A Method for Improving the Robustness of Wireless Sensor Networks with Hierarchical Topology Reconstruction

Abstract

The present invention discloses a method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, belonging to the field of wireless sensor networks, and comprising the following steps: initializing the topology structure; dividing the nodes into three layers, namely the core layer, the intermediate layer and the peripheral layer; selecting a node set within the communication range from the wireless sensor network for edge reconnection; establishing a convergence state monitoring mechanism based on the moving average method, and starting a multi-strategy collaborative optimization mechanism when it is detected that the random edge reconnection process falls into a stagnant state; analyzing the optimized wireless sensor network to determine whether all converge. The present invention proposes three strategies starting from the characteristics of the "onion-like" network structure, and effectively breaks through the local convergence limitation of the traditional random edge reconnection algorithm through the hierarchical topology reconstruction mechanism. Without changing the network degree distribution, it drives the network topology structure to evolve towards the "onion-like" structure with high robustness characteristics.

Description

Technical Field

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

[0002] A wireless sensor network (WSN) is a network composed of a large number of miniature, low-power, and distributed sensor nodes. Therefore, optimizing the network topology to enhance its robustness has become an important research direction.

[0003] A large number of studies on wireless sensor network topology optimization have been carried out at home and abroad, and various algorithms have been proposed, such as the hill-climbing algorithm, simulated annealing algorithm, and genetic algorithm, etc. These algorithms have enhanced the network robustness to a certain extent, but there are significant deficiencies: firstly, the optimization effect is limited and it is difficult to meet the actual requirements; secondly, as the network scale increases, the effect of enhancing its robustness 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 enhancing the robustness of a wireless sensor network with 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 problems is: a method for enhancing the robustness of a wireless sensor network with hierarchical topology reconstruction, including the following steps:

[0006] S1, Topology Structure Initialization: Based on the initial topology structure of the wireless sensor network, obtain the position information of all nodes and their corresponding neighbor node lists;

[0007] S2, Node Layering: According to the obtained node information, calculate the importance of each node in the wireless sensor network, and divide the nodes into three layers according to the importance degree, namely the core layer, the intermediate layer, and the peripheral layer;

[0008] S3, Edge Reconnection Evaluation: Select a node set within the communication range from the wireless sensor network for edge reconnection, evaluate the impact on the robustness of the wireless sensor network after reconnection, and decide whether to accept the reconnection operation according to the evaluation result;

[0009] S4, Topology Optimization: Establish a convergence state monitoring mechanism based on the moving average method. When it is detected that the random edge reconnection process is in a stagnant state, start a multi-strategy collaborative optimization mechanism, including a core layer topology enhancement strategy, an inter-layer connection optimization strategy, and a peripheral layer structure reorganization strategy;

[0010] S5, Effect Analysis: Analyze the optimized wireless sensor network, judge whether it has fully converged, and verify whether the goal of enhancing the robustness of the wireless sensor network is achieved.

[0011] The above method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction. In step S2, calculating the importance of each node in the wireless sensor network is achieved by calculating three metrics for each node. The three metrics include degree centrality, betweenness centrality, and closeness centrality. Degree centrality is defined as the number of direct connections of a node, intuitively reflecting the influence of the node within a local range. The calculation formula for degree centrality is as follows:

[0012] ;

[0013] In the formula: 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.

[0014] The above 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 on the shortest path between other nodes in the wireless sensor network, and is used to identify the nodes that play a key bridging role in the wireless sensor network. The calculation formula for betweenness centrality is as follows:

[0015] ;

[0016] In the formula: 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.

[0017] The above method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction. In step S2, closeness centrality is defined as the reciprocal 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 closeness centrality is as follows:

[0018] ;

[0019] In the formula: represents the closeness centrality of node i; represents the distance from node i to node j.

[0020] The above method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction. In step S2, the K-means clustering algorithm is used to perform clustering analysis on the nodes of the wireless sensor network with the degree centrality, betweenness centrality, and closeness centrality of the nodes as feature indicators; the number of clusters K is set, and the initial centroids are selected using the max-min method, and through iterative calculation until the sum of squared errors within the clusters converges, and finally the nodes of the wireless sensor network are divided into three layers: the core layer, the intermediate layer, and the peripheral layer.

[0021] The above method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction. The specific steps of step S3 are as follows:

[0022] S31, Conditions for selecting the edges to be reconnected: In each reconnection process, randomly select an edge from the wireless sensor network, and then traverse all the edges within the communication distance of the nodes, and select the edge to be reconnected with the selected edge; there are no additional connections between the selected edges to be reconnected, that is, the reconnected edges are independent edges; the four end nodes of the reconnected edges are within the same communication range, that is, they can communicate with each other, which is the basis for reconnection.

