CN114205849A - Wireless sensor network node credible coverage deployment optimization method based on integer programming - Google Patents
Wireless sensor network node credible coverage deployment optimization method based on integer programming Download PDFInfo
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Abstract
The invention discloses a wireless sensor network node credible coverage deployment optimization method based on integer programming, which comprises the following steps: (1) the method for formulating the air pollution sensor deployment optimization model by combining the credible information coverage and integer linear programming comprises the following substeps: (1.1) carrying out grid discretization on a map by taking given urban air pollution map data as input to obtain a group of regional point sets P to be deployed; (1.2) constructing an air pollution sensor deployment optimization model based on trusted information coverage, designing estimation errors and interpolation by using the urban air pollution data set in the step (1.1), defining air pollution sensor coverage constraints and network connectivity constraints by combining air pollution specific scene parameters, and formulating the deployment optimization model of air pollution deployment by using an integer linear programming method; (2) and respectively carrying out optimization solution on the two integer linear plans by using a variable linear relaxation method and a binary search method. The invention has low deployment cost, high efficiency and strong universality.
Description
Technical Field
The invention belongs to the field of wireless sensor networks, and particularly relates to a wireless sensor network node credible coverage deployment optimization method based on integer programming.
Background
Along with the increasing environmental pollution, the urban monitoring demand for air pollution is gradually increased. Furthermore, air pollution is becoming a major threat to human health in urban environments, and effective monitoring of pollutant emissions is at the heart of many sustainable development efforts. The wireless sensor network is widely applied to environmental application and aims to sense physical phenomena such as temperature, humidity and air pollution. In this application environment, the use of wireless sensor networks enables us to understand the changes of the phenomenon in the monitored area, and to make appropriate decisions about the influence of the phenomenon. Deployment optimization is a major challenge in wireless sensor network design. The problem is how to determine the optimal locations of sensors and receivers, ensuring network connectivity and coverage quality, while optimizing objective functions such as deployment costs. Due to the particularity of a monitoring area and the influence of the environment, the monitoring is not accurate enough due to too few deployed sensors, and the redundancy of the nodes is caused due to too many deployed sensors. Therefore, it is particularly important how to accurately deploy the air pollution sensor nodes at minimum cost. In recent years, most of deployment research aiming at wireless sensor networks is based on a disk coverage model, and spatial correlation and information synergy among sensor nodes are not explored, so that redundancy is generated among the sensor nodes. The deployment of the air pollution sensor has special environmental requirements, physical conditions such as wind speed and temperature have great influence on the monitoring of the air pollution concentration, the deployment conditions under multiple scenes are not considered in the conventional sensor deployment method, and certain defects exist in coverage precision, so that the air pollution cannot be accurately monitored.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a wireless sensor network node credible coverage deployment optimization method based on integer programming, aiming at improving the coverage rate of an air pollution sensor and reducing the coverage cost by combining credible information coverage and utilizing the space correlation of air pollution concentration in an area to be deployed and the information synergistic effect among sensor nodes; an integer linear programming model under a large-scale scene is solved through a heuristic algorithm based on variable linear relaxation and binary search, an optimal deployment position is obtained, and therefore the technical problem of deployment of the air pollution sensor in the wireless sensor network is solved.
