the overall connectivity of the network is maintained for a longer time, thus showing higher robustness. However, in malicious and destructive attacks, attackers preferentially remove hub nodes with the highest degree values. Since the connectivity of the BA network is highly dependent on these hub nodes, once they are removed, the network structure quickly splits, resulting in a sharp drop in the size of the maximum connected subgraph. Therefore, the initial BA network has low robustness to malicious and destructive attacks.

[0053] Figure 5 The change trend of the maximum connected subgraph size of the improved network of 100 nodes optimized by the algorithm of the present invention under three attack modes (random attack, malicious attack and destructive attack) is shown. The data comes from the average value of multiple experiments. The horizontal axis represents the number of attacks, that is, the number of nodes removed in the improved network; the vertical axis represents the ratio of the maximum connected subgraph of the network after the attack, which is used as a quantitative indicator of network robustness. The higher the value, the better the degree of connectivity retention of the network, and thus the higher the robustness of the network.

[0054] Figure 5The analysis shows that as the number of attacks increases, the ratio of the maximum connected subgraph shows a gradual downward trend in all three attack modes until the network is completely disconnected. Specifically, the number of attacks required for the network to be completely disconnected is: destructive attack (37 times), malicious attack (57 times), and random attack (96 times). It can be seen that the robustness of the improved network to different attack modes is from high to low: random attack > malicious attack > destructive attack.

[0055] Will Figure 5 Compared with Figure 4 (the robustness performance of the initial BA network), the critical points of complete disconnection of the initial BA network under the same attack mode are: destructive attack (24 times), malicious attack (43 times) and random attack (96 times). The critical points of complete disconnection of the improved network under destructive attack and malicious attack modes are significantly higher than those of the initial BA network, indicating that the improved network optimized by the algorithm of the present invention is consistent with the initial BA network under random attacks, and its robustness under destructive attacks and malicious attacks is better than that of the initial BA network.

[0056] Table 2 shows the comparison between the method of the present invention and the existing methods in improving the robustness of the initial BA network. From the data in Table 2, it can be seen that the method of the present invention performs better than the existing optimization algorithms in improving the network robustness. At the same time, the robustness improvement variance of the method of the present invention is significantly smaller than that of other methods, indicating that its optimization effect is more stable and has higher reliability.

[0057] Figure 6 The robustness changes of wireless sensor networks under different network scales (100, 200, and 300 nodes) of the algorithm proposed in the present invention and existing algorithms, namely HC (hill climbing algorithm), SA (simulated annealing algorithm), GA (genetic algorithm), and AEDE (adaptive evolutionary algorithm) are demonstrated, aiming to verify the superiority of the algorithm of the present invention in improving network robustness.

[0058] Combined analysis of Table 2 and Figure 6 It can be seen that when the network scale is 100, 200 and 300 nodes respectively, the robustness of the present invention always maintains the highest level, significantly better than other algorithms. According to the ranking of robustness improvement effect from high to low, they are: AEDE, GA, SA, HC. Among them, compared with the existing optimal algorithm AEDE, the algorithm of the present invention shows significant performance improvement under different network scales: when the network scale is 100 nodes, the improvement is 5.62%; when the network scale is 200 nodes, the improvement increases to 6.76%; when the network scale is 300 nodes, it increases to 6.32%.

[0059] In addition, combining Table 2 and Figure 6 It can be seen from the data that the robustness improvement effect of the existing algorithms (HC, SA, GA, AEDE) shows a gradual downward trend with the increase of network scale. However, compared with other algorithms, the robustness of the algorithm of the present invention remains stable under different network scales, and its improvement percentage is not significantly affected by the change of network scale, showing insensitivity to network scale.

[0060] like Figure 7 As shown, Figure 7 The convergence factor is shown The impact of different values ​​on the robustness of the network under malicious attacks and the number of iterations is derived from the average of multiple experiments. Figure 7 It is found that as the convergence factor The value of the network is reduced, the robustness R of the network under malicious attacks and the number of iterations are increased, and the convergence factor When the values ​​are 0.001 and 0.00001, the robustness of the network is 0.20716 and 0.24173 respectively, and the number of iterations is 247 and 297 respectively. According to the robustness accuracy of the present invention is 0.0001, it is concluded that the robustness under these two values ​​is very close. In order to improve the running efficiency of the code, the convergence factor is The value of is set to 0.0001, which can reduce the running time of the code without affecting the accuracy of robustness R.

