CN109587752B - Wireless sensor network topology construction method based on multiple linear regression model - Google Patents

Abstract

The invention provides a wireless sensor network topology construction method based on a multiple linear regression model, aiming at improving the connectivity and stability of a network by eliminating the limitation on the node degree in the network, and comprising the following steps: initializing a wireless sensor network; acquiring a training data set of a multiple linear regression model through an initialization network, and constructing the multiple linear regression model of the number of non-cluster head nodes in a management area according to the training data set; the cluster head calculates the number of non-cluster head nodes and the average node degree of a management area of the cluster head according to a multiple linear regression model, the cluster head establishes a communication link with the non-cluster head nodes in the management area in a multi-hop mode with the maximum hop count as the average node degree, and finally wireless sensor network topology is formed. The invention calculates the number of non-cluster-head nodes in a cluster head management area through a multiple linear regression model to determine the node degree in the cluster head, and aims to solve the problem of limitation on the node degree and improve the connectivity and stability of a network.

Description

Wireless sensor network topology construction method based on multiple linear regression model

Technical Field

The invention belongs to the technical field of optical communication, relates to a networking technology of a communication network, and particularly relates to a wireless sensor network topology construction method based on a multiple linear regression model, which can be used for a wireless sensor network with limited node degree.

Background

The Wireless Sensor Network (WSN) is a distributed Sensor network, the end of the WSN is a Sensor capable of sensing and checking the outside world, and the sensors in the WSN communicate in a Wireless mode, including Wireless communication technologies such as Wireless laser communication, microwave communication and visible light communication, and the WSN has the advantages of flexible networking, low cost and the like. However, as the nodes in the WSN are not stationary but continuously move, the access degrees of the nodes in the WSN are continuously changed, which inevitably causes the problem of high node degree limitation in the WSN network, and causes the problem of unbalanced isolated nodes and energy in the network, thereby having important influence on the connectivity and stability of the WSN network. In addition, the WSN is easily influenced by the atmospheric channel environment, the connectivity and the stability of the WSN are further influenced, the defects caused by the single link characteristics of the WSN can be made up to the maximum extent by reasonable and effective network topology construction, and the connectivity and the stability of the WSN are improved.

Aiming at the problems of limited WSN communication node degree and the like, the existing solutions mainly comprise the following three types: (1) a physical layer modification method based on a multi-transceiver system; (2) a hybrid network method based on microwave and wireless laser combination; (3) a topology construction and routing method based on hierarchy. Aiming at the method (1), an FSO multi-transceiving system is adopted, the communication coverage of each node is expanded, the node degree is improved, and the influence of an FSO unidirectional link on the networking quality is reduced on a physical layer; according to the method (2), FSO and RF are combined to form a mixed network, the RF is adopted in a small-scale network through hierarchical control, and the FSO is adopted in a network relay.

However, the modification method for the physical layer has high cost and great technical difficulty, and for the hybrid network, the problem is not solved fundamentally because the hybrid network is only the hybrid network, and the problem of node degree limitation still exists. At present, the problem of node degree limitation is mainly solved by adopting a topology construction method. The topology construction and routing method mainly adopts a specific hierarchical network topology structure, the functions of the nodes are determined before the network is established, hierarchical communication is realized by distinguishing common nodes and cluster head nodes, and on the basis, a specific routing algorithm is adopted to discover neighbor nodes and a base station and establish a link. For example, a patent application with publication number CN 106162792 a, entitled "many-to-one data routing method with limited node degree in wireless sensor network" discloses a many-to-one data routing method with limited node degree in wireless sensor network. The nodes in the wireless sensor network are converted into corresponding super virtual nodes, the virtual nodes corresponding to the same wireless sensor node are combined, and the optimal data routing path of each wireless sensor node under the condition of degree limitation is selected. Aiming at the problem of node degree limitation in the wireless sensor network, the invention can select an optimized data routing path under the condition of a potential link. However, the invention considers the optimal routing selection under the condition of potential links to solve the problem of node degree limitation, and does not fundamentally solve the problem of node degree limitation, and if no potential links exist, the invention still has the problem of node degree limitation, further influences the energy balance and link stability of the network, and has negative influence on the connectivity and stability of the network.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a wireless sensor network topology construction method based on a multiple linear regression model, aiming at improving the connectivity and stability of a network by eliminating the limitation on the node degree in the network.

