CN102761881A - Method for solving optimal coverage control set of static node in wireless sensor network - Google Patents

Abstract

The invention discloses a method for solving an optimal coverage control set of a static node in a wireless sensor network. With the adoption of the method provided by the invention, on the premise of keeping a certain coverage rate, a part of nodes enter a sleep state, so that the quantity of working nodes is reduced, the network energy consumption is reduced, and the network survival time is prolonged. Furthermore, a node set which has fewer working nodes, suitable sensing radius combination and low energy consumption, and meets certain coverage requirements can be found out by not considering communication and calculation energy consumption among nodes, considering energy consumption of a node sensing module, and using a property that the nodes have adjustable sensing radii. Three sub-functions, namely, energy consumption of the network node sensing module, a network coverage rate and a network node sleep rate, can be established, and a fitness function of a genetic algorithm is commonly formed by the three sub-functions; and the model is solved by using the genetic algorithm. An optimal working node combination with a large coverage range, fewer working nodes and low energy consumption, and an optimal sensing radius combination of the working nodes can be obtained.

Description

The optimum Coverage Control collection of wireless sensor network static node method for solving

Technical field

The present invention relates in the wireless sensor network, the method for solving based on the optimum Coverage Control collection of static node belongs to sensor technology, wireless communication technology field.

Background technology

Wireless sensor network is by the finite energy that is distributed in a large number in the monitored area, and has the microsensor node of perception, calculating and communication capacity, the wireless network that constitutes through the self-organizing mode.Along with the fast development of technology such as compunication, integrated circuit, the extensive use of wireless sensor network has become possibility.But before concrete the application, must confirm the deployment scheme of sensor node according to the certain applications environmental criteria, a kind of situation is that sensor node is static, lays particular emphasis on according to the monitored area how rationally to lay node or scheduling node operating state.A kind of in addition situation is that the node in the network moves, and how mainly to study the optimized nodes layout.Coverage Control is mainly studied both of these case as a basic problem in the wireless sensor network, is promptly guaranteeing how to realize the maximization of network coverage, so that reliable Monitoring Service to be provided under certain service quality prerequisite.

Because the common price of mobile node is comparatively expensive; For the covering performance that guarantees network with control cost; Lay the zone of node for being difficult for certainty; Often in the monitored area, lay the static sensor nodes in a large number, and node distribution has randomness usually, can occur overlapping between the sensing scope of many nodes.In this case; Regular meeting causes certain point of monitored area or certain zone to be monitored by a plurality of node simultaneously; Data meeting height correlation, redundancy that the close node in position was collected are high; Cause node when Data transmission, can comprise bulk redundancy information, and the extra increase energy consumption of redundant data meeting; In addition, the working node number that is positioned at the same area is many more, and channel competition will be fiercer, and the possibility of data packet collisions is just big more.

Therefore, be necessary to make the stronger node alternation of correlation, thereby reduce additional energy consumption as much as possible, reduce working node density, avoid communication contention aware, thereby prolong network life through the dormancy/operating state of scheduling node.The wireless sensor network optimal control to disposing at random just under the prerequisite that guarantees certain covering performance, reduces the working node number, seeks the covering combination of an optimum.

Wireless sensor node energy consumption module comprises sensor assembly, processor module and wireless communication module, and along with the development of integrated circuit technique, it is very low that the power consumption of processor and sensor assembly becomes, and most of energy consumption is on wireless communication module.

Summary of the invention

The objective of the invention is defective, the optimum Coverage Control collection of a kind of wireless sensor network static node method for solving is provided to the prior art existence.