[0061] In summary, the algorithm proposed in the present invention has significant advantages in improving the robustness of wireless sensor networks. It is superior to existing algorithms at all network scales and reduces the sensitivity to network scale. Its performance improvement effect becomes more competitive as the network scale increases, ensuring that a stable optimization effect can be maintained in large-scale networks.

Claims

1. A method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, characterized in that: The following steps are involved: S1, topology initialization: based on the initial topology of the wireless sensor network, obtain the location information of all nodes and their corresponding neighbor node lists; S2, node stratification: Based on the acquired node information, the importance of each node in the wireless sensor network is calculated, and the nodes are divided into three layers according to their importance, namely the core layer, the middle layer and the peripheral layer; S3, edge reconnection evaluation: select a set of nodes within the communication range from the wireless sensor network for edge reconnection, evaluate the impact of reconnection on the robustness of the wireless sensor network, and decide whether to accept the reconnection operation based on the evaluation results; S4, topology optimization: establish a convergence status monitoring mechanism based on the moving average method. When it is detected that the random edge reconnection process is stagnant, start the multi-strategy collaborative optimization mechanism, including the core layer topology enhancement strategy, the inter-layer connection optimization strategy, and the peripheral layer structure reorganization strategy; S5, effect analysis: analyze the optimized wireless sensor network to determine whether it has fully converged and verify whether the goal of enhancing the robustness of the wireless sensor network has been achieved.

2. The method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 1 is characterized in that: In step S2, the importance of each node in the wireless sensor network is calculated by calculating three indicators of each node, including degree centrality, betweenness centrality and closeness centrality. Degree centrality is defined as the number of direct connections of a node, which directly reflects the influence of the node in the local area. The degree centrality calculation formula is as follows: ； Where: represents the degree centrality of node i; is the number of connections of node i, that is, the number of neighbor nodes of node i; Represents the total number of nodes in the wireless sensor network.

3. The method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 2 is characterized in that: In step S2, betweenness centrality is defined as the frequency of a node being located on the shortest path between other node pairs in the wireless sensor network, and is used to identify nodes that play a key bridging role in the wireless sensor network. The betweenness centrality calculation formula is as follows: ； Where: represents the betweenness centrality of node i; represents the number of shortest paths connecting node s and node t and passing through node i; Represents the number of shortest paths connecting node s and node t.

4. The method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 2 is characterized in that: In step S2, proximity centrality is defined as the inverse of the average shortest path length from the node to all other nodes in the wireless sensor network, reflecting the central position of the node in the global network. The calculation formula of proximity centrality is as follows: ； Where: represents the proximity centrality of node i; Represents the distance from node i to node j.

5. The method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 2 is characterized in that: In step S2, a K-means clustering algorithm is used to perform cluster analysis on the wireless sensor network nodes using the degree centrality, betweenness centrality and proximity centrality of the nodes as characteristic indicators; the number of clusters K is set, and the maximum-minimum method is used to select the initial centroid, and iterative calculation is performed until the sum of squared errors within the cluster converges, and finally the wireless sensor network nodes are divided into three layers: a core layer, an intermediate layer and a peripheral layer.