In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:

(1) initializing the wireless sensor network:

(1.1) the wireless sensor network node determines the information of the wireless sensor network node:

each node D_iDetermining location coordinates L including itself_iResidual energy E_iCommunication distance R_iAnd node degree de_i，D_i∈{D₁,D₂,…,D_mM represents the number of the wireless sensor network nodes, and m is more than or equal to 2;

(1.2) the wireless sensor network node acquires a neighbor node information set:

each node D_iCommunication distance R through APT system_iInner neighbor node { D₁,D₂,…,D_zScanning, and combining the scanned information of all neighbor nodes into a neighbor node information set V_i，V_i＝{I₁,I₂,…I_a,…,I_z}，I_a＝{L_a,E_a,R_a,de_aZ represents the number of neighbor nodes; z is more than or equal to 1, and a is more than or equal to 1;

(1.3) the wireless sensor network node determines cluster head and non-cluster head nodes:

each node D_iCalculating the energy ED required by the node to establish links with all the neighbor nodes_iAnd ED is combined_iWith all its neighbor nodes { ED₁,ED₂…ED_zThe node corresponding to the maximum value in the data is used as a cluster head CD_jOther nodes as non-cluster-head nodes { ND₁,ND₂,…,ND_q}，CD_j∈{CD₁,CD₂,…,CD_kK represents the number of cluster head nodes, q represents the number of non-cluster head nodes, k is more than or equal to 1, and q is equal to z;

wherein E is_iRepresenting the residual energy of node i, E_jRepresenting the residual energy of node j, d_ijRepresenting the euclidean distance between node i and node j,

x_irepresents L_iAbscissa of (a), x_jRepresents L_jAbscissa of (a), y_iRepresents L_iOrdinate of (a), y_jRepresents L_jThe ordinate of (a);

(1.4) the wireless sensor network node determines the management area where the wireless sensor network node is located:

each cluster head CD_jAt a communication distance R_jThe area determined for the radius is the management area A of the cluster head_jEach non-cluster head node ND_iDetermine its position coordinate L_iBelong to { A₁,A₂,…,A_j,A_kWhich management area in (L), if L_i∈A_jThen ND_iIs contained in the management area A_jInternal;

(2) the cluster head determines the number of non-cluster head nodes in the cluster head:

each cluster head CD_jStatistics management area A_jAt 0 to T_lNumber of non-cluster-head nodes in time set N_j，N_j＝{n₁,n₂,…n_c,n_l}，n_cIs shown at T_gThe number of non-cluster-head nodes, l represents each cluster-head CD_jThe number of times of statistics, l is more than or equal to 30, T_gRepresents 0 to T_lCD per cluster head in time_jThe counting frequency is the time corresponding to c, 0 to T_lA period of time representing the completion of initialization, 0 ≦ T_g≤T_l，T_l≥0；

(3) Constructing a multiple linear regression model Y:

with each cluster head CD_jManagement area A_jInner non-cluster head node number set N_jAs a training data set for a multiple linear regression model and from the training data set N_jDetermining a management area A_jMultiple linear regression model parameters { b) of number of middle non-cluster head nodes₀,b₁,…,b_pAnd constructing a multiple linear regression model Y:

Y＝b₀+b₁n₁+b₂n₂+…+b_pn_p

wherein p represents the number of non-cluster head nodes related to Y, and p is more than or equal to 1;

(4) the cluster head calculates the number of non-cluster head nodes in the management area:

each cluster head CD_jCalculating a management area A according to the multiple linear regression model Y_jAt 0 to T_lThen T_dNumber of non-cluster-head nodes at time Y_j，T_d＞T_l；

