CN103281697B - A kind of wireless sensor network topology reconstructing method of center type - Google Patents

Abstract

The present invention discloses a kind of wireless sensor network topology reconstructing method of center type, concrete steps are: first for given regular network structure, the correlation between the network coverage and failure node number is discussed, for the failure node number determining to reach minimum reparation needed for certain network coverage provides foundation.Then, mathematical description is carried out to the scheduling problem of supporting node, the marriage problem of supporting between node and failure node is converted into integer programming problem to solve, the nodes-distributing method be optimized, i.e. network topology reconstructing method.Meanwhile, the nodes-distributing method of random network structure is discussed.Finally, by emulation experiment proposed method verified and analyze.The present invention will find the Optimum Matching scheme between node and failure node to be repaired needing movement under the prerequisite of the single support node maximum moving distance of restriction, make the movement of the support node of all needs movement always apart from minimum.

Description

A kind of wireless sensor network topology reconstructing method of center type

Technical field

The present invention relates to a kind of wireless sensor network topology reconstructing method of center type, the optimization that can realize supporting in wireless sensor network node distributes, failure node in network replaced fast and repairs, ensureing the Monitoring Performance of network, embodying intellectuality and the self organization ability of network.

Background technology

Wireless sensor network has the feature that networking mode is flexible, monitoring information is comprehensive, intelligence degree is high compared with legacy network, is a kind of brand-new information gathering and treatment technology, extends the ability of mankind's obtaining information widely.Based on the plurality of advantages of wireless sensor network, it is in industrial and agricultural production, national defense and military, communication and logistics, health care, space exploration, and multiple field such as building management, forecast of natural calamity has broad application prospects and huge using value.Although effective node deployment strategy can be optimized network monitor performance when network initial deployment, but because individual node structure is simple, finite energy, often lost efficacy because of the reason such as environmental interference, depleted of energy, this makes topology of networks change, and network monitor performance is subject to appreciable impact.

Summary of the invention

Goal of the invention: if when there is node failure, the residue node resource that can make full use of in network is readjusted network topology structure, namely the Monitoring Performance improving network is reconstructed by network topology, not only can farthest prolong network lifetime, can also significantly improve the adaptivity of network, fault-tolerance and intelligence degree, this practical application for promotion wireless sensor network is very significant.Lost efficacy for part of nodes in wireless sensor network, the problem of network monitor hydraulic performance decline, the invention provides a kind of wireless sensor network topology reconstructing method of center type.

Technical scheme: a kind of wireless sensor network topology reconstructing method of center type, characteristic of network environment is as follows: (1) any node i can carry out omnirange perception, its coverage be one be the center of circle with node i, the circle being radius with the perceived distance r of node i, namely (2) any node i can carry out omnirange communication, its communication context be one be the center of circle with node i, the circle being radius with the communication distance R of node i, namely (3) the perceived distance r of all nodes is identical respectively with communication distance R; (4) all nodes meet the condition of R>=2r; (5) all nodes have position consciousness; (6) all nodes are all in same two dimensional surface.

Wireless sensor network comprises multiple wireless sensor node, is called for short node.Node is divided into stationary nodes according to whether having locomotivity and supports node.All the time active state is in, for obtaining the information of area to be monitored after stationary nodes is deployed.Can lose efficacy because of depleted of energy and external interference in network operation process.Supporting node and be in resting state with conserve energy when network initial deployment, can active state being transferred to when occurring that stationary nodes lost efficacy, for repairing the stationary nodes of inefficacy.

The covering performance of wireless sensor network can by solving the network coverage to evaluate.Owing to reaching and keeping covering completely of whole area to be monitored often to need to spend higher cost, and when failure node number is no more than some, network covering property still can meet application demand, the present invention is by calculating, obtain the law curve of the network coverage with failure node number of variations, according to this curve can determine easily in order to reach a certain coverage rate answer the failure node number of minimum reparation.

In network operation process, convergence center in network is responsible for collecting and is merged the information that stationary nodes transmits, convergence center has sufficient energy and higher computing ability, can network global information be obtained, comprise node present position, node operating state (active, dormancy or inefficacy) and the current network coverage etc.Utilize these information, convergence center is regularly assessed network monitor performance, and judging whether needs to carry out network reconfiguration, namely supports node and repairs failure node.In addition, this convergence center can also require according to the covering performance of network the minimal amount independently determining the failure node that must repair, once detect that the network coverage is lower than a certain set point, the minimal amount of the failure node according to required reparation is carried out the design supporting node optimization distribution method by this convergence center, plans network reconfiguration strategy.

Take into account single support node energy consumption and all support node energy consumptions in network reconfiguration simultaneously, namely two optimization problems are discussed below: (P1) is when repairing required minimal number failure node, how to distribute the support node of needs movement, make the maximum moving distance of single support node minimum? (P2) when required minimal number failure node can be repaired, how to distribute the support node of needs movement, make the movement of these support nodes always apart from minimum?

The network coverage is defined as allly enlivening the coverage of stationary nodes and the ratio of whole network coverage, that is:

$c_r=\frac{S_s}{S}\×100\%---\left(1\right)$

Wherein, S _srepresent all area coverages enlivening stationary nodes, S represents the scope of area to be monitored.