The optimum Coverage Control collection of wireless sensor network static node of the present invention method for solving, said method is following:

Node S in the wireless sensor network _iCoordinate be (x _i, y _i), the coordinate of arbitrfary point p is (x in the two dimensional surface monitored area _p, y _p), node n then _iDetection probability to impact point p is:

$C_p(n_i,p)=\left\{\begin{array}{cc}1,& \mathrm{ifd}(n_i,p)\&le;R_s-R_e\\ e^{(-{\mathrm{\&lambda;}}_1{\mathrm{\&alpha;}}_1^{{\mathrm{\&beta;}}_1}/({\mathrm{\&alpha;}}_2^{{\mathrm{\&beta;}}_2}+{\mathrm{\&lambda;}}_2)),}& \mathrm{if}{R}_s-R_e<d(n_i,p)<R_s+{\mathrm{<figure-callout\; id="0"\; label="R\; e"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">R</figure-callout>}}_e\\ 0,& \mathrm{otherwise}\end{array}\right.$

Wherein, d (n _i, p) be sensor node n _iEuclidean distance with impact point p; R _e(0<r _e<r _s) be sensing node reliable measurement property parameter; α ₁=R _e-R _s+ d (n _i, p), α ₂=R _e+ R _s-d (n _i, p); λ ₁, λ ₂, β ₁, β ₂Be the measurement parameter relevant with the sensing node characteristic;

Therefore, n sensor node in the whole two dimensional surface monitored area to the joint-detection probability of impact point p is:

$C_p(n_{\mathrm{all}},p)=1-\underset{i=n}{\mathrm{\&Pi;}}(1-C_p(n_i,p))---\left(1\right)$

Wherein, n _AllBe the sensor node set of measuring target point, the joint-detection probability is not less than the threshold value c that sets according to network demand _Th, then impact point can be by effective detected condition:

$\underset{x_p,y_p}{\min }\left\{C_p(n_{\mathrm{all}},p)\right\}\&GreaterEqual;C_{\mathrm{th}}---\left(2\right)$

Area dividing to be measured is become m * n grid, again cell is reduced to pixel, the network coverage is defined as the ratio that the cell quantity that satisfies formula (2) requirement accounts for total cell quantity, that is:

$C_r=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(n_{\mathrm{all}},p)}{m\&times;n}---\left(3\right)$

According to formula (2) and formula (3), can obtain network coverage function f ₁:

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(S^{\&prime;},p)}{m\&times;n}---\left(4\right)$

Wherein, the monitored area is divided into m * n grid cell, and some p joint-detection probability must be greater than probability threshold value c in the monitored area _ThJust can be calculated in the network coverage.

Node dormancy rate function f ₂:

$f_2=\frac{\left|S\right|-\left|S^{\&prime;}\right|}{\left|S\right|}---\left(5\right)$

Wherein | S ' | the node number of expression work, | the total node number of S| for laying;

In the node of in the monitored area, laying, the working node set is N={n ₁, n ₂... n _n, node sensing radius does Wherein

Expression node n _iThe sensing radius, and Expression node n _iArea coverage,

Expression node n _iEnergy consumption;

The area coverage of working node is that the union of all working node area coverage is:

${\mathrm{<figure-callout\; id="1"\; label="S\; n"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">S</figure-callout>}}_{n_{}}\&cup;S_{n_2}\&cup;...\&cup;S_{n_n}=\underset{i=1}{\overset{n}{\&cup;}}{S}_{n_i}$

The average energy consumption of overlay area is:

$\stackrel{\&OverBar;}{E}=\frac{{\mathrm{<figure-callout\; id="1"\; label="E\; n"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">E</figure-callout>}}_{n_{}}+E_{n_2}+...+E_{n_{\mathrm{<figure-callout\; id="1"\; label="n\; S\; n"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">n</figure-callout>}}}}{S_{n_{}}}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{R}_{{\mathrm{sn}}_i}}{\underset{i=1}{\overset{n}{\&cup;}}{S}_{n_i}}u$

The overlay area average energy mouse function f of the covering consumption of whole wireless sensor network is described ₃For:

$f_3=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{R}_{{\mathrm{sn}}_i}^2/S\_\mathrm{work}$

Wherein,

Expression working node n _iThe sensing radius, S_work representes working node set institute region covered area; The overall goal function is:

f=w ₁f ₁+w ₂f ₂-w ₃f ₃ (7)

Wherein, w ₁+ w ₂+ w ₃=1, overall goal functional value f is worth greatly more between 0～1, shows that the coverage optimization effect is excellent more.

