Heterogeneous internet of things topology key node identification method combined with mutation theory

Abstract

The application discloses a method for identifying key nodes of a heterogeneous Internet of Things (IoT) topology based on mutation theory, and belongs to the field of computers and information. First, an initial topology of the heterogeneous IoT is constructed, a topology set is generated by random disturbance, and performance indexes such as robustness, redundancy, communication efficiency and global clustering coefficient are calculated. Then, the indexes are normalized by using a mutation series method, the correlation between the indexes is evaluated based on a Pearson correlation coefficient, and a network performance mutation value is obtained by layer-by-layer fusion. Next, a deliberate attack process is simulated, a corresponding relationship between a node deletion sequence and performance evolution is established, and a performance evolution function is fitted. Finally, a cusp mutation model is established, critical nodes causing network performance mutation are identified by analyzing the equilibrium state, singular set and bifurcation set of the model, and the application breaks through the limitations of traditional static network indexes, can accurately capture the mutation behavior of network performance, is objective, and provides a theoretical basis for topology optimization and fault-tolerant design of the IoT.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer and information technology, in particular to a method for identifying key nodes in a topological network. BACKGROUND

[0002] The Internet of Things (IoT) is a network system that connects various physical devices, sensors, and terminals through the Internet, aiming to achieve data collection, exchange, and intelligent management. With the rapid development of 6G technology, IoT applications have been widely developed. Network topology (or "IoT topology") refers to the connection and communication relationship between nodes in the IoT network. Due to its complexity and heterogeneity, the failure of any node can trigger a chain reaction, significantly affecting network stability. The reasons for node failure can be various, such as hardware failure, malicious attack, or environmental change, especially when a key node fails, which can cause a sharp decline in network performance or even system collapse. How to efficiently identify key nodes in a heterogeneous IoT topology has become a key scientific problem that needs to be solved.

[0003] In the IoT topology, the definition of a key node is often based on the importance of the node in the network. Traditional network topology analysis methods, such as degree centrality, betweenness centrality, and closeness centrality, can identify nodes with many connections and large traffic, but have obvious limitations. Most of these methods are based on the static structure of the network and do not fully consider the evolution process of the network when it faces dynamic attacks or disturbances. When the network is attacked or disturbed externally, its performance decline is not linear, but suddenly collapses in an "avalanche" after a certain critical point. This behavior indicates that not all nodes in the network are equivalent, and the failure of some nodes may lead to the collapse of the entire network, while the failure of other nodes may only cause local impact. This sudden phenomenon is difficult to capture and predict by traditional static network indicators, so new theories must be introduced to describe this evolution process.

[0004] Catastrophe theory is an important branch of nonlinear science that mainly studies the catastrophic behavior and structural changes of a system under certain conditions. The core idea of this theory is that a system under certain control parameters will enter an unstable "catastrophic set" region, where the state of the system may suddenly change. In the IoT topology, the failure of a key node often does not gradually affect network performance, but suddenly triggers a large-scale collapse of the network, which is highly consistent with the catastrophic behavior in catastrophe theory. By using catastrophe theory, we can study the critical behavior of the IoT topology and identify the key nodes that may cause system collapse. The introduction of catastrophe theory enables us to better understand the dynamic evolution process of the IoT topology and provides theoretical support for designing more robust network topologies. SUMMARY

[0005] To solve the above problems, the application discloses a heterogeneous Internet of Things topology key node identification method combined with mutation theory.

[0006] The specific technical scheme is as follows:

[0007] The heterogeneous Internet of Things topology key node identification method combined with mutation theory comprises the following steps:

[0008] Step 1, network topology construction: a plurality of sensor nodes are randomly deployed in a set area, and nodes are randomly connected to construct an initial network topology T;

[0009] Step 2, performance index calculation and perturbation analysis: a plurality of indexes closely related to the performance of the Internet of Things network are selected, the initial network topology T is randomly disturbed to form a network topology perturbation set A, and the performance index value of each network topology in the set A is calculated;

[0010] Step 3, index normalization and correlation evaluation: the performance index values obtained in step 2 are normalized to convert the original values into mutation orders in the interval [0, 1]; then, the degree of correlation between each performance index is evaluated using the Pearson correlation coefficient method;

[0011] Step 4, network performance mutation value calculation: according to the correlation degree between the indexes obtained in step 3, the complementary index average value and the non-complementary index minimum value are used as the criteria to gradually fuse each performance index, and finally a comprehensive network performance mutation value x is calculated;