The set of the inefficacy stationary nodes in a certain reconstruct cycle is designated as N _f.Suppose to reach certain network coverage, must at least repair q≤| N _f| individual failure node.The set of all support nodes is designated as M.For convenience of explanation without loss of generality again, order simultaneously | M|=|N _f| :=n _f.The weight matrix of the spacing of all support nodes and failure node is set up according to the positional information of network node wherein, i and j represents support node and failure node respectively, w _ijrepresent the Euclidean distance of supporting between node i and failure node j.In network reconfiguration process, each support node can only repair a failure node, and support node linearly moves in path.Such as, if support node i will repair failure node j, then node i is supported by mobile w _ijthe distance position that arrives failure node j it is repaired, the displacement of namely supporting when node i repairs failure node j is w _ij.

Order is when failure node is repaired, and in the support node of all needs movements, the maximum of single support node motion distance is d, and first optimization problem (P1), for determining the minimum value of d, is designated as d ^*, when q failure node is at least repaired in expression, the minimum value of the maximum moving distance of single support node in the support node of all needs movements.Thus, following Mathematical Modeling is provided:

$d^{*}=\underset{X}{\min }d---\left(2\right)$

Constraints $\left\{\begin{array}{c}{\mathrm{\Σ}}_{i=1}^{n_f}{x}_{\mathrm{ij}}=1,j=1,...,n_f;\\ {\mathrm{\Σ}}_{j=1}^{n_f}{x}_{\mathrm{ij}}=1,i=1,...,n_f;\\ {\mathrm{\Σ}}_{\mathrm{ij}}{x}_{\mathrm{ij}}{1}_{\{w_{\mathrm{ij}}\≤d\}}\≥q;\\ x_{\mathrm{ij}}=0\mathrm{or}1,i,j=1,...,n_f.\end{array}\right.---\left(3\right)$

Wherein, be 0/1 oriental matrix, work as w _ijduring≤d, x _ij=1, represent that supporting node i and failure node j matches one by one, namely support node i can transfer active state to and the position moving to failure node j is repaired it; Work as w _ijduring > d, x _ij=0, represent that support node i and failure node j do not match.In formula (3), the 3rd constraints illustrates at least q failure node and must be repaired the requirement that could meet network covering property.

Second optimization problem (P2) will based on d ^*finding optimum support peer distribution strategy makes the displacement sum of all support nodes minimum, farthest to save node energy.Here d is supposed ^*value solved by P1 and obtained, then have following Mathematical Modeling:

$X^{*}=\arg \underset{X}{\min }\underset{1\≤i,j\≤n}{\mathrm{\Σ}}{x}_{\mathrm{ij}}{w}_{\mathrm{ij}}{1}_{\{w_{\mathrm{ij}}\≤d^{*}\}}---\left(4\right)$

Constraints $\left\{\begin{array}{c}{\mathrm{\Σ}}_{i=1}^{n_f}{x}_{\mathrm{ij}}=1,j=1,...,n_f;\\ {\mathrm{\Σ}}_{j=1}^{n_f}{x}_{\mathrm{ij}}=1,i=1,...,n_f;\\ x_{\mathrm{ij}}=0\mathrm{or}1,i,j=1,...,n_f.\end{array}\right.---\left(5\right)$

Wherein, for unit indicator function, if w _ij≤ d ^*, then otherwise

P1 is solved, if $d_{\min }=\underset{1\≤i,j\≤n_f}{\min }{w}_{\mathrm{ij}},$ $d_{\max }=\underset{1\≤i,j\≤n_f}{\max }{w}_{\mathrm{ij}}.$ For if the maximum moving distance of single support node is restricted to d, the maximum of the failure node number that now can be repaired must be determined.The problems referred to above can be modeled as one and assign assignment problem (AssignmentProblem, AP):

$q\left(d\right)=\max \underset{1\≤i,j\≤n_f}{\mathrm{\Σ}}{x}_{\mathrm{ij}}{1}_{\{w_{\mathrm{ij}}\≤d\}}---\left(6\right)$

Constraints $\left\{\begin{array}{c}{\mathrm{\Σ}}_{i=1}^{n_f}{x}_{\mathrm{ij}}=1,j=1,...,n_f;\\ {\mathrm{\Σ}}_{j=1}^{n_f}{x}_{\mathrm{ij}}=1,i=1,...,n_f;\\ x_{\mathrm{ij}}=0\mathrm{or}1,i,j=1,...,n_f.\end{array}\right.---\left(7\right)$

P2 is solved, because target function is only to meeting w _ij≤ d ^*support node i and failure node j carry out pairing and solve.Therefore, peer distribution problem is smallest match problem.Order:

This formula is based on the following fact: the maximum having limited single support node i movable distance due to the present invention in P1 is d ^*, therefore, work as w _ij> d ^*time, even if there is x _ij=1, this coupling also will not adopt.This can realize by the following method in Algorithm for Solving process: work as w _ij> d ^*time, make w _ijbe an abundant large value, e.g., w _ij=d ^*+ 1, i.e. w _i' _j=-d ^*-1.Owing to being solve maximum matching problem, therefore w _i' _j=-d ^*coupling corresponding to-1 can not be considered in computational process.Through type (8), namely smallest match problem of the present invention is converted into maximum matching problem.Maximum matching problem derivation algorithm calculation process is as follows:

1) initialization:

$m_{T_i\→x_{\mathrm{ij}}}^{\left(0\right)}=-\underset{m\≠i}{\max }{w}_{\mathrm{mj}---\left(9\right)}^{\′}$

$m_{B_j\→x_{\mathrm{ij}}}^{\left(0\right)}=-\underset{l\≠j}{\max }{w}_{\mathrm{il}}^{\′}---\left(10\right)$

represent w' _mjthe opposite number of maximum, represent w _i' _lthe opposite number of maximum;

2) kth step iteration:

$m_{T_i\→x_{\mathrm{ij}}}^{\left(k\right)}=-\underset{m\≠j}{\max }\{m_{B_m\→x_{\mathrm{im}}}^{(k-1)}+w_{\mathrm{im}}^{\′}\}---\left(11\right)$

$m_{B_j\→x_{\mathrm{ij}}}^{\left(k\right)}=-\underset{l\≠i}{\max }\{m_{T_l\→x_{\mathrm{lj}}}^{(k-1)}+w_{\mathrm{lj}}^{\′}\}---\left(12\right)$

3) after kth step iteration, calculate:

$M_{\mathrm{ij}}^{\left(k\right)}=m_{T_i\→x_{\mathrm{ij}}}^{\left(k\right)}+m_{B_j\→x_{\mathrm{ij}}}^{\left(k\right)}+w_{\mathrm{ij}}^{\′}---\left(13\right)$

Iteration result based on kth step estimates x _ijvalue: if otherwise

Beneficial effect: relative to prior art, the wireless sensor network topology reconstructing method of center type provided by the invention, convergence center in network is responsible for collecting network information, when network covering property declines and can not meet application demand, the support node motion then transferring redundancy is repaired failure node to failure node position or is substituted, thus improves or recover the Monitoring Performance of network.Because the energy of supporting entrained by node is also limited, support node motion apart from longer, the energy of consumption is also more.Therefore, in network reconfiguration process, limit the maximum moving distance of single support node in moving process be conducive to balancing the energy loss that each supports node.Meanwhile, the total distance of movement reducing all support nodes is conducive to saving the energy of whole network.Therefore, the present invention will find the Optimum Matching scheme between node and failure node to be repaired needing movement under the prerequisite of the single support node maximum moving distance of restriction, make the movement of the support node of all needs movement always apart from minimum.

Accompanying drawing explanation

Fig. 1 is network topology structure schematic diagram;

Fig. 2 is the change curve of the network coverage and failure node number;

Fig. 3 is that node optimization distributes derivation algorithm flow chart;

Fig. 4 is initial situation schematic diagram when there is node failure in network;

Fig. 5 is the relation curve schematic diagram of the minimum value being repaired failure node number and single support node maximum moving distance;

Fig. 6 is the single minimum value of support node maximum moving distance and the relation curve schematic diagram of the network coverage;

The peer distribution situation schematic diagram that centered by Fig. 7, lower 10 failure nodes of formula peer distribution strategy are repaired;

The peer distribution situation schematic diagram that centered by Fig. 8, lower 20 failure nodes of formula peer distribution strategy are repaired;

Fig. 9 is the network diagram of random topologies;

Figure 10 is the situation schematic diagram that the network of random topologies has node failure;

The peer distribution situation schematic diagram (d that centered by Figure 11, lower 20 failure nodes of formula peer distribution strategy are repaired ^*=12.3853m);

The peer distribution situation schematic diagram (d that centered by Figure 12, lower 20 failure nodes of formula peer distribution strategy are repaired ^*=∞).

Embodiment

Below in conjunction with specific embodiment, illustrate the present invention further, these embodiments should be understood only be not used in for illustration of the present invention and limit the scope of the invention, after having read the present invention, the amendment of those skilled in the art to the various equivalent form of value of the present invention has all fallen within the application's claims limited range.

One, network configuration and the network coverage

1.1 network topology structure

As shown in Figure 1, wherein, stationary nodes is expressed as "●" to the network topology structure considered in the present invention, to be deployed in node rule in area to be monitored and to remain active state; Mobile node is expressed as "○", is deployed in area to be monitored randomly.In the present invention, claim mobile node for reconstruct support node, hereinafter referred to as support node.Be in resting state with conserve energy when network initial deployment, can active state be transferred to when node failure, for repairing the stationary nodes of inefficacy.In order to keep certain network coverage to meet the application demand of network, partly the inefficacy stationary nodes of (even whole) needs to be repaired by the support node of redundancy.It should be noted that, although the network configuration here based on a kind of rule is discussed, but designed peer distribution strategy stands good in other forms of network configuration, in simulation analysis, the present invention discusses the application of proposed nodes-distributing method under random topologies network condition.

1.2 network characteristics explanations

(1) any node i can carry out omnirange perception, its coverage be one be the center of circle with node, the circle being radius with the perceived distance r of node, namely

(2) any node i can carry out omnirange communication, its communication context be one be the center of circle with node, the circle being radius with the communication distance R of node, namely

(3) the perceived distance r of all nodes is identical respectively with communication distance R;

(4) all nodes meet the condition of R >=2r;

(5) all nodes have position consciousness;

(6) all nodes are all in same two dimensional surface.