In order to achieve the above object, according to an aspect of the present invention, there is provided a method for optimizing trusted coverage deployment of a wireless sensor network node based on integer programming, the method including the following steps:
(1) the method for formulating the air pollution sensor deployment optimization model by combining the credible information coverage and integer linear programming comprises the following substeps:
(1.1) taking given urban air pollution map data as input, carrying out grid discretization on the map to obtain a group of region point sets P to be deployed, taking each discrete point P belonging to P as a region point to be deployed, and taking a decision variable xpAnd ypTo respectively specify whether to deploy a sensor node or a sink node at a point p, and only one sensor node or sink node can be deployed at the same point x to be deployedp+yp≤1,p∈P；
(1.2) constructing an air pollution sensor deployment optimization model based on trusted information coverage, designing estimation errors and interpolation by using the urban air pollution data set in the step (1.1), defining air pollution sensor coverage constraints and network connectivity constraints by combining air pollution specific scene parameters, and formulating the deployment optimization model of air pollution deployment by using an integer linear programming method;
(1.2.1) inputting the urban air pollution data into an atmospheric diffusion simulator to obtain the simulated air pollution concentration A of the deployment areapThe meteorological physical parameters and the pollutant discharge parameters directly influence the magnitude of the simulated air concentration, and the simulated air pollution concentration ApWith true air pollution concentration RpAnalog error of (A)p-Rp∈[-ap,ap]Combined with measurement of air pollution concentration McpConcentration of true air pollutionDegree RpSensor transmission error Mcp-Rp∈[-tp,tp]To obtain the simulated air pollution concentration ApAnd measuring air pollution concentration McpError range of (Mc)p-Ap∈[-tp-ap,tp+ap]；
(1.2.2) obtaining the covering quality of the air pollution sensor according to tolerance estimation errors, obtaining a variation function under an air pollution scene after considering the wind speed and the wind direction, combining a kriging interpolation, and constructing a linear kriging system by using a Lagrange multiplier method according to the linear unbiased characteristic of the kriging interpolation;
(1.2.3) dividing the deployment area into a plurality of representative reconstruction neighborhoods according to the variation, obtaining an interpolation weight value of an estimation error of the undeployed sensor area by using the Kriging linear system in the step (1.2.2), obtaining an estimation concentration of the undeployed area by using the interpolation weight value, and establishing the coverage quality of the sensor network under multiple scenes by using a credible information coverage model as a basic coverage model;
(1.2.4) constructing network connectivity such that each deployed sensor is capable of generating a flow unit when transmitting information in the network, and all flow units in the sensor network are capable of being received by the sink node;
(1.2.5) taking the sensor network coverage requirement in the step (1.2.3) and the sensor network connectivity requirement in the step (1.2.4) as constraint conditions of integer linear programming taking the deployment cost as an optimization target;
(1.2.6) taking the deployment cost and the connectivity requirement of the sensor network in the step (1.2.4) as constraint conditions of integer linear programming taking the network coverage quality as an optimization target;
(2) respectively carrying out optimization solution on two integer linear plans by using a variable linear relaxation and binary search method, and comprising the following substeps:
(2.1) linearly relaxing decision variables of the integer linear programming taking the deployment cost as the optimization target in the step (1.2.5) into decimal numbers, and solving the deployment positions of the linear programming updating nodes through multiple iterations to obtain an approximate solution of the integer linear programming taking the deployment cost as the optimization target;
(2.2) subdividing the integer linear plan of the given deployment budget in the step (1.2.6) by utilizing binary search to tolerate estimation errors in a given threshold range, and obtaining an approximate solution of the integer linear plan of the given deployment budget when the error range reaches the given threshold range.
In an embodiment of the present invention, the step (1.2.2) is specifically:
maximum tolerance estimation error phi for deploying air pollution sensors to cover qualitypThe construction is carried out, and the calculation formula is as follows:
Φp＝UB(|Mcp-Ecp|)
estimated error EcpCan be expressed as a weighted average, Ec, of the measured values of the nodes in the reconstructed neighborhood point set S in the region to be deployed according to the Krigin interpolationpThe calculation formula is as follows:
wherein, ΛiRefers to the interpolation weight value, and the weight lambada in the formula is based on the linear unbiased condition of common krigingiThe sum being equal to 1, i.e.
In order to obtain the optimal weight coefficient, the Lagrange multiplier method is used for converting the weight coefficient lambdaiMinimizing, for n +1 unknowns, a linear kriging system consisting of n +1 equations can be obtained, the expression being as follows:
wherein n is the number n ═ S (p) of points to be deployed in the reconstruction neighborhood, γ is a Gaussian variation function combined with an air pollution coefficient w, and the air pollution coefficient w is determined by the wind speed
And wind directionIncluded angle
Calculated, the formula is as follows:
wherein d represents the Euclidean distance between two sensors, C0+ C is called the base value and a is the range.