Distribute for highdensity node in the monitored area, so-called optimum covering set is meant and can keeps the impregnable minimum node set of the whole network coverage.This node set can farthest cover should the zone, and the node beyond this subclass all can be in the dormant state of low-power consumption.

The present invention is based on the consideration of energy efficient, the network coverage, Coverage Control in Wireless Sensor Networks is optimized, foundation is the regional coverage optimization model of purpose with energy efficient with satisfying certain covering requirement.On the basis that guarantees certain coverage rate, make a part of redundant node get into the low-power consumption resting state, form and cover optimum set of node.The search mission of node is exactly from a large amount of sensor nodes, to select one group of optimum node, utilizes this model of genetic algorithm for solving.

Further; Do not consider inter-node communication and calculating energy consumption, only consider the energy consumption of node sensing module, utilize node to have the attribute of scalable sensing radius; It is few to seek one group of working node number; Sensing radius combination simultaneously is suitable, and energy consumption is low, and satisfies certain node set that requires that covers.Network node sensing module energy consumption, the network coverage have been set up; And 3 subfunctions of network node dormancy rate; Constitute the fitness function of genetic algorithm jointly by these 3 subfunctions; Adopt this model of genetic algorithm for solving, obtained an optimum working node combination that coverage is big, the working node number is few and energy consumption is low and the optimum sensing radius of working node and made up.

Description of drawings

Fig. 1 genetic algorithm flow process;

Fig. 2 sketch map of encoding.

Embodiment

Optimum covering set based on genetic algorithm

According to the characteristics of wireless sensor network, suppose:

1) the capable switch operating/resting state of node in the network, and comprise a Centroid in the network, Centroid has stronger data processing and computing capability, is used to realize wireless sensor network node selection optimization;

2) positional information of each node in the network can be obtained through certain mode;

3) each node in the network has identical primary power, perception radius R _sWith communication radius R _c, and R is arranged _c=2R _s

Suppose in the monitored area, to dispose N node at random, use n _iRepresent i node in the wireless sensor network, then node set is S={n ₁, n ₂, n ₃..., n _N.The monitored area is divided into grid point, and the coordinate of establishing arbitrary mess point p in the zone is (x _p, y _p), ask a working node subclass S ', make network coverage Cr (S ') maximum and working node number | S ' | minimum.Be converted into function representation, just keep the coverage rate function f ₁Value maximum, node dormancy rate function f simultaneously ₂Also big.

1. fitness function

Fitness value promptly is to calculate the resulting value of fitness function, and its size is by the foundation of upgrading individual extreme value in the genetic algorithm.In the process of wireless sensor network coverage optimization, fitness function is the judgement of optimization searching, is link maximum in the operand.

Adopt node Probability Detection model probability to come the computing network coverage rate as measurement model.If the node s in the wireless sensor network _iCoordinate be (x _i, y _i).The coordinate of supposing arbitrfary point p in the two dimensional surface monitored area is (x _p, y _p), node n then _iDetection probability to impact point p is:

$C_p(n_i,p)=\left\{\begin{array}{cc}1,& \mathrm{ifd}(n_i,p)\&le;R_s-R_e\\ e^{(-{\mathrm{\&lambda;}}_1{\mathrm{\&alpha;}}_1^{{\mathrm{\&beta;}}_1}/({\mathrm{\&alpha;}}_2^{{\mathrm{\&beta;}}_2}+{\mathrm{\&lambda;}}_2)),}& \mathrm{if}{R}_s-R_e<d(n_i,p)<R_s+{\mathrm{<figure-callout\; id="0"\; label="R\; e"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">R</figure-callout>}}_e\\ 0,& \mathrm{otherwise}\end{array}\right.$

Wherein, d (n _i, p) be sensor node n _iEuclidean distance with impact point p; R _e(0<r _e<r _s) be sensing node reliable measurement property parameter; α ₁=R _e-R _s+ d (n _i, p), α ₂=R _e+ R _s-d (n _i, p); λ ₁, λ ₂, β ₁, β ₂Be the measurement parameter relevant with the sensing node characteristic.