1.3 the network coverage

The covering performance of wireless sensor network can by solving the network coverage to evaluate.Particularly, in the present invention, the network coverage is defined as allly enlivening the coverage of stationary nodes and the ratio of whole network coverage, that is:

$c_r=\frac{S_s}{S}\×100\%---\left(1\right)$

Wherein, S _srepresent all area coverages enlivening stationary nodes, S represents the scope of area to be monitored.

Under normal conditions, we wish that the deployment of network node can reach the covering to area to be monitored maximum magnitude, but, reach and keep covering completely of whole area to be monitored often to need to spend higher cost.In view of when failure node number is no more than certain limit, network covering property still can meet application demand, the present invention is directed to above-mentioned this kind of regular network topological structure, utilize computer simulation node random failure, the rule of the network coverage with failure node number of variations is obtained, as shown in Figure 2 by the computational methods of gridding.In figure, n _frepresent failure node number.Each n is corresponded in figure _fc _rvalue is the average result of 100 experiments.According to Fig. 2 can determine easily in order to reach a certain coverage rate answer the failure node number of minimum reparation.

Two, network topology reconstructing method

In network operation process, convergence center in network is responsible for collecting and is merged the information that stationary nodes transmits, convergence center has sufficient energy and higher computing ability, can network global information be obtained, comprise node present position, node operating state (active, dormancy or inefficacy) and the current network coverage etc.Utilize these information, convergence center is regularly assessed network monitor performance, and judging whether needs to carry out network reconfiguration.This convergence center can also require according to the covering performance of network the minimal amount independently determining the failure node that must repair, once detect that the network coverage is lower than a certain set point, the minimal amount of the failure node according to required reparation is carried out the design supporting node optimization distribution method by this convergence center, plans network reconfiguration strategy.

2.1 problems describe

For convenience of explanation, the set of the inefficacy stationary nodes in a certain reconstruct cycle is designated as N _f.Suppose to reach certain network coverage, must at least repair q≤| N _f| individual failure node.The set of all support nodes is designated as M.For convenience of explanation without loss of generality again, order simultaneously | M|=|N _f| :=n _f.The weight matrix of the spacing of all support nodes and failure node is set up according to the positional information of network node wherein, i and j represents support node and failure node respectively, w _ijrepresent the Euclidean distance of supporting between node i and failure node j.In network reconfiguration process, each support node can only repair a failure node, and support node linearly moves in path.Such as, if support node i will repair failure node j, then node i is supported by mobile w _ijthe distance position that arrives failure node j it is repaired, the displacement of namely supporting when node i repairs failure node j is w _ij.

Because the energy of supporting entrained by node is also limited, therefore, the maximum moving distance limiting them in network reconfiguration process is conducive to conserve energy, but this may reduce and by the failure node number successfully repaired, and then can affect the network covering property after repairing.Therefore, following compromise problem has been drawn from single support node motion energy consumption and all support node motion total energy consumptions two angles respectively here:

How does problem 1, when repairing required minimal number failure node, distribute the support node of needs movement, makes the maximum moving distance of single support node minimum?

How does problem 2, when repairing required minimal number failure node, distribute the support node of needs movement, makes the movement of these support nodes always apart from minimum?

But often wish to take into account single support node energy consumption and all support node energy consumptions in network reconfiguration, therefore, comprehensive above-mentioned two problems, has following optimization problem simultaneously:

How does problem 3, when the mobile ultimate range of the single support node needing movement is limited, when repairing required minimal number failure node, distribute the support node of these needs movements, makes the movement of these support nodes always apart from minimum?

In order to solve problem 3, consider to adopt following thinking to carry out modeling to this problem: first to problem 1 modeling, then on the basis of problem 1, carry out modeling to problem 2, be converted into two optimization problems connected each other by problem 3.

Order is when failure node is repaired, and in the support node of all needs movements, the maximum of single support node motion distance is d, and first optimization problem (P1), for determining the minimum value of d, is designated as d ^*, when q failure node is at least repaired in expression, the minimum value of the maximum moving distance of single support node in the support node of all needs movements.Thus, following Mathematical Modeling is provided:

$d^{*}=\underset{X}{\min }d---\left(2\right)$

Constraints $\left\{\begin{array}{c}{\mathrm{\Σ}}_{i=1}^{n_f}{x}_{\mathrm{ij}}=1,j=1,...,n_f;\\ {\mathrm{\Σ}}_{j=1}^{n_f}{x}_{\mathrm{ij}}=1,i=1,...,n_f;\\ {\mathrm{\Σ}}_{\mathrm{ij}}{x}_{\mathrm{ij}}{1}_{\{w_{\mathrm{ij}}\≤d\}}\≥q;\\ x_{\mathrm{ij}}=0\mathrm{or}1,i,j=1,...,n_f.\end{array}\right.---\left(3\right)$

Wherein, be 0/1 oriental matrix, work as w _ijduring≤d, x _ij=1, represent that supporting node i and failure node j matches one by one, namely support node i can transfer active state to and the position moving to failure node j is repaired it; Work as w _ijduring > d, x _ij=0, represent that support node i and failure node j do not match.In formula (3), the 3rd constraints illustrates at least q failure node and must be repaired the requirement that could meet network covering property.