6. The method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 2, characterized in that: The specific steps of step S3 are as follows: S31, select the conditions that the reconnected edge must meet: randomly select an edge from the wireless sensor network during each reconnection process, then traverse all edges within the node communication distance, and select an edge to reconnect with the selected edge; there is no additional connection between the edges selected for reconnection, that is, the reconnected edges are independent of each other; the four end nodes of the reconnected edge are within the same communication range, that is, they can communicate with each other, which is the basis for reconnection; S32, setting two reconnection strategies: assuming that two edges are selected, one reconnection strategy is to connect the head nodes of the two edges to the head nodes and the tail nodes to the tail nodes, and the other reconnection strategy is to cross-connect the head nodes and the tail nodes of the two edges, so that the degree of each node in the wireless sensor network will not change; Set a control factor It is used to measure the advantages and disadvantages of the two reconnection strategies, that is, to perform degree difference analysis. The specific formula of degree difference analysis is as follows: ； in, The range is 0.1-1, , , , are the degrees of nodes i, j, k and l respectively, and the numerator Represents the maximum degree difference of the new connection after the exchange; the denominator Represents the maximum degree difference of the original connection; the entire ratio represents the relative size of the maximum degree difference of the new connection relative to the original connection, and the entire ratio must be less than ; If the reconnection strategy does not meet the formula conditions, the reconnection operation will not be performed; S33, make a final decision: if the robustness of the wireless sensor network is improved after the reconnection, accept the reconnection; otherwise, abandon the reconnection and proceed to the next step of reconnection. The specific formula for evaluating the robustness R is as follows: ； in Represents the total number of nodes in the largest connected subgraph in the wireless sensor network after removing n nodes.

7. The method for improving the robustness of a wireless sensor network by hierarchical topology reconstruction according to claim 6, characterized in that: In step S4, three strategies are used to optimize the topological structure of the wireless sensor network, so that the topological structure of the wireless sensor network evolves into an "onion-like" network structure. The characteristics of the "onion-like" network structure are: high-degree nodes form the core of the onion; nodes with the same degree are interconnected and form a ring; low-degree nodes are located outside the ring, serving as a protective layer to protect high-degree core nodes; The core layer topology enhancement strategy is as follows: traverse the core layer node set, sort based on the degree difference of the edges, select the two edges with the largest degree difference and the second largest degree difference as candidate edges, then reconnect the two candidate edges, analyze the degree difference of the results after the two reconnection methods, retain the results that meet the constraints and have the smallest degree difference, and then calculate their robustness. If the robustness is improved, accept the reconnection, otherwise retain the original network structure; mark the reconnected edges and prohibit repeated operations in subsequent iterations.

8. The method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 6, characterized in that: In step S4, the inter-layer connection optimization strategy is: There are two methods. The first one is core layer-middle layer edge reconnection. It traverses the core layer and the middle layer node set, and filters the edges that meet the cross-layer connection constraints, that is, one end of the edge is a core layer node, and the other end is a middle layer node. The second one is middle layer-peripheral layer edge reconnection. It traverses the middle layer and the peripheral layer node set, and filters the edges that meet the cross-layer connection constraints, that is, one end of the edge is a middle layer node, and the other end is a peripheral layer node. In both methods, two edges with the largest edge degree difference and the second largest edge degree difference are selected as candidate edges, and the selected edges are reconnected. The degree difference analysis is performed on the results after the two reconnection methods, and the results that meet the constraints and have the smallest degree difference are retained, and then their robustness is calculated. If the robustness is improved, the reconnection is accepted, otherwise the original network structure is retained; the reconnected edges are marked to prohibit repeated operations in subsequent iterations.

9. The method for improving the robustness of a wireless sensor network by hierarchical topology reconstruction according to claim 6, characterized in that: In step S4, the strategy for reorganizing the peripheral layer structure is: Traverse the peripheral layer node set, sort based on the edge degree difference, select the two edges with the largest edge degree difference and the second largest edge degree difference as candidate edges, then reconnect the two candidate edges, analyze the degree difference of the results after the two reconnection methods, retain the result that meets the constraints and has the smallest degree difference, and then calculate its robustness. If the robustness is improved, accept the reconnection, otherwise retain the original network structure; mark the reconnected edges and prohibit repeated operations in subsequent iterations.

10. The method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 1, characterized in that: In step S5, a moving average method is used to determine whether the global edge reconnection has fallen into a local solution. The local optimal solution refers to the optimization process converging to a suboptimal state at a certain stage. The formula is as follows: ； in Indicates the number of iterations of the current algorithm, that is, the number of edge reconnections; Indicates The robustness index of the current wireless sensor network in the iteration; Indicates the size of the calculation window, that is, the calculation of the nearest The average value of the robustness of the wireless sensor network in iterations; Indicates The moving average of iterations reflects the trend within the window; ； Indicates the change in adjacent moving averages; Indicates the set threshold value. is the convergence factor, when continuous If the number of times is less than the set threshold, it means that the global edge reconnection optimization has stagnated.

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