[0023] S32, Set two reconnection strategies: Assume 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 node of one edge with the tail node of the other edge, so that the degree of each node in the wireless sensor network does not change.

[0024] Set a regulation factor used to measure the advantages and disadvantages of the two reconnection strategies, that is, perform degree difference analysis. The specific formula for degree difference analysis is as follows:

[0025] ;

[0026] Among them, ranges from 0.1 to 1, , , , are the degree values of nodes i, j, k, and l respectively. The numerator represents the maximum degree difference of the new connection after exchange; the denominator represents the maximum degree difference of the original connection; the whole ratio represents the relative size of the maximum degree difference of the new connection relative to the original connection, and the whole ratio must be less than ; If the reconnection strategy does not meet the formula conditions, the reconnection operation is not performed.

[0027] S33, Make the final decision: If the robustness of the wireless sensor network is improved after reconnection, accept this reconnection; otherwise, abandon this reconnection and proceed to the next reconnection. The specific formula for evaluating the robustness R is as follows:

[0028] ;

[0029] where represents the total number of nodes in the largest connected subgraph of the wireless sensor network after removing n nodes.

[0030] In the above method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, in step S4, three strategies are adopted to optimize the topology of the wireless sensor network, evolving the topology of the wireless sensor network towards an "onion-like" network structure. The characteristics of the "onion-like" network structure are as follows: the high-degree nodes form the core of the onion; the nodes with the same degree are connected to each other and form a ring; the low-degree nodes are located outside the ring, serving as a protective layer to protect the high-degree core nodes.

[0031] The core layer topology enhancement strategy is as follows: traverse the core layer node set, sort based on the degree difference of edges, select two edges with the largest degree difference and the second largest degree difference as candidate edges, then reconnect the two candidate edges, perform degree difference analysis on the results of the two reconnection methods, retain the result that satisfies the constraint conditions and has the smallest degree difference, then calculate its robustness, and if the robustness is improved, accept the reconnection, otherwise retain the original network structure; mark the reconnected edges to prohibit repeated operations in subsequent iterations.

[0032] In the above method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, in step S4, the inter-layer connection optimization strategy is as follows:

[0033] It includes two methods. The first one: core layer - middle layer edge reconnection. Traverse the core layer and the middle layer node sets, and filter the edges that satisfy 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: middle layer - outer layer edge reconnection. Traverse the middle layer and the outer layer node sets, and filter the edges that satisfy the cross-layer connection constraints, that is, one end of the edge is a middle layer node and the other end is an outer layer node. In both methods, two edges with the largest edge degree difference and the second largest edge degree difference are respectively selected as candidate edges, the selected edges are reconnected, perform degree difference analysis on the results of the two reconnection methods, retain the result that satisfies the constraint conditions and has the smallest degree difference, then calculate its robustness, and if the robustness is improved, accept the reconnection, otherwise retain the original network structure; mark the reconnected edges to prohibit repeated operations in subsequent iterations.

[0034] In the above method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, in step S4, the outer layer structure reorganization strategy is as follows:

[0035] Traverse the set of peripheral layer nodes, sort based on the degree difference of edges, select two edges with the largest and the second largest edge degree differences as candidate edges, then reconnect the two candidate edges, perform degree difference analysis on the results after the two reconnection methods, retain the result that meets the constraint conditions 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 to prevent repeated operations in subsequent iterations.

[0036] In the above method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, in step S5, the moving average method is used to determine whether the global edge reconnection has fallen into a local solution. A local optimal solution refers to the optimization process converging to a sub-optimal state at a certain stage. The formula is as follows:

[0037] ;

[0038] where represents the number of iterations of the current algorithm, that is, the number of times of edge reconnection; represents the th iteration of the robustness index of the current wireless sensor network; represents the size of the calculation window, that is, calculate the average value of the robustness of the wireless sensor network in the recent iterations; represents the moving average value of the th iteration, reflecting the trend within the window;

[0039] ;

[0040] represents the change amount of adjacent moving average values; represents the set threshold, is the convergence factor. When is continuously times less than the set threshold, it means that the global edge reconnection optimization has stalled.