[0012] Step 5, simulation attack and mutation value calculation: the nodes in the initial network topology T are sorted from high to low according to their degree centrality; the nodes are deleted one by one to simulate deliberate attacks, a new network topology Ti is formed after each node is deleted, and steps 2 to 4 are repeated for each Ti to calculate the corresponding network performance mutation value xi;

[0013] Step 6, performance function fitting: the correspondence between the node deletion order or time ti and the network performance mutation value xi is established, and a performance evolution function x(t) with time as the independent variable and network performance as the dependent variable is obtained by function fitting method;

[0014] Step 7, cusp mutation model establishment: a cusp mutation model for describing the performance of the network topology is constructed, and the potential function is defined as , wherein x is the network performance, a and b are control variables, and the model satisfies ;

[0015] Step 8, model critical behavior analysis: the equilibrium surface and singular point set of the cusp mutation model are calculated to determine the critical condition leading to the mutation of the network performance;

[0016] Step 9, model parameter association: substituting the performance evolution function x(t) obtained in step 6 into the cusp catastrophe model in step 7, deducing the constraint equation required to be satisfied by the control variables a and b at different times t;

[0017] Step 10, catastrophe phenomenon detection: within the set value range of the control variable a, solving the corresponding control variable b according to the constraint equation obtained in step 9, and checking whether the parameters (a, b) satisfy the bifurcation set equation of the cusp catastrophe model; if yes, it is determined that a performance catastrophe occurs at the time point;

[0018] Step 11, key node identification: according to the detection result of step 10, the node inducing network performance catastrophe is identified as the key node in the heterogeneous Internet of Things topology.

[0019] The set region in step 1 is a 500m × 500m square region, and the number of deployed sensor nodes is 300.

[0020] The index closely related to the network performance in step 2 includes robustness R index, redundancy, communication efficiency and global clustering coefficient.

[0021] The normalization process in step 3 is specifically:

[0022] For the performance index positively correlated with network performance, the following first membership function is used for normalization:

[0023]

[0024] For the performance index negatively correlated with network performance, the following second membership function is used for normalization:

[0025]

[0026] Where x' represents the original calculated value of the performance index, and respectively represent the minimum value and the maximum value of all values of the performance index in the network topology disturbance set A, and X represents the mutation degree obtained after normalization.

[0027] When using the Pearson correlation coefficient method to evaluate the correlation degree in step 3, the absolute correlation coefficient |r| ≥ 0.5 is set as high correlation, and |r| < 0.5 is set as no correlation.

[0028] The specific process of step 4 is to fuse each performance index layer by layer:

[0029] First, the correlation between the robustness R index and the communication efficiency is evaluated, if highly correlated, the arithmetic mean of the two is calculated, if not correlated, the minimum value of the two is taken, and the result is recorded as the intermediate variable y;

[0030] Then, the correlation between the redundancy and the global clustering coefficient is evaluated, if highly correlated, the arithmetic mean of the two is calculated, if not correlated, the minimum value of the two is taken, and the result is recorded as the intermediate variable z;

[0031] Finally, the correlation between the intermediate variables y and z is evaluated, if highly correlated, the arithmetic mean of y and z is calculated, if not correlated, the minimum value of y and z is taken, and the final result is taken as the network performance mutation value x.

[0032] The equilibrium curve in step 8 is determined by the equation The singular point set is determined by the equation .

[0033] The bifurcation set equation in step 10 is .

[0034] The setting value range of the control variable a in step 10 is [-5, 5].

[0035] The advantages of the present application are: the present application breaks the limitations of traditional static network analysis methods by deeply integrating mutation theory and mutation series method, and the technical effect is that the mutation behavior of heterogeneous Internet of Things when suffering from attack can be accurately captured and quantified, so as to identify the key nodes that may really cause systemic failure; the method adopts a multi-index fusion mechanism, which significantly improves the objectivity and comprehensiveness of the evaluation results, and provides a new type of practical solution for building a highly robust Internet of Things topology. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The flowchart of the heterogeneous Internet of Things topology key node identification method combined with mutation theory in the embodiments of the present application is shown;

[0037] Figure 2 The evolution behavior diagram of the cusp mutation model is shown. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0039] The specific mode, structure and action of a key node identification method of an isomer Internet of Things topology combining mutation theory designed according to the present application are described in detail below with reference to the accompanying drawings.

[0040] Step 1: 300 sensor nodes are randomly deployed in a 500*500 region, the number of edges connected to each node is determined, random connection is performed, the connection relationship of these nodes and edges is stored as an adjacency matrix or graph representation, and an initial network topology is constructed .