(5) The cluster head acquires the wireless sensor network topology:

(5.1) CD per cluster head_jAccording to the management area A_jNumber of inner non-cluster head nodes Y_jAnd node degree de_jCalculating CD_jAt T_dMean nodosity λ of time_j：

(5.2) CD per cluster head_jCluster head with its neighbors { CD₁,CD₂,…CD_uEstablishing a communication link to form an upper-layer mesh structure containing k cluster heads; and the maximum hop count is lambda_jMultiple hop method and CD_jManagement area A_jInner non-cluster head node [ ND ]₁,ND₂,…,ND_hAnd (6) establishing a communication link to form k lower-layer star structures which take the cluster head as the center and contain h non-cluster-head nodes, wherein the upper-layer star structure and the lower-layer star structure jointly form a wireless sensor network topology.

Compared with the prior art, the invention has the following advantages:

1. according to the method, the number of non-cluster-head nodes in the cluster head management area is predicted by adopting a multiple linear regression model, and the average degree of the nodes in the cluster head is calculated, so that the access degree of the non-cluster-head nodes in the cluster head is smaller than the average node degree, a potential link is not required to be selected, the problem of node degree limitation is solved, and compared with the prior art, the connectivity and the stability of a wireless sensor network are improved.

2. According to the invention, the problems of energy imbalance, limited communication distance and unstable link are solved by eliminating the problem of node degree limitation and adopting a multi-hop method to establish the communication link, and compared with the prior art, the connectivity and stability of the wireless sensor network are further improved.

Drawings

FIG. 1 is a block diagram of an implementation process of the present invention.

FIG. 2 is a block diagram of an implementation process of constructing a multiple linear regression model according to the present invention.

Detailed Description

The invention is described in further detail below with reference to the following figures and examples:

the wireless sensor network includes a wireless optical network and a microwave network, and the embodiment adopts the wireless optical network for description.

Referring to fig. 1, the present invention includes the steps of:

step 1) initializing a wireless optical network;

before the wireless optical network is not initialized, each node is an isolated node, and each node does not know information of other nodes in the network, so that the wireless optical network needs to be initialized so as to acquire the information of other nodes in the network, and then cluster heads and non-cluster-head nodes are determined so as to determine each management area in the wireless optical network.

Step 1.1) the wireless optical network node determines the information of itself:

each node D_iDetermining location coordinates L including itself_iResidual energy E_iCommunication distance R_iAnd node degree de_i，D_i∈{D₁,D₂,…,D_mM represents the number of wireless optical network nodes, and m is more than or equal to 2;

the position coordinates, residual energy, communication distance and node degree in the wireless optical network node information influence the establishment of the wireless optical network communication link, thereby influencing the topology establishment of the wireless optical network. The radio optical network node needs to determine its own information. The wireless optical network node information of the invention is as follows: the number of the wireless optical network nodes is 100, the position coordinates of each node are positioned in a 10 km-10 km interval, the initial value of the residual energy is 0.5J, the communication distance is 2km, and the node degree is 8;

step 1.2) the wireless optical network node acquires a neighbor node information set:

each node D_iCommunication distance R through APT system_iInner neighbor node { D₁,D₂,…,D_zScanning and combining the scanned information of all neighbor nodes into a neighbor nodeInformation set V_i，V_i＝{I₁,I₂,…I_a,…,I_z}，I_a＝{L_a,E_a,R_a,de_aZ represents the number of neighbor nodes; z is more than or equal to 1, and a is more than or equal to 1;

in the initialization stage of the wireless optical network, each node is an isolated node, so that the wireless optical network node can only acquire the information of neighbor nodes in the communication distance of the wireless optical network node, including position coordinates, residual energy, the communication distance and node degree.