[0041] The beneficial effects of the present invention are as follows: First, according to the importance of nodes in the wireless sensor network, the nodes in the network are divided into three layers: the core layer, the intermediate layer, and the peripheral layer. Then, the edges of the node set within the communication range are reconnected. Next, a convergence state monitoring mechanism based on the moving average method is established. When it is detected that the random edge reconnection process is 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 starting from the characteristics of the "onion-like" network structure. Through the hierarchical topology reconstruction mechanism, it effectively breaks through the local convergence limitation of the traditional random edge reconnection algorithm. Without changing the network degree distribution, it drives the network topology to evolve towards the "onion-like" structure with high robustness characteristics. The present invention shows non-sensitivity to the network scale, that is, when dealing with wireless sensor networks of different scales, the improvement of its network robustness is relatively stable compared with other algorithms. Brief Description of the Drawings

[0042] Figure 1 It is the overall flowchart provided by the present invention.

[0043] Figure 2 It is the schematic diagram of edge reconnection of the present invention.

[0044] Figure 3 is the regulatory factor It is the schematic diagram of the influence on the effect of the present invention.

[0045] Figure 4 It is the curve graph of the change in robustness of the initial wireless sensor network under three types of attacks.

[0046] Figure 5 It is the curve graph of the change in robustness of the improved wireless sensor network under three types of attacks.

[0047] Figure 6 It is the comparison graph of the improvement in robustness under malicious attacks between the method of the present invention and the existing method.

[0048] Figure 7 is the convergence factor It is the schematic diagram of the influence of the value on the network robustness and the number of iterations. Detailed Embodiment

[0049] The present invention will be further described below in conjunction with the drawings and embodiments.

[0050] As Figure 1 shown, a method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction includes the following steps:

[0051] S1, Topology Structure Initialization: Based on the initial topology structure of the wireless sensor network, obtain the location information of all nodes and their corresponding neighbor node lists.

[0052] S2, Node Layering: According to the obtained node information, calculate the importance of each node in the wireless sensor network, and divide the nodes into three layers based on the importance level, namely the core layer, the middle layer, and the peripheral layer.

[0053] Calculating the importance of each node in the wireless sensor network is achieved by calculating three metrics for each node. The three metrics include degree centrality, betweenness centrality, and closeness centrality. Degree centrality is defined as the number of direct connections of a node, which intuitively reflects the influence of the node within a local range. The formula for degree centrality is as follows:

[0054] ;

[0055] In the formula: 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.

[0056] Betweenness centrality is defined as the frequency with which a node lies on the shortest path between other nodes in the wireless sensor network, and is used to identify the nodes that play a key bridging role in the wireless sensor network. The formula for betweenness centrality is as follows:

[0057] ;

[0058] In the formula: 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.

[0059] Closeness centrality is defined as the reciprocal 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 formula for closeness centrality is as follows:

[0060] ;

[0061] In the formula: represents the closeness centrality of node i; represents the distance from node i to node j.

[0062] By combining the use of these three metrics, it is possible to comprehensively evaluate the importance of nodes from multiple dimensions such as local influence, bridging effect, and global centrality, thereby providing more comprehensive and accurate results for network layering.

[0063] The K-means clustering algorithm is adopted, using the degree centrality, betweenness centrality, and closeness centrality of nodes as feature metrics to perform clustering analysis on the nodes of the wireless sensor network; the number of clusters K is set to 3, and the initial centroids are selected using the max-min method, and through iterative calculation until the sum of squared errors within the clusters converges. Finally, the nodes of the wireless sensor network are divided into three layers: the core layer, the intermediate layer, and the peripheral layer. In this way, the optimal layering boundary can be automatically determined, while ensuring that the nodes within the layer have high similarity, and the nodes between layers maintain significant differences, thus realizing the scientific layering of the network structure.

[0064] S3. Edge reconnection evaluation: Select a set of nodes within the communication range from the wireless sensor network for edge reconnection, evaluate the impact on the robustness of the wireless sensor network after reconnection, and decide whether to accept the reconnection operation according to the evaluation results.

[0065] The specific steps of the step S3 are as follows:

[0066] S31. Conditions for the edges to be reconnected: Randomly select an edge from the wireless sensor network during each reconnection process, and then traverse all the edges within the communication distance of the nodes to select the edge to be reconnected with the selected edge; there are no additional connections between the selected edges to be reconnected, that is, the reconnected edges are independent of each other; the four end nodes of the reconnected edges are within the same communication range, that is, they can communicate with each other, which is the basis for reconnection.