Therefore, n sensor node in the whole two dimensional surface monitored area to the joint-detection probability of impact point p is:

$C_p(n_{\mathrm{all}},p)=1-\underset{i=n}{\mathrm{\&Pi;}}(1-C_p(n_i,p))---\left(1\right)$

Wherein, n _AllSensor node set for measuring target point.To cover requirement in order satisfying, to require the joint-detection probability to be not less than the threshold value c that sets according to network demand usually _Th, then impact point can be by effective detected condition:

$\underset{x_p,y_p}{\min }\left\{C_p(n_{\mathrm{all}},p)\right\}\&GreaterEqual;C_{\mathrm{th}}---\left(2\right)$

The wireless sensing node monitored area of laying at random is normally irregular, can't directly find the solution the area coverage of network with analytic method.For effective evaluation network coverage performance, adopt gridding method that area dividing to be monitored is become grid, just cell is reduced to a little again, analyzes the coverage rate of each wireless sensor node to this point, and wherein the distance between adjacent mesh is determined by covering precision.

Suppose area dividing to be measured is become m * n grid, again cell is reduced to pixel.Among the present invention, the network coverage is defined as the ratio that the cell quantity that satisfies formula (2) requirement accounts for total cell quantity, that is:

$C_r=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(n_{\mathrm{all}},p)}{m\&times;n}---\left(3\right)$

According to formula (2) and formula (3), can obtain network coverage function f ₁:

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(S^{\&prime;},p)}{m\&times;n}---\left(4\right)$

Wherein, the monitored area is divided into m * n grid cell, and some p joint-detection probability must be greater than probability threshold value c in the monitored area _ThJust can be calculated in the network coverage.

Node dormancy rate function f ₂:

$f_2=\frac{\left|S\right|-\left|S^{\&prime;}\right|}{\left|S\right|}---\left(5\right)$

Wherein | S ' | the node number of expression work, | the total node number of S| for laying, in order these two subfunctions to be converted to max function, so definition overall goal function is:

f=w ₁f ₁+w ₂f ₂ (6)

W wherein ₁And w ₂Be the corresponding weights of sub-goal function, sum of the two is 1.Overall goal functional value f is worth greatly more between 0～1, shows that the coverage optimization effect is excellent more.Target function f in the formula (6) directly as the fitness function of GA, and is adopted the criterion that is the bigger the better.

2. encode

To the characteristics of node random distribution in the wireless sensor network, adopt the binary coding mode, this is that coding and decoding is simple to operate comparatively speaking because of binary coding, intersection, variation etc. also are convenient to realize.With a string binary coding a _i={ a ₁, a ₂..., a _NRepresent the whether selected situation of node in the network, and the selection situation of node is individual corresponding each other with chromosome, and 1 this locational node of expression is chosen as working node, and 0 representes not choose.

If population is made up of the M individuals, N node arranged in the monitored area, the initialization population is 0/1 coding:

$p\begin{array}{}\end{array}=\left\{\begin{array}{cccc}{a}_{11}& a_{12}& ...& a_{1N}\\ a_{21}& a_{22}& ...& a_{2N}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_{M1}& a_{M2}& ...& a_{\mathrm{MN}}\end{array}\right\}$

3. algorithm operating

In the optimized Algorithm that the present invention proposes, it is individual that selection operation adopts roulette method commonly used to select; The employing single-point intersects; For the gene that guarantees parents obtains keeping as much as possible, adopt the method for circulation reorganization in filial generation; In addition, if offspring's adaptation functional value surpasses substituted individuality, operation takes place then to replace.Particular flow sheet is as shown in Figure 1.