Step 1.3) the wireless optical network node determines a cluster head node and a non-cluster head node:

each node D_iCalculating the energy ED required by the node to establish links with all the neighbor nodes_iAnd ED is combined_iWith all its neighbor nodes { ED₁,ED₂…ED_zThe node corresponding to the maximum value in the data is used as a cluster head CD_jOther nodes as non-cluster-head nodes { ND₁,ND₂,…,ND_q}，CD_j∈{CD₁,CD₂,…,CD_kK represents the number of cluster head nodes, and q represents the number of non-cluster head nodes; k is more than or equal to 1, and q is equal to z;

wherein E is_iRepresenting the residual energy of node i, E_jRepresenting the residual energy of node j, d_ijRepresenting the euclidean distance between node i and node j,

x_irepresents L_iAbscissa of (a), x_jRepresents L_jAbscissa of (a), y_iRepresents L_iOrdinate of (a), y_jRepresents L_jThe ordinate of (a);

due to the problems of limited node degree, unbalanced energy, unstable link and the like of the wireless optical network, the problems can be effectively solved by adopting a layered topology. The upper layer is composed of cluster heads, and the lower layer is composed of non-cluster-head nodes with the cluster heads as centers, so that a layered wireless optical network topology is constructed. Therefore, there is a need to determine cluster and non-cluster nodes in a wireless optical network.

Step 1.4) the wireless optical network node determines the management area where the wireless optical network node is located:

each cluster head CD_jAt a communication distance R_jThe area determined for the radius is the management area A of the cluster head_jEach non-cluster head node ND_iDetermine its position coordinate L_iBelong to { A₁,A₂,…,A_j,A_kWhich management area in (L), if L_i∈A_jThen ND_iIs contained in the management area A_jInternal;

each cluster head needs to determine its management area in order to determine the non-cluster head nodes with which a communication link needs to be established, forming a cluster head-centered infrastructure.

Step 2) determining the number of non-cluster-head nodes in the cluster head

Each cluster head CD_jStatistics management area A_jAt 0 to T_lNumber of non-cluster-head nodes in time set N_j，N_j＝{n₁,n₂,…n_c,…n_l}，n_cIs shown at T_gThe number of non-cluster-head nodes, l represents each cluster-head CD_jThe number of times of statistics, l is more than or equal to 30, T_gRepresents 0 to T_lCD per cluster head in time_jThe time 0 corresponding to the counting frequency c is more than or equal to T_g≤T_l，T_l≥0；

Since a training data set is required for constructing the multiple linear regression model, the training data set needs to be collected for the initialized wireless optical network. And taking the non-cluster-head node number set of the management area in a period of time after initialization is completed as a training data set of the multiple linear regression model to construct the multiple linear regression model.

Step 3), constructing a multiple linear regression model Y:

the number of non-cluster head nodes is related to the number of non-cluster head nodes several times before. The formalization is represented as: number of non-cluster head nodes Y and first pNumber of non-cluster-head nodes of time n₁,n₂,…,n_pThe correlation is set as the correlation weight coefficients { b }₀,b₁,…,b_pThen the model of the number of non-cluster-head nodes Y is:

Y＝b₀+b₁n₁+b₂n₂+…+b_pn_p

determining a correlation weight coefficient b from a training data set₀,b₁,…,b_pAnd (4) constructing a multivariate linear regression model of the number Y of the non-cluster-head nodes. Therefore, the core of constructing the multiple linear regression model Y is to determine the related weight coefficients { b }₀,b₁,…,b_p}. Referring to fig. 2, constructing the multiple linear regression model includes the steps of:

step 3.1) based on the training data set N_jBuilding a management area A_jInner non-cluster head node number matrix Y' and feature matrix X, N_j＝{n₁,n₂,…n_c,…n_l}：

Wherein n is_cIs shown at T_gNumber of non-cluster-head nodes, T_gRepresents 0 to T_lCD per cluster head in time_jThe counting frequency is the time corresponding to c, and T is more than or equal to 0_g≤T_l，0～T_lIndicates a period of time after initialization is completed, T_l≧ 0, e ═ l-p +1, l denotes per cluster head CD_jThe number of statistics, l ≧ 30, p denotes and manages the region A_jThe number of non-cluster head nodes related to the non-cluster head node number matrix Y' in the cluster is p is more than or equal to 1, and r is equal to c-1;

by training the data set N_jBuilding a management area A_jThe non-cluster head node number matrix Y' and the feature matrix X in the cluster can be usedAnd estimating a non-cluster head node quantity matrix Y' by using the characteristic matrix X.