[0067] S32. Set two reconnection strategies: Assume that two edges are selected. One reconnection strategy is to connect the head nodes of the two edges with the head nodes and the tail nodes with the tail nodes, and the other reconnection strategy is to cross-connect the head node of one edge with the tail node of the other edge, so that the degree of each node in the wireless sensor network does not change.

[0068] 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 evolve the initial wireless sensor network structure towards the "onion-like" network structure, and the characteristic of the "onion-like" network structure is that nodes with similar degree values are connected to each other. For such a characteristic, a regulation factor is set to measure the advantages and disadvantages of the two reconnection strategies, that is, to perform degree difference analysis. The specific formula for degree difference analysis is as follows:

[0069] ;

[0070] Among them, ranges from 0.1 to 1, , , , are the degree values of nodes i, j, k, and l respectively. The numerator represents the maximum degree difference of the newly connected edges after the exchange; the denominator represents the maximum degree difference of the original connections; the whole ratio represents the relative size of the maximum degree difference of the new connections relative to the original connections, and the whole ratio must be less than ; By comparing the influence of different on the network robustness, it is obtained that the network robustness is the largest when is equal to 0.9. Therefore, the value of is set to 0.9. By comparing the relative degree differences of the new connections and the original connections, a dimensionless measurement method is provided to evaluate and compare different rewiring strategies. By adopting the above formula, the computational complexity can be effectively reduced, and it is not necessary to calculate the network robustness after each edge rewiring. It can quickly evaluate the advantages and disadvantages of the two rewiring strategies, reduce the computational overhead, and select the edge rewiring strategy with the best rewiring effect. If the rewiring strategy does not meet the formula conditions, the rewiring operation is not performed, thereby optimizing the computational efficiency;

[0071] S33, make the final decision: In step S32, by analyzing the wireless sensor network structure, an edge rewiring strategy beneficial to the evolution of the network into an "onion-like" structure is selected. However, the final decision still needs to be made based on the robustness of the wireless sensor network after rewiring. If the robustness of the wireless sensor network after rewiring is improved, this rewiring is accepted; otherwise, this rewiring is abandoned and the next rewiring is carried out. The specific formula for evaluating the robustness R is as follows:

[0072] ;

[0073] where represents the total number of nodes in the largest connected subgraph of the wireless sensor network after removing n nodes. This formula quantifies the network robustness of the wireless sensor network under malicious attacks against degree (that is, deleting the node with the largest degree in the wireless sensor network and its connected edges each time), and is used as an evaluation of the robustness.

[0074] S4, topology optimization: Establish a convergence state monitoring mechanism based on the moving average method. When it is detected that the random edge rewiring process is in a stagnant state, start a multi-strategy collaborative optimization mechanism, including a core layer topology enhancement strategy, an inter-layer connection optimization strategy, and a peripheral layer structure reorganization strategy.

[0075] In step S4, to solve the problem that the global edge reconnection strategy is prone to falling into local solutions, when its optimization process stalls, three strategies are adopted to optimize the topology of the wireless sensor network, evolving the topology of the wireless sensor network towards an "onion-like" network structure and increasing the robustness of the wireless sensor network. The characteristics of the "onion-like" network structure are as follows: the high-degree nodes form the core of the onion; the nodes with the same degree are connected to each other and form a ring; the low-degree nodes are located outside the ring and serve as a protective layer to protect the high-degree core nodes.

[0076] 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, perform degree difference analysis on the results of the two reconnection methods, retain the result that meets the constraint conditions 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 to prevent 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, enabling the high-degree nodes to form a tightly interconnected core subgraph, which conforms to the characteristic of the "onion-like" network that "the high-degree nodes form the core of the onion", providing a robust central foundation for the wireless sensor network.

[0077] The inter-layer connection optimization strategy includes two methods. The first method is the core layer - middle layer edge reconnection. Traverse the core layer and middle layer node sets, and filter 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 method is the middle layer - outer layer edge reconnection. Traverse the middle layer and outer layer node sets, and filter 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 an outer layer node. In both methods, select the two edges with the largest edge degree difference and the second largest edge degree difference as candidate edges, reconnect the selected edges, perform degree difference analysis on the results of the two reconnection methods, retain the result that meets the constraint conditions 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 to prevent repeated operations in subsequent iterations and ensure the coverage efficiency of the search space. The inter-layer connection optimization strategy optimizes the connection between the core layer and the middle layer, strengthens the hierarchical structure of the wireless sensor network, ensures that the middle layer effectively connects the core and the periphery, conforms to the characteristic of the "onion-like" network that "the nodes with the same degree are connected to each other and form a ring", and promotes the formation of a hierarchical ring topology.