The optimum covering set that node sensing radius is adjustable

Consider a large amount of sensor nodes, be deployed in the target monitoring zone at random.Set up a kind of dispatching method, let and wherein have only the node of minority in running order, and other node all is in resting state.On this basis, utilize node to have the attribute of scalable sensing radius, target is that will to set up one group of working node number few, and sensing radius combination simultaneously is suitable, and energy consumption is low, and satisfies certain node set that requires that covers.

The present invention adopts energy consumption model, only considers the energy consumption of node sensing module, does not consider communication and calculating energy expense.When the perception radius of node was zero, the energy consumption of this node also was zero.According to the different energy consumption models, the energy consumption of the sensing module of a working node is proportional to R _s ²Or R _i ⁴, R _sSensing radius for working node.Among the present invention, be u*R with the energy consumption of sensing module _s ²Example, u is a constant.

In the node of supposing in the monitored area, to lay, the working node set is N={n ₁, n ₂... n _n, node sensing radius does

Wherein

Expression node n _iThe sensing radius, and

Expression node n _iArea coverage,

Expression node n _iEnergy consumption.

The area coverage of working node is that the union of all working node area coverage is:

${\mathrm{<figure-callout\; id="1"\; label="S\; n"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">S</figure-callout>}}_{n_{}}\&cup;S_{n_2}\&cup;...\&cup;S_{n_n}=\underset{i=1}{\overset{n}{\&cup;}}{S}_{n_i}$

The average energy consumption of overlay area is:

$\stackrel{\&OverBar;}{E}=\frac{{\mathrm{<figure-callout\; id="1"\; label="E\; n"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">E</figure-callout>}}_{n_{}}+E_{n_2}+...+E_{n_n}}{S_{n_1}\&cup;S_{n_2}\&cup;...\&cup;S_{n_n}}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{R}_{{\mathrm{sn}}_i}}{\underset{i=1}{\overset{n}{\&cup;}}{S}_{n_i}}u$

Therefore, can on the basis of formula (6), increase an overlay area average energy mouse function f ₃, be used to describe the covering consumption of whole wireless sensor network, be designated as:

$f_3=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{R}_{{\mathrm{sn}}_i}^2/S\_\mathrm{work}$

Wherein,

Expression working node n _iThe sensing radius, S_work representes working node set institute region covered area.In order to convert these 3 subfunctions to max function, so definition overall goal function is:

f=w ₁f ₁+w ₂f ₂-w ₃f ₃ (7)

In this wireless sensor network,, relate to the optimum sensing radius combination of optimum working node combination and working node with the fitness function of formula (7) as genetic algorithm; w ₁+ w ₂+ w ₃=1, w ₁, w ₂, w ₃Occurrence can confirm according to network coverage performance requirement.

Code Design

Same this model of genetic algorithm for solving that adopts; Adopt the binary coding form; Scope like

code length and node radius-adjustable; And the node number is relevant, and wherein the node radius converts binary-coded length to and is:

Wherein, R _Max, R _MinThe bound of expression node radius-adjustable.Suppose that network has N node, then each individual lengths in the colony is N*R_Bit+N, the encode series whether the 1st to N node in preceding N bit representation network of each individual coding selected, 1 this node of expression is selected, 0 represent not selected; Back N*R_Bit corresponding the radius code of network node, the radius code of node i is b _i={ b _I0b _I1B _{I (R_bit-1)}, length is the R_Bit position.Specifically as shown in Figure 2.