Second optimization problem (P2) will based on d ^*finding optimum support peer distribution strategy makes the displacement sum of all support nodes minimum, farthest to save node energy.Here d is supposed ^*value solved by P1 and obtained, then have following Mathematical Modeling:

$X^{*}=\arg \underset{X}{\min }\underset{1\≤i,j\≤n}{\mathrm{\Σ}}{x}_{\mathrm{ij}}{w}_{\mathrm{ij}}{1}_{\{w_{\mathrm{ij}}\≤d^{*}\}}---\left(4\right)$

Constraints $\left\{\begin{array}{c}{\mathrm{\Σ}}_{i=1}^{n_f}{x}_{\mathrm{ij}}=1,j=1,...,n_f;\\ {\mathrm{\Σ}}_{j=1}^{n_f}{x}_{\mathrm{ij}}=1,i=1,...,n_f;\\ x_{\mathrm{ij}}=0\mathrm{or}1,i,j=1,...,n_f.\end{array}\right.---\left(5\right)$

Wherein, for unit indicator function, if w _ij≤ d ^*, then otherwise

Sum up above-mentioned two optimization problems can see, P1 is conceived in network reconfiguration process, make the mobile energy consumption of single support node minimum, P2, then when considering that single support node energy is limited, makes the mobile energy consumption sum of the support node of all needs movement minimum.In above-mentioned optimization problem, due to single support node motion ultimate range and the total displacement of all support nodes all limited, therefore, the energy ezpenditure solved farthest reducing single support node of optimization problem, balance the energy consumption between each node simultaneously, be conducive to prolong network lifetime.In addition, it is worth mentioning that, if in network reconfiguration process, each support node is at the uniform velocity to arrive corresponding failure node position, and each rate travel of supporting node is identical, then above-mentioned optimization problem means that the time making network reconfiguration shortens as far as possible, thus improves the adaptive capacity of network to dynamic environment.

2.2 node optimizations distribute derivation algorithm

Provide node optimization distribution derivation algorithm below respectively to solve the problems referred to above.First, d is obtained by solving P1 ^*.On this basis, by solving the peer distribution result that P2 is optimized.

First P1 is solved.If $d_{\min }=\underset{1\≤i,j\≤n_f}{\min }{w}_{\mathrm{ij}},$ $d_{\max }=\underset{1\≤i,j\≤n_f}{\max }{w}_{\mathrm{ij}}.$ For if the maximum moving distance of single support node is restricted to d, the maximum of the failure node number that now can be repaired must be determined.The problems referred to above can be modeled as one and assign assignment problem (AssignmentProblem, AP):

$q\left(d\right)=\max \underset{1\≤i,j\≤n_f}{\mathrm{\Σ}}{x}_{\mathrm{ij}}{1}_{\{w_{\mathrm{ij}}\≤d\}}---\left(6\right)$

Constraints $\left\{\begin{array}{c}{\mathrm{\Σ}}_{i=1}^{n_f}{x}_{\mathrm{ij}}=1,j=1,...,n_f;\\ {\mathrm{\Σ}}_{j=1}^{n_f}{x}_{\mathrm{ij}}=1,i=1,...,n_f;\\ x_{\mathrm{ij}}=0\mathrm{or}1,i,j=1,...,n_f.\end{array}\right.---\left(7\right)$

In order to solve the d in P1 ^*, to w _ijarrange by ascending order.For ease of illustrate, suppose for if 1≤i ₁≤ i ₂≤ n _f, then meanwhile, for if 1≤j ₁≤ j ₂≤ n _f, then namely supposing to reach certain network covering property requirement, at least needing to repair q failure node.First, carry out initialization, make d=w _1j, and q=j, 1≤j≤n _f, obtaining the value of q (d) in formula (6) by solving AP, easily knowing q (d)≤q.If q (d) < is q, then increase the value of d successively, even d=w _{1 (j+1)}, the value of new q (d) is again obtained by solving AP.Repeat above step, certainly exist make q (d ^*) equal the minimum value of the required failure node number repaired, i.e. q (d ^*)=q.In the process repeating above step, if j=n _f, then w is made _{i (j+1)}:=w _{(i+1) 1}.So far, the d in P1 ^*can obtain.Figure 3 shows that above-mentioned algorithm flow, wherein, initial phase represents the minimum value q being determined the required failure node number repaired by convergence center according to network covering property requirement, and AP represents and solves formula (6) and formula (7).

For P2, its objective is based on d ^*finding optimum support peer distribution strategy makes the displacement sum of all support nodes minimum, namely in the present invention the target function of P2 only to meeting w _ij≤ d ^*support node i and failure node j carry out pairing and solve.Therefore, peer distribution problem is smallest match problem.In order to solve P2, make here:

This formula is based on the following fact: the maximum having limited single support node i movable distance due to the present invention in P1 is d ^*, therefore, work as w _ij> d ^*time, even if there is x _ij=1, this coupling also will not adopt.This can realize by the following method in Algorithm for Solving process: work as w _ij> d ^*time, make w _ijbe an abundant large value, e.g., w _ij=d ^*+ 1, i.e. w _i' _j=-d ^*-1.Owing to being solve maximum matching problem, therefore w _i' _j=-d ^*coupling corresponding to-1 can not be considered in computational process.Through type (8), namely smallest match problem of the present invention is converted into maximum matching problem.