[0078] The strategy for restructuring the outer layer structure is as follows: traverse the set of outer layer nodes, sort them based on the degree difference of edges, select two edges with the largest and the second largest edge degree differences as candidate edges, then reconnect the two candidate edges, conduct a degree difference analysis on the results of the two reconnection methods, retain the result that meets the constraint conditions 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 to prevent repeated operations in subsequent iterations and ensure the coverage efficiency of the search space. By restructuring the outer layer structure, the strategy for restructuring the outer layer structure forms a sparse protective layer composed of low-degree nodes, enhancing the robustness of the wireless sensor network, which conforms to the characteristics of the onion-shaped network that "low-degree nodes are located outside the ring and serve as a protective layer to protect high-degree core nodes", providing an effective external barrier for the core.

[0079] 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.

[0080] The common goal of the core layer topology enhancement strategy, the inter-layer connection optimization strategy, and the outer layer structure restructuring strategy is to avoid the optimization process falling into a local optimal solution (i.e., a local solution), thus breaking through the bottleneck of improving network robustness. To achieve this goal, the moving average method is used to determine whether the global edge reconnection has fallen into a local solution. A local optimal solution refers to the optimization process converging to a sub-optimal state at a certain stage, and the formula is as follows:

[0081] ;

[0082] where represents the number of iterations of the current algorithm, that is, the number of edge reconnections; represents the th iteration of the robustness index of the current wireless sensor network; represents the size of the calculation window, that is, calculate the average value of the robustness of the wireless sensor network in the recent iterations; represents the moving average value of the th iteration, reflecting the trend within the window;

[0083] ;

[0084] represents the change amount of adjacent moving average values; represents the set threshold, is the convergence factor. When consecutive 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 evolve the network towards an "onion-like" topology, but the improvement in robustness will weaken with iteration. Therefore, the objective function of the present invention is defined as robustness. In the optimization algorithm, the relative change rate of the objective function is often used as a convergence criterion. According to Figure 7 the results, the optimal value of the convergence factor is determined to be 0.0001. This value can not only ensure the optimization accuracy of the robustness index, but also take into account the computational efficiency of the algorithm, avoiding the risks of over-iteration or premature convergence.

[0085] Detecting whether the edge reconnection optimization has stagnated by using the moving average method has the following advantages: Smoothness: The moving average method effectively reduces the influence of random interference on the judgment of the optimization trend 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: By detecting the stagnation state of the robustness index trend, the moving average method can accurately judge whether the optimization process has reached a local solution, improving 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.

[0086] Table 1 shows the values of the parameters involved in the moving average method;

[0087]

[0088] To verify the effect of the control algorithm for enhancing the robustness of wireless sensor networks proposed by the present invention through the edge reconnection mechanism, a BA (Barabási-Albert) network model is used to generate a network, where m = 3, and m represents the number of m edges added when a new node joins and connects to the nodes within the communication range; the network range is 500m × 500m, and the node communication radius is 200m. To be closer to the actual situation, the maximum degree of nodes is limited to 30, and it is ensured that 50% of the nodes are within their respective communication ranges.

[0089] Figure 2 shows the initial BA network ( Figure 2 the left figure in Figure 2 ), and the improved network structure obtained by optimizing through the algorithm of the present invention (

[0090] the right figure in Figure 2It can be seen that the "onion-like" network structure has the following characteristics: Nodes with a larger degree (higher-order nodes) tend to be highly interconnected, forming the core of the network; there is also a certain degree of interconnection between nodes with similar degrees, constituting the intermediate layer; while nodes with a lower degree are distributed in the outer layer, presenting a peripheral structure. This structure is similar to the layered wrapping form of an onion: the core is composed of higher-order nodes, and the outer layer is gradually wrapped by lower-degree nodes, showing obvious hierarchy and symmetry as a whole.

[0091] This "onion-like" network structure significantly improves the robustness of the network, enabling it to effectively resist various types of attacks, including random attacks, malicious attacks, and destructive attacks. The improvement in network robustness stems from the interconnection of higher-order nodes and the hierarchical protection mechanism, and these characteristics jointly ensure the connectivity and stability of the network under attacks.

[0092] Figure 3 shows a curve of the network robustness R with respect to changing, where the abscissa represents the size, with a value range from 0.1 to 1; the ordinate represents the quantified value of the network robustness. Curve analysis shows that when increases from 0.1 to 0.9, the network robustness shows a continuous increasing trend with the increase of ; however, when reaches 1, the network robustness decreases instead. Therefore, the network robustness reaches the maximum value when = 0.9, indicating that the optimal parameter value is = 0.9.