In an embodiment of the present invention, the step (1.2.3) is specifically:
dividing a square of a deployment region with variable range a as side length to obtain a group of representative reconstruction point sets CS, and obtaining a plurality of reconstruction neighborhood point sets S (p) with each reconstruction point as a center, wherein the variable range a is twice of the communication range of the air pollution sensor, and the minimum weight coefficient Lambda obtained by a Kriging system in the step (1.2.2)iCalculating the estimation error EcpThe quality of coverage is defined using a trusted information coverage model from the point of view of information reconstruction and estimation, i.e. the estimation error is less than or equal to a given threshold epsilon for a given kriging interpolationpIs considered to be covered by the trust, the coverage quality constraint based on the trust information coverage model is defined as:
|Mcp-Rp|≤εp
by simulating the air pollution concentration ApSensor transmission error tpAnd simulation error a of atmosphere simulatorpThe measured value of the air pollution concentration is represented, and then the maximum tolerance error is linearly relaxed, so that a coverage quality definition based on a credible information coverage model is obtained, and the formula is as follows:
wherein xp,ypAnd S (p) is a reconstructed neighborhood point set.
In an embodiment of the present invention, the step (1.2.4) is specifically:
utilizing network flows to construct a network connectivity problem, a sensor node can transmit flow units to neighboring nodes within its communication range, constructing the following network connectivity constraints:
fpq≤N*(yp+xp*Cpq),(p,q)∈Ψ(p)
fpq≤N*(yp+xq*Cpq),(p,q)∈Ψ(p)
where Ψ (p) is a neighboring node within communication range of the point p deployed sensor, CpqFor the adjacency matrix between the sensors disposed at points p and q, the adjacency matrix C is formed if the two sensors disposed at points p and q can communicatepq1, if two sensors cannot communicate, the adjacency matrix CpqIs 0, fpqThe number of flow units generated in the process of transmitting the collected information from the sensor of the deployment point p to the sensor of the deployment point q, N is the total number of the nodes of the area to be deployed, and is used for converging the node ypAll flow units sent by the whole sensor network can be accepted, and the following network connectivity requirements are constructed:
in an embodiment of the present invention, the step (1.2.5) is specifically:
will deploy cost
As an optimization target, where δpIn order to deploy the deployment cost of a common sensor,
to deploy a sink node sensorThe cost of deployment of the device;
and (4) obtaining a coverage constraint according to the coverage quality definition in the step (1.2.3):
wherein xp,ypRespectively, a decision variable representing whether a sensor node or a sink node is deployed at point p, ApIs the simulated air pollution concentration generated by an atmospheric diffusion simulator, apIs the simulation error generated by the simulator, tpIs the transmission error of the information transmitted between the sensors, ΛiIs the optimal interpolation weight in the kriging interpolation, and S (p) is a reconstruction neighborhood point set taking each reconstruction point CS as a central point;
integrating the following network connectivity constraints according to the network connectivity requirements in step (1.2.4):
fpq≤N*(yp+xp*Cpq),(p,q)∈Ψ(p)
fpq≤N*(yp+xq*Cpq),(p,q)∈Ψ(p)
where Ψ (p) is a neighboring node within communication range of the point p deployed sensor, CpqFor the adjacency matrix disposed between the sensors at points p and q, fpqThe number of flow units generated in the process of transmitting the collected information from the sensor of the deployment point p to the sensor of the deployment point q is N, and N is the total number of nodes of the area to be deployed.
In an embodiment of the present invention, the step (1.2.6) is specifically:
converting the integer linear programming optimization target in the step (1.2.5) from the deployment cost zeta to the maximum tolerance estimation error epsilon, and obtaining the integer linear programming with the deployment budget and the network connectivity as constraints and the network coverage quality as the optimization target;
obtaining a deployment cost constraint according to the budget:
ζ≤F
and F is a deployment budget, and an integer linear programming which takes the coverage quality as a target and takes the deployment cost and the network connectivity as constraints is obtained by combining the network connectivity constraint conditions in the step (1.2.5).