Maximum matching problem derivation algorithm calculation process:

1) initialization:

$m_{T_i\&RightArrow;x_{\mathrm{ij}}}^{\left(0\right)}=-\underset{m\&NotEqual;i}{\max }{w}_{\mathrm{mj}---\left(9\right)}^{\&prime;}$

$m_{B_j\&RightArrow;x_{\mathrm{ij}}}^{\left(0\right)}=-\underset{l\&NotEqual;j}{\max }{w}_{\mathrm{il}}^{\&prime;}---\left(10\right)$

2) kth step iteration:

$m_{T_i\&RightArrow;x_{\mathrm{ij}}}^{\left(k\right)}=-\underset{m\&NotEqual;j}{\max }\{m_{B_m\&RightArrow;x_{\mathrm{im}}}^{(k-1)}+w_{\mathrm{im}}^{\&prime;}\}---\left(11\right)$

$m_{B_j\&RightArrow;x_{\mathrm{ij}}}^{\left(k\right)}=-\underset{l\&NotEqual;i}{\max }\{m_{T_l\&RightArrow;x_{\mathrm{lj}}}^{(k-1)}+w_{\mathrm{lj}}^{\&prime;}\}---\left(12\right)$

3) after kth step iteration, calculate:

$M_{\mathrm{ij}}^{\left(k\right)}=m_{T_i\&RightArrow;x_{\mathrm{ij}}}^{\left(k\right)}+m_{B_j\&RightArrow;x_{\mathrm{ij}}}^{\left(k\right)}+w_{\mathrm{ij}}^{\&prime;}---\left(13\right)$

Iteration result based on kth step estimates x _ijvalue: if otherwise

To sum up, two optimization problems above proposed all are solved.

Three, simulation analysis

3.1 regular topological structure networks

The present invention is based on MATLAB7.0 platform and carry out simulating, verifying to above-mentioned carried algorithm, the perceived distance of sensor node is r=5m, all nodes with interval be deployed in area to be monitored regularly, area to be monitored area is suppose within a certain reconstruct cycle, have 20 stationary nodes to lose efficacy in network, as shown in Figure 4, in figure, "×" represents failure node.According to Fig. 2, easily determine at least to repair the minimum covering performance that how many failure nodes can ensure network.In simulations, suppose to work as c _rwhen>=75%, network covering property can meet application requirement, now, as shown in Figure 2, at least should repair 10 failure nodes, i.e. q>=10.

By solving P1, obtain the minimum value d of failure node number q and the corresponding single support node maximum moving distance repaired ^*between variation relation curve, and d ^*and the variation relation curve between the network coverage, respectively as shown in Figure 5 and Figure 6.As shown in Figure 5, q is larger, d ^*larger, the failure node be namely repaired is more, and the displacement of individual node is larger.In figure, it is very slow that a-b section, c-d section and e-f section curve values increase ground, this means in these stages, more failure node be made to be repaired, and only need increase d a little ^*value.Correspondingly, as shown in Figure 6, d ^*larger, c _rlarger, in figure, it is very rapid that a '-b ' section, c '-d ' section and e '-f ' section curve values increase ground, this means in these stages, supports node and only need pay more the Monitoring Performance that little mobile cost just can improve network to a greater degree.

By solving P2, can at different d ^*under the restriction of value, obtain corresponding peer distribution result.Here, when providing q=10 and q=20 respectively, peer distribution result when namely having 10 and 20 failure nodes to be repaired respectively.Accordingly, d ^*be respectively 3.6385m and 14.9533m.Figure 7 shows that the result that 10 failure nodes are repaired, as seen from the figure, each failure node is repaired by the support node nearest apart from oneself, and these support great majority in node is all that the perception nearest apart from failure node can reach support node.This tallies with the actual situation completely, indicates the correctness of method proposed by the invention.Figure 8 shows that the result that 20 failure nodes are repaired, can see, in this case, is not that each failure node is repaired by the support node nearest apart from it.Such as, following three assembly are observed to result: support node 19 and failure node 10, support node 14 and failure node 16, support node 15 and failure node 17.Now, the total cost of movement of these pairing results is w _19,10+ w _15,17+ w _14,16=29.5549m.But as we can see from the figure, the failure node that distance supports node 14 nearest with supporting node 19 is node 10, and the perception that failure node 10 is distance supports node 14 nearest can reach failure node, w _14,10< w _19,10.Intuitively, support node 14 and should repair failure node 10.Therefore, if again match to above three groups of support nodes and failure node, can obtain: support node 14 and failure node 10, support node 15 and failure node 16, support node 19 and failure node 17, now moving total cost is w _14,10+ w _19,17+ w _15,16=29.2730m is less than the total cost of the movement of above-mentioned real income.So method of the present invention is seemingly incorrect, because the result redistributed can make mobile total cost less, and the peer distribution result of real income does not obtain the minimum value of mobile total cost.It is emphasized, however, that center type node optimum allocation method of the present invention obtains under the prerequisite that the displacement of single support node is limited, object is the energy ezpenditure balancing all support nodes.And when redistributing, the maximum moving distance of all support nodes is at least w _19,17> w _19,10=d ^*, this means that the energy consumption of supporting node 19 can increase, the total time that simultaneously failure node may be caused to repair extends, and namely network reconfiguration needs the time more grown just can complete.Therefore, when each support node has identical energy, nodes-distributing method proposed by the invention can reduce the energy loss of single support node as far as possible, avoids supporting individually node and cannot complete network reconfiguration task because of depleted of energy prematurely.Based on d ^*the restriction of value, 20 of obtaining as shown in Figure 8 support the optimal distributing scheme of node.