[0093] is used to regulate the constraint strength of edge rewiring. When takes a larger value, the constraint conditions for edge rewiring are relatively loose, allowing more edge rewiring operations to be executed; when takes a smaller value, the constraint conditions for edge rewiring tend to be strict, and the exchange operation is only allowed when the degree difference of the newly created connection is significantly smaller than that of the original connection. By analyzing the change trend of the network robustness with respect to , the optimal value of can be determined, so as to achieve a balance between the convergence speed and optimization performance of the algorithm.

[0094] To quantify the improvement effect of the optimization algorithm on the network robustness, three types of attacks are respectively imposed on the initial BA network and the improved network, and the evaluation is carried out by analyzing the change of the ratio of the size of the largest connected subgraph (that is, the proportion of the number of nodes in the largest connected subgraph to the total number of nodes). The three types of attack methods are defined as follows:

[0095] Random attack: In each attack, a node is randomly selected from the network, and the node and all its connecting edges are deleted. Malicious attack: In each attack, the node with the highest degree in the current network and all its connecting edges are deleted, and the degrees of the nodes in the network are updated before each attack to ensure that the node with the highest current degree is always targeted. Destructive attack: In each attack, a node is randomly selected, and the node, all the nodes connected to it, and the relevant connecting edges are deleted. Since the deleted node is randomly selected each time, the scope of the attack is uncertain.

[0096] By comparing the change in the ratio of the size of the largest connected subgraph of 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 visually verified.

[0097] Figure 4 It shows the change trend of the size of the largest connected subgraph of the initial network with 100 nodes under three attack modes (random attack, malicious attack, and destructive attack). The data is from the average value of multiple experiments. The abscissa represents the number of attacks, that is, the number of nodes removed from the initial BA network; the ordinate represents the ratio of the largest connected subgraph of the network after the attack, which is used as a quantitative index of the network robustness. The higher the value, the better the retention degree of the network connectivity, and thus the higher the network robustness.

[0098] Figure 4 It shows that as the number of attacks increases, the ratio of the largest connected subgraph shows a gradually decreasing trend under 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), random attack (96 times). It can be seen from this that the robustness of the initial BA network to different attack modes from high to low is: random attack > malicious attack > destructive attack.

[0099] This difference in robustness stems from the topological structure characteristics of the BA network. The node degree distribution of the BA network follows the power-law characteristic, showing that a small number of nodes (i.e., hub nodes) have significantly higher degree values, while most node degree values are low. In the random attack, nodes are removed with equal probability, and the probability of attacking hub nodes is low, so the overall connectivity of the network is maintained for a longer time, thus showing higher robustness. However, in the malicious attack and destructive attack, the attacker preferentially removes the hub nodes with the highest degree values. Since the connectivity of the BA network highly depends on these hub nodes, once they are removed, the network structure quickly splits, resulting in a sharp drop in the size of the largest connected subgraph. Therefore, the initial BA network has low robustness to malicious attacks and destructive attacks.

[0100] Figure 5Shows the change trend of the size of the largest connected subgraph of the improved network with 100 nodes optimized by the algorithm of the present invention under three attack modes (random attack, malicious attack, and destructive attack). The data is from the average value of multiple experiments. The abscissa represents the number of attacks, that is, the number of nodes removed in the improved network; the ordinate represents the ratio of the largest connected subgraph of the network after the attack, which is used as a quantitative index of network robustness. The higher the value, the better the retention degree of the network connectivity, and thus the higher the network robustness.

[0101] Figure 5 Analysis shows that as the number of attacks increases, the ratio of the largest connected subgraph shows a gradually decreasing trend under the 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 from this that the robustness of the improved network to different attack modes from high to low is: random attack > malicious attack > destructive attack.

[0102] Compare Figure 5 with Figure 4 (the robustness performance of the initial BA network), it can be known that the complete disconnection critical points of the initial BA network under the same attack modes are: destructive attack (24 times), malicious attack (43 times), and random attack (96 times). The complete disconnection critical points of the improved network under the 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 attack, and its robustness under destructive attack and malicious attack is better than that of the initial BA network.