[0041] Step 2: Select indicators closely related to the performance of the Internet of Things network, including the robustness R indicator of the network, redundancy, communication efficiency and global clustering coefficient, and the calculation formulas of the indicators are as follows:

[0042] (2)

[0043] (3)

[0044] (4)

[0045] (5)

[0046] In formula (2), the is the number of triangles formed by three nodes connected in the network, represents a path including three nodes in the network, which is not necessarily completely connected, i.e. a combination of one node connected to another two nodes through edges. In formula (3), the represents the shortest path length from node p to node q. In formula (4), the symbol is the total number of nodes, represents the number of rounds of node removal, is the number of nodes in the largest connected subgraph of the network after the attack. In formula (5), the is the number of edges in the network topology, is the number of nodes. Then, random disturbance is performed on the initial network topology, edges are randomly exchanged to form a network topology disturbance set , and the robustness R indicator, redundancy, communication efficiency and global clustering coefficient of each network topology in the set are obtained.

[0047] Step 3: Normalize the robustness R index, redundancy, communication efficiency and global clustering coefficient, and convert the original values of each index to the mutation scale of [0, 1] using the membership function method. Since the robustness R index, communication efficiency and global clustering coefficient are positively correlated with network performance, we use formula (6), while the redundancy is negatively correlated with network performance, we use formula (7) for conversion:

[0048] (6)

[0049] (7)

[0050] denotes the index value, denotes the minimum value of the index value, denotes the maximum value of the index value, denotes the converted mutation scale. Then use the Pearson product-moment correlation coefficient to evaluate the correlation degree of each index, the specific formula is as follows:

[0051] (8)

[0052] In formula (8), n is the sample size, are the standardized evaluation index values, are the standardized evaluation index means, is the correlation coefficient, indicates that the two indexes are highly correlated, indicates that the two indexes are not correlated.

[0053] Step 4: If the robustness R index and communication efficiency are complementary related, take the average of the two, if the robustness R index and communication efficiency are not related, take the smaller value, we record the value as , then calculate the value of redundancy and global clustering coefficient according to the same method, then evaluate the correlation of and , according to the correlation degree, get the final network performance mutation value .

[0054] Step 5: Sort the nodes of the initial network topology from high to low according to the degree centrality, then delete the network nodes one by one to simulate the deliberate attack behavior of the network, for each network topology after deleting the network nodes, calculate the robustness R index, redundancy, communication efficiency and global clustering coefficient. Then according to the correlation of each index in step 4, calculate the network performance mutation value of each network topology .

[0055] Step 6: Establish network topology and time The correspondence is then determined by the time the node was deleted. As an independent variable, the mutation value of network performance As the dependent variable, a function fitting method is used to model the data. This is achieved by fitting the time of node deletion. With performance mutation value The relationship between the two is used to obtain the performance change curves of the network topology during node removal and the corresponding functions. .

[0056] Step 7: Establish a cusp mutation model for network topology performance. The specific mathematical formula is as follows:

[0057]

[0058] (9)

[0059] Formula (9) Indicates network topology performance. These are two control variables that affect changes in network topology performance.

[0060] Step 8: Using the cusp catastrophe model, obtain the equilibrium state and singular set of the model itself. The equilibrium state refers to the stable or unstable point to which the system state variables tend under given control parameters. These points are potential functions. The critical point is where the first derivative of the potential function with respect to the state variable x is zero:

[0061] (10)

[0062] The singular set of a model describes the critical points or inflection points that the system experiences when transitioning from an equilibrium state to a new state. The singular set is represented by the points where the second derivative of the potential function with respect to the state variable x is zero.

[0063] (11)

[0064] The critical behavior of network topology performance changes is determined by using equilibrium states and singular sets.

[0065] Step 9: For the network performance function fitted in Step 6 The established cusp mutation model needs to be satisfied because... Given the information, the control variables can be determined. The equations that are satisfied for any time We have

[0066] (12)

[0067] Step 10: Analysis of the function equation satisfied by the control variable, using formula (10), (11) can be obtained Equation to be satisfied:

[0068] (13)

[0069] Formula (13) represents the critical state of the cusp catastrophe model. Then at different times , the value of the control variable is fixed, the value range is , through formula (12), the corresponding value is obtained, and then it is checked whether the control variable satisfies the bifurcation set formula (13). If it is satisfied, there is a catastrophe phenomenon.

[0070] Step 11: Since step 6 establishes the correspondence between the network topology and the time , for each node there is a corresponding network topology . In the check of step 10, it is actually a check for each node. For the nodes with catastrophe phenomenon, they are the key nodes.