Step 3.2) multiple linear regression model parameters b₀,b₁,…,b_pRespectively initializing random numbers from 0 to 1;

step 3.3) to the multiple linear regression model parameters { b₀,b₁,…,b_pTranspose to get transpose matrix b^TAnd the feature matrices X and b^TThe product of (a) is used as a predicted non-cluster head node number matrix Z:

Z＝X×b^T

and 3.4) calculating the residual square sum Q (b) of the multiple linear regression model Y through Z by adopting a least square method, judging whether the residual square sum Q (b) is smaller than a preset threshold epsilon or not, and if yes, { b₀,b₁,…,b_pIs the management area A_jAnd (3) performing multiple linear regression model parameters of the number of middle non-cluster head nodes, otherwise, executing the step (3.5), wherein the calculation formula of Q (b) is as follows:

wherein, Y_i'line i, Z of the matrix Y' representing the number of non-cluster-head nodes_iAn ith row representing a predicted non-cluster head node number matrix Z;

the common methods adopting the least square method include methods of solving a sum of squares of residual errors, solving a square difference of squares, solving a variance and the like, and the method adopts the method of solving the sum of squares of residual errors to judge whether a preset threshold value is met, determines parameters of the multiple linear regression model and constructs the multiple linear regression model.

Step 3.5) determining b by gradient descent method₀,b₁,…,b_pUpdate function b of }_i', by b_i' Pair { b₀,b₁,…,b_pUpdate and replace the update result with b₀,b₁,…,b_pExecution of step (3.3), wherein b_iThe expression of' is:

wherein b is_i∈{b₀,b₁,…,b_p}，n_i∈N_iAnd α represents the learning rate of gradient descent.

Due to b₀,b₁,…,b_pThe initialization is random, so the residual sum of squares Q (b) of the multiple linear regression model Y does not necessarily satisfy the preset threshold epsilon, therefore, the pair { b }is needed₀,b₁,…,b_pUpdate so that it meets a preset threshold epsilon.

Step 3.6) according to the management area A_jMultiple linear regression model parameters { b) of number of middle non-cluster head nodes₀,b₁,…,b_pConstructing a multiple linear regression model Y;

Y＝b₀+b₁n₁+b₂n₂+…+b_pn_p

wherein p represents the number of non-cluster head nodes related to Y, and p is more than or equal to 1;

the number of non-cluster-head nodes in the management area can be determined through the construction of the multiple linear regression model, and therefore energy can be distributed reasonably and the topological structure can be optimized.

Step 4), the cluster head calculates the number of non-cluster-head nodes in the management area:

each cluster head CD_jCalculating a management area A according to the multiple linear regression model Y_jAt 0 to T_lThen T_dNumber of non-cluster-head nodes at time Y_j，T_d＞T_l；

The cluster head can determine the average node degree of the cluster head through the number of non-cluster head nodes in the management area, the average node degree in the cluster head is determined, and when a communication link is established between the non-cluster head nodes and the cluster head, the problem of limited node degree can be solved as long as the actual access degree of the cluster head is not more than the average node degree, so that the topology construction is more reasonable.

Step 5), the cluster head acquires the wireless optical network topology;

first, the cluster head calculates an average node degree by the number of non-cluster-head nodes in its management area. Then, a communication link is established between the cluster head and the neighbor cluster head to form a mesh-type upper layer structure containing the cluster head, and a communication link is established with the non-cluster head nodes in the management area of the cluster head in a multi-hop mode with the maximum hop count as the average node degree to form a star-type lower layer structure containing the non-cluster head nodes with the cluster head as the center, and the upper layer mesh structure and the lower layer star structure jointly form a wireless optical network topological structure.