[0103] Table 2 shows the effect comparison between the method of the present invention and the existing methods in improving the robustness of the initial BA network. It can be seen from the data in Table 2 that the method of the present invention performs better than the existing optimization algorithms in improving network robustness. At the same time, the variance of the robustness improvement 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;

[0104]

[0105] Figure 6 Shows the change of the robustness of the wireless sensor network under different network scales (100, 200, 300 nodes) of the algorithm proposed by the present invention and the existing algorithms, namely HC (hill climbing algorithm), SA (simulated annealing algorithm), GA (genetic algorithm), AEDE (adaptive evolutionary algorithm), aiming to verify the superiority of the algorithm of the present invention in improving network robustness.

[0106] Combined with the analysis of Table 2 and Figure 6It can be seen that when the network scales are 100, 200, and 300 nodes respectively, the robustness of the present invention always remains at the highest level, significantly superior to other algorithms. According to the ranking of the robustness improvement effects 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 amplitude is 5.62%; when it is 200 nodes, the improvement amplitude increases to 6.76%; when it is 300 nodes, it increases to 6.32%.

[0107] In addition, combined with the data in Table 2 and Figure 6 it can be known that the robustness improvement effects of the existing algorithms (HC, SA, GA, AEDE) show a gradually decreasing trend with the increase of the 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 the network scale, showing non-sensitivity to the network scale.

[0108] As Figure 7 shown,[[]]END]] Figure 7 shows the influence of the convergence factor with different values on the robustness of the network under malicious attacks and the number of iterations. The data is from the average value of multiple experiments. It can be obtained from Figure 7 that as the value of the convergence factor decreases, both the robustness R of the network under malicious attacks and the number of iterations increase. When the value of the convergence factor is 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 0.0001 in the present invention, it can be obtained that the robustness at these two values is very close. In order to improve the running efficiency of the code, the value of the convergence factor is set to 0.0001, so that without affecting the accuracy of the robustness R, the running time of the code can be reduced.

[0109] In summary, the algorithm proposed by the present invention has significant advantages in improving the robustness of wireless sensor networks, is superior to existing algorithms under all network scales, reduces the sensitivity to network scale, and its performance improvement effect is more competitive with the increase of network scale, ensuring a stable optimization effect in large-scale networks.

Claims

1. A method for improving the robustness of a wireless sensor network with hierarchical topology reconstruction, characterized in that It 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; S2, Node layering: According to the obtained node information, calculate the importance of each node in the wireless sensor network, and divide the nodes into three layers according to the degree of importance, namely the core layer, the intermediate 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 on the robustness of the wireless sensor network after reconnection, and decide whether to accept the reconnection operation according to the evaluation results; The specific steps of step S3 are as follows: S31, Conditions for the edges to be reconnected: Randomly select an edge from the wireless sensor network during each reconnection process, and then traverse all the edges within the node communication distance to select the edge to be reconnected with the selected edge; there is no additional connection between the selected edges to be reconnected, that is, the reconnected edges are independent of each other; the four end nodes of the reconnected edges are within the same communication range, that is, they can communicate with each other, which is the basis for reconnection; S32, Set two reconnection strategies: Assume that two edges are selected. One reconnection strategy is to connect the head nodes of the two edges and the tail nodes of the two edges, and the other reconnection strategy is to cross-connect the head node of one edge with the tail node of the other edge, so that the degree of each node in the wireless sensor network does not change; S33, Make a final decision: If the robustness of the wireless sensor network is improved after reconnection, accept this reconnection; otherwise, abandon this reconnection and proceed to the next reconnection; S4, Topology optimization: Establish a convergence state monitoring mechanism based on the moving average method. When it is detected that the random edge reconnection process is in a stagnant state, start a 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; In step S4, three strategies are used to optimize the topology of the wireless sensor network, so that the topology of the wireless sensor network evolves into an "onion-like" network structure. The characteristics of the "onion-like" network structure are: the high-degree nodes form the core of the onion; the nodes with the same degree are connected to each other and form a ring; the low-degree nodes are located outside the ring as a protective layer to protect the high-core nodes; The core layer topology enhancement strategy is: Traverse the core layer node set, sort based on the degree difference of the edges, select two edges with the largest degree difference and the second largest degree difference as candidate edges, then reconnect the two candidate edges, perform degree difference analysis on the results after the two reconnection methods, retain the result that meets the constraint conditions 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 to prevent repeated operations in subsequent iterations; 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 is achieved.