Claims

1. A method for identifying key nodes in heterogeneous IoT topologies based on catastrophe theory, characterized in that: The method comprises the following steps: Step 1, network topology construction: randomly deploying a plurality of sensor nodes in a set area, and randomly connecting the nodes to construct an initial network topology T; Step 2, performance index calculation and perturbation analysis: selecting a plurality of indexes closely related to the performance of the Internet of Things network, randomly perturbing the initial network topology T to form a network topology perturbation set A, and calculating the performance index value of each network topology in the set A; Step 3, index normalization and correlation evaluation: normalizing each performance index value obtained in step 2 to convert the original value to a mutation degree in the interval [0, 1]; Then, the degree of correlation between each performance index is evaluated using the Pearson correlation coefficient method; Step 4, network performance mutation value calculation: according to the correlation degree between the indexes obtained in step 3, the average value of complementary indexes and the minimum value of non-complementary indexes are taken as the criteria, and each performance index is fused layer by layer to finally calculate a comprehensive network performance mutation value x; Step 5, simulation attack and mutation value calculation: according to the degree centrality, the nodes in the initial network topology T are sorted from high to low; each node is deleted in turn to simulate deliberate attacks, and a new network topology Ti is formed after each node is deleted, and steps 2 to 4 are repeated for each Ti to calculate the corresponding network performance mutation value xi; Step 6, performance function fitting: a corresponding relationship between the node deletion order or time ti and the network performance mutation value xi is established, and a performance function x(t) with time as the independent variable and network performance as the dependent variable is obtained by function fitting method; Step 7, cusp catastrophe model establishment: a cusp catastrophe model for describing the network topology performance is constructed, and a potential function is defined as where x is the network performance, a and b are control variables, and the model satisfies ; Step 8, model critical behavior analysis: the equilibrium surface and singular point set of the cusp catastrophe model are calculated to determine the critical condition leading to network performance mutation; Step 9, model parameter correlation: the performance function x(t) fitted in step 6 is substituted into the cusp catastrophe model in step 7 to derive the constraint equation required to be satisfied by the control variables a and b at different times t; Step 10, mutation phenomenon detection: within the set value range of the control variable a, the corresponding control variable b is solved according to the constraint equation obtained in step 9, and it is verified whether the parameters (a, b) satisfy the bifurcation set equation of the cusp catastrophe model; if yes, it is determined that a performance mutation occurs at this time point; Step 11, key node identification: according to the detection result of step 10, the node inducing network performance mutation is identified as the key node in the heterogeneous Internet of Things topology; The specific process of step 4 is as follows: Firstly, the correlation between the robustness R index and the communication efficiency is evaluated, and if highly correlated, the arithmetic mean of the two is calculated, and if not correlated, the minimum value of the two is taken, and the result is recorded as an intermediate variable y; Then, the correlation between the redundancy and the global clustering coefficient is evaluated, and if highly correlated, the arithmetic mean of the two is calculated, and if not correlated, the minimum value of the two is taken, and the result is recorded as an intermediate variable z; Finally, the correlation between the intermediate variables y and z is evaluated, and if highly correlated, the arithmetic mean of y and z is calculated, and if not correlated, the minimum value of y and z is taken, and the final result is taken as the network performance mutation value x.

2. The method of claim 1, wherein, The region set in step 1 is a square region of 500m*500m, and the number of deployed sensor nodes is 300.

3. The method of claim 1, wherein, The indexes closely related to the performance of the Internet of Things network in step 2 include robustness R index, redundancy, communication efficiency and global clustering coefficient.

4. The method according to claim 1 or 3, characterized in that, The normalization processing in step 3 is specifically: For the performance indexes positively correlated with the network performance, the following first membership function is used for normalization: ； For the performance indexes negatively correlated with the network performance, the following second membership function is used for normalization: ； wherein x' represents the original calculated value of the performance indicator, and respectively represent the minimum and maximum values of the performance indicator in all values in the set A of network topology perturbations, and X represents the normalized mutation scale.

5. The method of claim 1, wherein, When the Pearson correlation coefficient method is used to evaluate the correlation degree in step 3, the absolute correlation coefficient |r|≥0.5 is set as high correlation, and |r|<0.5 is set as no correlation.

6. The method of claim 1, wherein, The equilibrium surface in Step 8 is given by the equation The singular set is determined by the equation The singular set is determined by the equation 7. The method according to claim 1 or 6, characterized in that, The bifurcation set equation described in step 10 is .

8. The method of claim 1, wherein, The set value range of the control variable a in step 10 is [-5, 5].

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