Step 5.1) per cluster head CD_jAccording to the management area A_jNumber of inner non-cluster head nodes Y_jAnd node degree de_jCalculating CD_jAt T_dMean nodosity λ of time_j：

The average node degree of the cluster head represents the average number of communication links which can be established by each non-cluster head node in the cluster head management area, and the number of the communication links which can be established maximally by the non-cluster head nodes in the cluster head is determined according to the average node degree of the cluster head, so that the problem that the actual number of the access links is larger than the node degree is solved.

Step 5.2) per cluster head CD_jCluster head with its neighbors { CD₁,CD₂,…CD_uEstablishing a communication link to form an upper-layer mesh structure containing k cluster heads; and the maximum hop count is lambda_jMultiple hop method and CD_jManagement area A_jInner non-cluster head node [ ND ]₁,ND₂,…,ND_hAnd establishing a communication link to form k lower-layer star structures which take the cluster head as the center and contain h non-cluster-head nodes, wherein the upper-layer star structure and the lower-layer star structure jointly form a wireless optical network topology.

Claims (1)

1. A wireless sensor network topology construction method based on a multiple linear regression model is characterized by comprising the following steps:

(1) initializing the wireless sensor network:

(1.1) the wireless sensor network node determines the information of the wireless sensor network node:

each node D_iDetermining location coordinates L including itself_iResidual energy E_iCommunication distance R_iAnd node degree de_i，D_i∈{D₁,D₂,…,D_mM represents the number of the wireless sensor network nodes, and m is more than or equal to 2;

(1.2) the wireless sensor network node acquires a neighbor node information set:

each node D_iCommunication distance R through APT system_iInner neighbor node { D₁,D₂,…,D_zScanning, and combining the scanned information of all neighbor nodes into a neighbor node information set V_i，V_i＝{I₁,I₂,…I_a,…,I_z}，I_a＝{L_a,E_a,R_a,de_aZ represents the number of neighbor nodes; z is more than or equal to 1, and a is more than or equal to 1;

(1.3) the wireless sensor network node determines cluster head and non-cluster head nodes:

each node D_iCalculating the energy ED required by the node to establish links with all the neighbor nodes_iAnd ED is combined_iWith all its neighbor nodes { ED₁,ED₂…ED_zThe node corresponding to the maximum value in the data is used as a cluster head CD_jOther nodes as non-cluster-head nodes { ND₁,ND₂,…,ND_q}，CD_j∈{CD₁,CD₂,…,CD_kK represents the number of cluster head nodes, q represents the number of non-cluster head nodes, k is more than or equal to 1, and q is equal to z;

wherein E is_iRepresenting the residual energy of node i, E_jTo representResidual energy of node j, d_ijRepresenting the euclidean distance between node i and node j,

x_irepresents L_iAbscissa of (a), x_jRepresents L_jAbscissa of (a), y_iRepresents L_iOrdinate of (a), y_jRepresents L_jThe ordinate of (a);

(1.4) the wireless sensor network node determines the management area where the wireless sensor network node is located:

each cluster head CD_jAt a communication distance R_jThe area determined for the radius is the management area A of the cluster head_jEach non-cluster head node ND_iDetermine its position coordinate L_iBelong to { A₁,A₂,…,A_j,A_kWhich management area in (L), if L_i∈A_jThen ND_iIs contained in the management area A_jInternal;

(2) the cluster head determines the number of non-cluster head nodes in the cluster head:

each cluster head CD_jStatistics management area A_jAt 0 to T_lNumber of non-cluster-head nodes in time set N_j，N_j＝{n₁,n₂,…n_c,…n_l}，n_cIs shown at T_gThe number of non-cluster-head nodes, l represents each cluster-head CD_jThe number of times of statistics, l is more than or equal to 30, T_gRepresents 0 to T_lCD per cluster head in time_jThe counting frequency is the time corresponding to c, 0 to T_lA period of time representing the completion of initialization, 0 ≦ T_g≤T_l，T_l≥0；