In an embodiment of the present invention, the step (2.1) specifically includes:
when the integer linear programming of the step (1.2.5) is applied to a large-scale scene, the decision variable x of the integer linear programming taking the deployment cost as the optimization target in the step (1.2.5) is usedp,ypRelaxed from {0,1} to [0,1 ]]Converting the integer linear programming into solving linear programming, and solving the decision variable x closest to 1 in the solution of the linear programming each timepSet to 1 as the constraint for the next linear program, repeat the operation until all decision variables xp,ypAnd changing to 0 or 1 to stop iteration so as to obtain the approximately optimal solution of the integer linear programming.
In an embodiment of the present invention, the step (2.2) is specifically:
when the integer linear programming of step (1.2.6) is applied to a large-scale scene, the binary search is carried out on [ Low, Upp ]]And (3) taking the binary value V ═ Low + Upp)/2 as the deployment cost xi of the solution corresponding to the maximum tolerance estimation error in the step (2.1)vThe deployment cost xi of the step (2.1) under the two-point value V isvXi, compared to the budget FvIf > F, the new dichotomy value Vnew(V + Low)/2, whereas VnewRepeat the binary operation until the maximum tolerated estimation error range [ V, V ] is 2 (V + Upp)/2new]Size of | V-VnewStopping if l is less than we given the threshold TH,obtaining an approximate maximum tolerated estimation error ε for the deployment cost J calculated using step (2.1), where Low is 0 and Upp ≦ Ap+2*ap。
Generally, compared with the prior art, the technical scheme of the invention has the following beneficial effects:
(1) the deployment cost is low: according to the method, the coverage quality of the network nodes of the air pollution sensor is established from the perspective of credible information coverage, and the sensing capability of the sensor can be more fully exerted by utilizing the spatial correlation between the air pollution concentrations of the area to be deployed and the information cooperation between the air pollution sensor nodes, so that the deployment cost is reduced;
(2) the efficiency is high: the method solves the integer linear programming in a large-scale scene by a heuristic method of variable linear relaxation and binary search, and improves the solving efficiency;
(3) the universality is strong: the integral linear programming constraint condition provided by the invention is integrated aiming at the network coverage quality and the network connectivity, and multi-scene weather factors are considered in the constraint condition, so that the integral linear programming constraint condition can be used under various weather pollution conditions.
Drawings
Fig. 1 is a schematic flowchart of a wireless sensor network node trusted coverage deployment optimization method based on integer programming according to the present invention;
FIG. 2 is a diagram illustrating the effect of comparing the trusted information overlay with the pie overlay in an embodiment of the present invention;
FIG. 3 is a diagram of the deployment effect summarized in the natural deployment area by the method of the present invention;
FIG. 4 is another deployment effect diagram summarized in a natural deployment area using the method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The terms used in the present invention or related techniques will be explained first:
and (4) trusted information coverage: in a random spatial field, a reconstruction function f is given, if reconstruction information phi (x) on a spatial position point x in the spatial field is smaller than or equal to a threshold epsilon proposed by a network user in practical application, namely phi (x) is less than or equal to epsilon, the spatial position point x is called to be covered by credible information.
Integer linear programming: integer linear programming is a mathematical method that assists people in scientific management. The mathematical theory and method for researching the extreme value problem of the linear objective function under the linear constraint condition limit all or part of variables in the plan to be integers, if the variables are limited to the integers in the linear model, the integral linear plan is called.
And (3) relaxation: a planning problem that requires some or all of the decision variables to take integer values is called integer planning. The remaining plans made up of the objective functions and constraint conditions are made slack for the integer plan, regardless of the integer condition.
Lagrange multiplier method: is a method of finding an extremum of a multivariate function where the variable is constrained by one or more conditions. The method converts an optimization problem with n variables and k constraints into an extremum problem with an equation set of n + k variables, the variables of which are not subject to any constraints. This approach introduces a new scalar unknown, the lagrange multiplier: coefficients for each vector in a linear combination of gradients of the constraint equations.