3.2 random topologies networks

Fig. 9 is the network of random topologies, and the perceived distance of sensor node is r=5m, and all nodes are deployed in area to be monitored randomly, and area to be monitored area is (50 × 50) m ², in figure, "○" represents support node.Suppose within a certain reconstruct cycle, have 20 stationary nodes to lose efficacy in network, as shown in Figure 10, in figure, "×" represents failure node.

Apply above-mentioned center type network topology reconstructing method and obtain peer distribution optimal result when 20 failure nodes are repaired as shown in figure 11.Now, d ^*=12.3853m, namely supports the distance between node 3 and failure node 39.At d ^*under unrestricted, i.e. d ^*utilize peer distribution optimal result that center type network topology reconstructing method obtains as shown in figure 12 during=∞.Relatively Figure 11,12 can find out, both differences are the pairing result between failure node 33,34,39 and support node 18,8,3.In Figure 11, the mobile cost of these pairing results is w _33,18+ w _34,8+ w _39,3=8.3066+10.9339+12.3853=31.6258m.Be w in Figure 12 _33,3+ w _34,18+ w _39,8=18.5558+1.4552+2.7792=22.7902m.In Figure 11 and 12, the total cost of the movement of all allocation result is respectively 129.9015m and 121.0659m.Although the result in Figure 11 does not reach global minima, compared with Figure 12, the distance of supporting node motion significantly reduces.

Claims (4)

1. a wireless sensor network topology reconstructing method for center type, is characterized in that:

Multiple wireless sensor nodes of wireless sensor network are divided into stationary nodes according to whether having locomotivity and support node;

Evaluating the covering performance of wireless sensor network by solving the network coverage, obtaining the law curve of the network coverage with failure node number of variations simultaneously, then determining the failure node number in order to reach minimum reparation corresponding to a certain coverage rate;

In network operation process, collected by the convergence center in network and merge the information that stationary nodes transmits, utilize described information, convergence center is regularly assessed network monitor performance, judge whether to need to carry out network reconfiguration, namely support node and repair failure node; In addition, this convergence center also requires according to the covering performance of network the minimal amount independently determining the failure node that must repair, once detect that the network coverage is lower than a certain set point, the minimal amount of the failure node according to required reparation is carried out the design supporting node optimization distribution method by this convergence center, carries out topology reconstruction to network;

In network topology reconstruct, take into account single support node energy consumption and all support node energy consumptions simultaneously, when required minimal number failure node can be repaired, distribute the support node needing movement, make the maximum moving distance of single support node minimum; When required minimal number failure node can be repaired, distribute the support node needing movement, make the movement of support node always apart from minimum;

Make the maximum moving distance of single support node minimum, specific implementation content is as follows,

The set of the inefficacy stationary nodes in a certain reconstruct cycle is designated as N _f, suppose to reach the default network coverage, must at least repair q≤| N _f| individual failure node; The set of all support nodes is designated as M; Order | M|=|N _f| :=n _f; The weight matrix of the spacing of all support nodes and failure node is set up according to the positional information of network node wherein, i and j represents support node and failure node respectively, w _ijrepresent the Euclidean distance of supporting between node i and failure node j; In network reconfiguration process, each support node can only repair a failure node, and support node linearly moves in path;

Order is when failure node is repaired, and in the support node of all needs movements, the maximum of single support node motion distance is that the minimum value of d, d is designated as d ^*, when q failure node is at least repaired in expression, the minimum value of the maximum moving distance of single support node in the support node of all needs movements; Thus, following Mathematical Modeling is provided:

$d^{*}=\underset{X}{min}d---\left(2\right)$

Constraints $\left\{\begin{array}{c}\begin{array}{cc}{\mathrm{\&Sigma;}}_{i=1}^{n_f}{x}_{ij}=1,& j=1,...,n_f;\end{array}\\ \begin{array}{cc}{\mathrm{\&Sigma;}}_{j=1}^{n_f}{x}_{ij}=1,& i=1,...,n_f;\end{array}\\ {\mathrm{\&Sigma;}}_{ij}{x}_{ij}{A}_{\{w_{ij}\&le;d\}}\&GreaterEqual;q;\\ \begin{array}{cc}{x}_{ij}=0or1,& i,j=1,...,n_f\end{array}\end{array}\right.---\left(3\right)$

Wherein, be 0/1 oriental matrix, work as w _ijduring≤d, x _ij=1, represent that supporting node i and failure node j matches one by one, namely support node i can transfer active state to and the position moving to failure node j is repaired it; Work as w _ijduring > d, x _ij=0, represent that support node i and failure node j do not match; In formula (3), the 3rd constraints illustrates at least q failure node and must be repaired the requirement that could meet network covering property, for unit indicator function;