(3) Constructing a multiple linear regression model Y:

with each cluster head CD_jManagement area A_jInner non-cluster head node number set N_jAs a training data set for a multiple linear regression model and from the training data set N_jDetermining a management area A_jMultiple linear regression model parameters { b) of number of middle non-cluster head nodes₀,b₁,…,b_pAnd constructing a multiple linear regression modelType Y:

Y＝b₀+b₁n₁+b₂n₂+…+b_pn_p

wherein p represents the number of non-cluster head nodes related to Y, and p is more than or equal to 1; determining a management area A_jMultiple linear regression model parameters { b) of number of middle non-cluster head nodes₀,b₁,…,b_pThe implementation steps are as follows:

(3.1) based on the training data set N_jBuilding a management area A_jInner non-cluster head node number matrix Y' and feature matrix X, N_j＝{n₁,n₂,…n_c,…n_l}：

Wherein n is_cIs shown at T_gNumber of non-cluster-head nodes, T_gRepresents 0 to T_lCD per cluster head in time_jThe counting frequency is the time corresponding to c, and T is more than or equal to 0_g≤T_l，0～T_lIndicates a period of time after initialization is completed, T_l≧ 0, e ═ l-p +1, l denotes per cluster head CD_jThe number of statistics, l ≧ 30, p denotes and manages the region A_jThe number of non-cluster head nodes related to the non-cluster head node number matrix Y' in the cluster is p is more than or equal to 1, and r is equal to c-1;

(3.2) multiple Linear regression model parameters { b }₀,b₁,…,b_pRespectively initializing random numbers from 0 to 1;

(3.3) parameters of the multivariate Linear regression model { b }₀,b₁,…,b_pTranspose to get transpose matrix b^TAnd the feature matrices X and b^TThe product of (a) is used as a predicted non-cluster head node number matrix Z:

Z＝X×b^T

(3.4) calculating the residual square sum Q (b) of the multiple linear regression model Y through Z by adopting a least square method, judging whether the residual square sum Q (b) is smaller than a preset threshold epsilon or not, and if yes, { b₀,b₁,…,b_pIs the management area A_jAnd (3) performing multiple linear regression model parameters of the number of middle non-cluster head nodes, otherwise, executing the step (3.5), wherein the calculation formula of Q (b) is as follows:

wherein, Y'_iRow i, Z of a matrix Y' representing the number of non-cluster head nodes_iAn ith row representing a predicted non-cluster head node number matrix Z;

(3.5) determination of { b ] by gradient descent method₀,b₁,…,b_pUpdate function b'_iThrough b'_iTo { b₀,b₁,…,b_pUpdate and replace the update result with b₀,b₁,…,b_p}, performing step (3.3), wherein b'_iThe expression of (a) is:

wherein b is_i∈{b₀,b₁,…,b_p}，n_i∈N_iα represents a learning rate of gradient descent;

(4) the cluster head calculates the number of non-cluster head nodes in the management area:

each cluster head CD_jCalculating a management area A according to the multiple linear regression model Y_jAt 0 to T_lThen T_dNumber of non-cluster-head nodes at time Y_j，T_d＞T_l；

(5) The cluster head acquires the wireless sensor network topology:

(5.1) CD per cluster head_jAccording to the management area A_jNumber of inner non-cluster head nodesY_jAnd node degree de_jCalculating CD_jAt T_dMean nodosity λ of time_j：

(5.2) CD per cluster head_jCluster head with its neighbors { CD₁,CD₂,…CD_uEstablishing a communication link to form an upper-layer mesh structure containing k cluster heads; and the maximum hop count is lambda_jMultiple hop method and CD_jManagement area A_jInner non-cluster head node [ ND ]₁,ND₂,…,ND_hAnd (6) establishing a communication link to form k lower-layer star structures which take the cluster head as the center and contain h non-cluster-head nodes, wherein the upper-layer star structure and the lower-layer star structure jointly form a wireless sensor network topology.

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