Each node radius can pass through computes:

$R_{\mathrm{si}}=R_{\min }+\frac{R_{\max }-R_{\min }}{2^{R\_\mathrm{Bit}}-1}\&CenterDot;\underset{b=0}{\overset{R\_\mathrm{Bit}-1}{\mathrm{\&Sigma;}}}{b}_{\mathrm{ib}}\&CenterDot;2^b$

Algorithm operating

The purpose of genetic manipulation is from initial population, to filter out than more excellent individuality to develop, and this just comprises that wherein duplicating excellent individual, two father's individualities carries out that single-point intersects and these three kinds of modes of variation of single body.To the progeny population after developing, be optimized criterion again and judge, so circulation is gone down, till reaching the termination Rule of judgment.Below main introduce when combining the coverage optimization problem three basic operations of genetic algorithm:

1. select

It is individual that the present invention adopts " roulette method " to select.After obtaining each individual fitness value, the ideal adaptation degree value in the whole colony is carried out normalization handle; Adding up then, it selects probable value, during each is taken turns, through producing [0,1] interior random number as pointer, confirms the individuality of selecting.

2. intersect

For the gene that guarantees parents obtains keeping as much as possible in filial generation, adopt the method for circulation reorganization, as choose m parent individual { 1,2; I ..., m} selects (1 for the first time; 2), select for the second time (2,3), select individual i of parent and parent individuality i+1 to carry out the single-point intersection the i time as parents.

Producing one [1,8] interior integer at random as the position, crosspoint, is 3 such as the position, crosspoint, then exchanges since the individual coding of 4 parents, obtains i and sub individual i+1.

3. variation

In mutation operation, different aberration rates is adopted in the radius combination of selecting node and node respectively, carry out mutation operation; The former aberration rate is bigger; Be in order to increase new individuality as far as possible, and the latter is the radius combination, aberration rate is a little bit smaller to be in order to reduce arithmetic cost; Because might corresponding node do not have selectedly, the change of its radii size then have much meanings.Such as, select 2 operating positions 3 and 8 at random, corresponding codes counter-rotating separately becomes 1,1 as 0 and becomes 0.

In addition, if in iterative process, the optimal solution of preservation is not upgraded, then with the individual directly replacement n+1 with high fitness value of n in generation in the minimum individuality of fitness value.The individuality that fitness is high is directly delivered among the next generation, avoid can not genetic replication situation.

When algorithm runs to set in advance greatest iteration algebraically; Algorithm stops; The maximum chromosome of fitness this moment is the approximate optimal solution of being asked, then to its wireless sensor network node and their each self-corresponding induction radius of decoding and just can obtain choosing.

Claims (5)

1. the optimum Coverage Control collection of wireless sensor network static node method for solving is characterized in that said method is following:

Node n in the wireless sensor network _iCoordinate be (x _i, y _i), the coordinate of arbitrfary point p is (x in the two dimensional surface monitored area _p, y _p), node n then _iDetection probability to impact point p is:

$C_p(n_i,p)=\left\{\begin{array}{cc}1,& \mathrm{ifd}(n_i,p)\&le;R_s-R_e\\ e^{(-{\mathrm{\&lambda;}}_1{\mathrm{\&alpha;}}_1^{{\mathrm{\&beta;}}_1}/({\mathrm{\&alpha;}}_2^{{\mathrm{\&beta;}}_2}+{\mathrm{\&lambda;}}_2)),}& \mathrm{if}{R}_s-R_e<d(n_i,p)<R_s+R_e\\ 0,& \mathrm{otherwise}\end{array}\right.$

Wherein, d (n _i, p) be sensor node n _iEuclidean distance with impact point p; R _e(0<r _e<r _s) be sensing node reliable measurement property parameter; α ₁=R _e-R _s+ d (n _i, p), α ₂=R _e+ R _s-d (n _i, p); λ ₁, λ ₂, β ₁, β ₂Be the measurement parameter relevant with the sensing node characteristic;

Therefore, n sensor node in the whole two dimensional surface monitored area to the joint-detection probability of impact point p is:

$C_p(n_{\mathrm{all}},p)=1-\underset{i=n}{\mathrm{\&Pi;}}(1-C_p(n_i,p))---\left(1\right)$