Make the movement of support node always apart from minimum, specific implementation content is as follows,

Will based on d ^*finding optimum support peer distribution strategy makes the displacement sum of all support nodes minimum, then have following Mathematical Modeling:

$X^{*}=\arg \underset{X}{min}\underset{1\&le;i,j\&le;n}{\&Sigma;}{x}_{ij}{w}_{ij}{A}_{\{w_{ij}\&le;d^{*}\}}---\left(4\right)$

Constraints $\left\{\begin{array}{cc}{\mathrm{\&Sigma;}}_{i=1}^{n_f}{x}_{ij}=1,& j=1,...,n_f;\\ {\mathrm{\&Sigma;}}_{j=1}^{n_f}{x}_{ij}=1,& i=1,...,n_f;\\ x_{ij}=0or1,& i,j=1,...,n_f\end{array}\right.---\left(5\right)$

Wherein, for unit indicator function, if w _ij≤ d ^*, then otherwise $A_{\{w_{ij}\&le;d^{*}\}}=0;$

If $d_{min}=\underset{1\&le;i,j\&le;n_f}{min}{w}_{ij},d_{max}=\underset{1\&le;i,j\&le;n_f}{\max }{w}_{ij};$ For $\&ForAll;d\&Element;\&lsqb;d_{\min },d_{max}\&rsqb;,$ If the maximum moving distance of single support node is restricted to d, the maximum of the failure node number that now can be repaired must be determined;

$q\left(d\right)=max\underset{1\&le;i,j\&le;n_f}{\&Sigma;}{x}_{ij}{A}_{\{w_{ij}\&le;d\}}---\left(6\right)$

Constraints $\left\{\begin{array}{cc}{\mathrm{\&Sigma;}}_{i=1}^{n_f}{x}_{ij}=1,& j=1,...,n_f;\\ {\mathrm{\&Sigma;}}_{j=1}^{n_f}{x}_{ij}=1,& i=1,...,n_f;\\ x_{ij}=0or1,& i,j=1,...,n_f\end{array}\right.---\left(7\right)$

Because target function is only to meeting w _ij≤ d ^*support node i and failure node j carry out pairing and solve; Therefore, peer distribution problem is smallest match problem; Order:

Because the maximum limiting single support node i movable distance is d ^*, therefore, work as w _ij> d ^*time, even if there is x _ij=1, this coupling also will not adopt; Work as w _ij> d ^*time, make w _ij=d ^*+ 1, i.e. w ' _ij=-d ^*-1; Owing to being solve maximum matching problem, therefore w ' _ij=-d ^*coupling corresponding to-1 can not be considered in computational process; Through type (8), namely smallest match problem is converted into maximum matching problem; Maximum matching problem derivation algorithm calculation process is as follows:

1) initialization:

$m_{T_i\&RightArrow;x_{ij}}^{\left(0\right)}=-\underset{m\&NotEqual;i}{max}{w}_{mj}^{\&prime;}---\left(9\right)$

$m_{B_j\&RightArrow;x_{ij}}^{\left(0\right)}=-\underset{l\&NotEqual;j}{max}{w}_{il}^{\&prime;}---\left(10\right)$

represent w ' _mjthe opposite number of maximum, represent w ' _ilthe opposite number of maximum;

2) kth step iteration:

$m_{T_i\&RightArrow;x_{ij}}^{\left(0\right)}=-\underset{m\&NotEqual;j}{max}\{m_{B_m\&RightArrow;x_{im}}^{(k-1)}+w_{im}^{\&prime;}\}---\left(11\right)$

$m_{B_j\&RightArrow;x_{ij}}^{\left(0\right)}=-\underset{l\&NotEqual;i}{max}\{m_{T_l\&RightArrow;x_{lj}}^{(k-1)}+w_{lj}^{\&prime;}\}---\left(12\right)$

3) after kth step iteration, calculate:

$M_{ij}^{\left(k\right)}=m_{T_i\&RightArrow;x_{ij}}^{\left(k\right)}+m_{B_j\&RightArrow;x_{ij}}^{\left(k\right)}+w_{ij}^{\&prime;}---\left(13\right)$

Iteration result based on kth step estimates x _ijvalue: if otherwise

2. the wireless sensor network topology reconstructing method of center type as claimed in claim 1, it is characterized in that: after described stationary nodes is deployed, be in active state all the time, for obtaining the information of area to be monitored, can lose efficacy because of depleted of energy and external interference in network operation process; Described support node is in resting state with conserve energy when network initial deployment, transfers active state to when occurring that stationary nodes lost efficacy, for repairing the stationary nodes of inefficacy.

3. the wireless sensor network topology reconstructing method of center type as claimed in claim 1, is characterized in that: described convergence center, for obtaining network global information, comprises node present position, node operating state and the current network coverage; Described node operating state comprises active, dormancy or the three kinds of states that lost efficacy.

4. the wireless sensor network topology reconstructing method of center type as claimed in claim 1, is characterized in that: the network coverage is defined as allly enlivening the coverage of stationary nodes and the ratio of whole network coverage, that is:

$c_r=\frac{S_s}{S}\&times;100\%---\left(1\right)$

Wherein, S _srepresent all area coverages enlivening stationary nodes, S represents the scope of area to be monitored.