2. The method for enhancing the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 1, wherein: In step S2, calculating the importance of each node in the wireless sensor network is achieved by calculating three metrics for each node. The three metrics include degree centrality, betweenness centrality, and closeness centrality. Degree centrality is defined as the number of direct connections of a node, intuitively reflecting the influence of the node within a local range. The formula for calculating degree centrality is as follows: Where: DC i represents the degree centrality of node i; k i is the number of connections of node i, that is, the number of neighbor nodes of node i; N 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, characterized in that: In step S2, betweenness centrality is defined as the frequency with which a node lies on the shortest path between other nodes in the wireless sensor network, and is used to identify the nodes that play a key bridging role in the wireless sensor network. The formula for calculating betweenness centrality is as follows: Where: BC i represents the betweenness centrality of node i; represents the number of the shortest paths connecting node s and node t and passing through node i; g st represents the number of the 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, wherein: In step S2, closeness centrality is defined as the reciprocal 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 formula for calculating closeness centrality is as follows: Where: CC i represents the closeness centrality of node i; d ij Indicates the distance from node i to node j.

5. The method for enhancing the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 2, characterized in that: In step S2, the K-means clustering algorithm is adopted, using the degree centrality, betweenness centrality, and closeness centrality of the nodes as feature metrics to perform clustering analysis on the nodes of the wireless sensor network; the number of clusters K is set, and the initial centroids are selected using the max-min method, and through iterative calculation until the sum of squared errors within the clusters converges. Finally, the nodes of the wireless sensor network are divided into three layers: the core layer, the intermediate layer, and the peripheral layer.

6. The method for enhancing the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 2, characterized in that: In step S32, a regulation factor α is set to measure the advantages and disadvantages of the two rewiring strategies, that is, degree difference analysis is performed. The specific formula for degree difference analysis is as follows: Among them, the range of α is 0.1 - 1, d i and d j and d k and d l are the degree values of nodes i, j, k, and l respectively. The numerator max(|d i - d k |, |d j - d l |) represents the maximum degree difference of the newly connected edges after the exchange; the denominator max(|d i - d j |, |d k - d l |) represents the maximum degree difference of the original connected edges; the whole ratio represents the relative size of the maximum degree difference of the newly connected edges relative to the original connected edges, and the whole ratio must be less than α; if the reconnecting strategy does not meet the formula conditions, the reconnecting operation is not performed; In step S33, the specific formula for evaluating the robustness R is as follows: Where MCS n represents the total number of nodes in the largest connected subgraph of the wireless sensor network after removing n nodes.

7. The method for enhancing 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 as follows: It includes two methods. The first one: core layer - intermediate layer edge rewiring. Traverse the node sets of the core layer and the intermediate layer, and filter 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 an intermediate layer node. The second one: intermediate layer - peripheral layer edge rewiring. Traverse the node sets of the intermediate layer and the peripheral layer, and filter the edges that meet the cross-layer connection constraints, that is, one end of the edge is an intermediate layer node and the other end is a peripheral layer node. In both methods, two edges with the largest and the second largest edge degree differences are respectively selected as candidate edges, the selected edges are rewired, degree difference analysis is performed on the results after the two rewiring methods, and the result that meets the constraint conditions and has the smallest degree difference is retained. Then its robustness is calculated. If the robustness is improved, the rewiring is accepted; otherwise, the original network structure is retained. The rewired edges are marked to 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 peripheral layer structure reorganization strategy is as follows: Traverse the peripheral layer node set, sort based on the edge degree differences, select two edges with the largest and the second largest edge degree differences as candidate edges, then rewire the two candidate edges, perform degree difference analysis on the results after the two rewiring methods, retain the result that meets the constraint conditions and has the smallest degree difference, then calculate its robustness. If the robustness is improved, the rewiring is accepted; otherwise, the original network structure is retained. The rewired edges are marked to prohibit repeated operations in subsequent iterations.

9. The method for enhancing the robustness of a wireless sensor network with hierarchical topology reconstruction according to claim 1, characterized in that: In the step S5, the moving average method is used to determine whether the global edge reconnection has fallen into a local solution. A local optimal solution refers to the situation where the optimization process converges to a sub-optimal state at a certain stage. The formula is as follows: where a represents the number of iterations of the current algorithm, that is, the number of times of edge reconnection; R i′ represents the robustness index of the current wireless sensor network at the i'-th iteration; w represents the size of the calculation window, that is, the average value of the robustness of the wireless sensor network calculated for the last w iterations; MA a represents the moving average at the a-th iteration, reflecting the trend within the window; ΔMA a = |MA a - MA a-1 | ≤ τ ΔMA a represents the change in the adjacent moving average; τ = β × MA a represents the set threshold value, β is the convergence factor, when ΔMA a is less than the set threshold value for k' consecutive times, it indicates that the global edge reconnection optimization has stalled.

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