Wherein, n _AllBe the sensor node set of measuring target point, the joint-detection probability is not less than the threshold value c that sets according to network demand _Th, then impact point can be by effective detected condition:

$\underset{x_p,y_p}{\min }\left\{C_p(n_{\mathrm{all}},p)\right\}\&GreaterEqual;C_{\mathrm{th}}---\left(2\right)$

Area dividing to be measured is become m * n grid, again cell is reduced to pixel, the network coverage is defined as the ratio that the cell quantity that satisfies formula (2) requirement accounts for total cell quantity, that is:

$C_r=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(n_{\mathrm{all}},p)}{m\&times;n}---\left(3\right)$

According to formula (2) and formula (3), can obtain network coverage function f ₁:

$f_1=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(S^{\&prime;},p)}{m\&times;n}---\left(4\right)$

Wherein, the monitored area is divided into m * n grid cell, and some p joint-detection probability must be greater than probability threshold value c in the monitored area _ThJust can be calculated in the network coverage.

Node dormancy rate function f ₂:

$f_2=\frac{\left|S\right|-\left|S^{\&prime;}\right|}{\left|S\right|}---\left(5\right)$

Wherein | S ' | the node number of expression work, | the total node number of S| for laying;

In the node of in the monitored area, laying, the working node set is N={n ₁, n ₂... n _n, node sensing radius does

Wherein

Expression node n _iThe sensing radius, and

Expression node n _iArea coverage, Expression node n _iEnergy consumption;

The area coverage of working node is that the union of all working node area coverage is:

$S_{n_1}\&cup;S_{n_2}\&cup;...\&cup;S_{n_n}=\underset{i=1}{\overset{n}{\&cup;}}{S}_{n_i}$

The average energy consumption of overlay area is:

$\stackrel{\&OverBar;}{E}=\frac{E_{n_1}+E_{n_2}+...+E_{n_n}}{S_{n_1}\&cup;S_{n_2}\&cup;...\&cup;S_{n_n}}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{R}_{{\mathrm{sn}}_i}}{\underset{i=1}{\overset{n}{\&cup;}}{S}_{n_i}}u$

The overlay area average energy mouse function f of the covering consumption of whole wireless sensor network is described ₃For:

$f_3=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{R}_{{\mathrm{sn}}_i}^2/S\_\mathrm{work}$

Wherein,

Expression working node n _iThe sensing radius, S_work representes working node set institute region covered area; The overall goal function is:

f=w ₁f ₁+w ₂f ₂-w ₃f ₃ (7)

Wherein, w ₁+ w ₂+ w ₃=1, overall goal functional value f is worth greatly more between 0～1, shows that the coverage optimization effect is excellent more.

2. the optimum Coverage Control collection of wireless sensor network static node according to claim 1 method for solving; It is characterized in that with the fitness function of said overall goal function genetic algorithm comprises that duplicating excellent individual, two father's individualities carries out that single-point intersects and these three kinds of modes of variation of single body as genetic algorithm.

3. based on the optimum Coverage Control collection of the described wireless sensor network static node of claim 2 method for solving; It is characterized in that adopting " roulette method " to select individuality the said excellent individual of duplicating: after obtaining each individual fitness value, the ideal adaptation degree value in the whole colony is carried out normalization handle; Adding up then, it selects probable value, during each is taken turns, through producing [0,1] interior random number as pointer, confirms the individuality of selecting.

4. the optimum Coverage Control collection of wireless sensor network static node according to claim 2 method for solving is characterized in that said two father's individualities are carried out the method that the single-point cross method adopts the circulation reorganization.

5. the optimum Coverage Control collection of wireless sensor network static node according to claim 2 method for solving; It is characterized in that the variation with said single body: different aberration rates is adopted in the radius combination to selecting node and node respectively; Carry out mutation operation, the former aberration rate is greater than the latter's aberration rate.

Images