As shown in fig. 1, the invention designs an integer programming based wireless sensor network node trusted coverage deployment optimization method, which includes the following steps:
(1) the method for formulating the air pollution sensor deployment optimization model by combining the credible information coverage and integer linear programming comprises the following substeps:
and (1.1) carrying out grid discretization on the map by taking given urban air pollution map data as input to obtain a group of region point sets P to be deployed. Each discrete point P E P is taken as a region point to be deployed. Will decide variable xpAnd ypTo respectively specify whether to deploy a sensor node or a sink node at a point p, and only one sensor node or sink node can be deployed at the same point x to be deployedp+yp≤1,p∈P。
(1.2) constructing an air pollution sensor deployment optimization model based on trusted information coverage, designing estimation errors and interpolation by using the urban air pollution data set in the step (1.1), defining air pollution sensor coverage constraints and network connectivity constraints by combining air pollution specific scene parameters, and formulating the deployment optimization model of air pollution deployment by using an integer linear programming method;
(1.2.1) inputting the urban air pollution data into an atmospheric diffusion simulator to obtain the simulated air pollution concentration A of the deployment areapAnd in the simulation process, the meteorological physical parameters and pollutant emission parameters directly influence the magnitude of the simulated air concentration. By simulating the air pollution concentration ApWith true air pollution concentration RpAnalog error of (A)p-Rp∈[-ap,ap]Combined with measurement of air pollution concentration McpWith true air pollution concentration RpSensor transmission error Mcp-Rp∈[-tp,tp]To obtain the simulated air pollution concentration ApAnd measuring air pollution concentration McpError range of (Mc)p-Ap∈[-tp-ap,tp+ap]；
(1.2.2) obtaining the covering quality of the air pollution sensor according to the tolerance estimation error, obtaining a variation function under the air pollution scene in consideration of wind speed and wind direction, and combining with a Krigin interpolation. According to the linear unbiased characteristic of the kriging interpolation, a linear kriging system is constructed by utilizing a Lagrange multiplier method;
the step (1.2.2) is specifically as follows:
the deployment coverage quality of the air pollution sensor is constructed by using the maximum tolerance estimation error, and the calculation formula is as follows:
Φp＝UB(|Mcp-Ecp|)
estimated error EcpCan be expressed as a weighted average, Ec, of the measured values of the nodes in the reconstructed neighborhood point set S in the region to be deployed according to the Krigin interpolationpThe calculation formula is as follows:
wherein, ΛiRefers to the interpolation weight values. According to the linear unbiased condition of common kriging, the weight Λ in the formulaiThe sum being equal to 1, i.e.
In order to obtain the optimal weight coefficient, the Lagrange multiplier method is used for converting the weight coefficient lambdaiAnd (4) minimizing. For n +1 unknowns, a linear kriging system consisting of n +1 equations can be obtained, the expression being as follows:
where n is the number of points to be deployed in the reconstruction neighborhood, n ═ s (p) |. Gamma is a gaussian variation function combined with an air pollution coefficient w determined by the wind speed
At an angle to the wind direction
Calculated, the formula is as follows:
wherein d represents the Euclidean distance between two sensors, C0+ C is called the base station value, a is variableThe process.
(1.2.3) dividing the deployment area into a plurality of representative reconstruction neighborhoods according to the variation, obtaining an interpolation weight value of an estimation error of the undeployed sensor area by using the Kriging linear system in the step (1.2.2), and obtaining the estimation concentration of the undeployed area by using the interpolation weight value. The coverage quality of the sensor network under multiple scenes is established by taking the credible information coverage model as a basic coverage model;
the step (1.2.3) is specifically as follows:
a deployment region is divided into squares with a variable range a as a side length to obtain a representative reconstruction point set CS, and a plurality of reconstruction neighborhood point sets S (p) are obtained by taking each reconstruction point as a center, wherein the variable range a is twice of the communication range of the air pollution sensor. The minimum weight coefficient Lambda obtained according to the Krigin system in the step (1.2.2)iCalculating the estimation error Ecp. The quality of coverage is defined using a trusted information coverage model from the point of view of information reconstruction and estimation, i.e. the estimation error is less than or equal to a given threshold epsilon for a given kriging interpolationpIs considered to be covered by the trust, the coverage quality constraint based on the trust information coverage model is defined as:
|Mcp-Rp|≤εp
by simulating the air pollution concentration ApSensor transmission error tpAnd simulation error a of atmosphere simulatorpThe measured value of the air pollution concentration is represented, and then the maximum tolerance error is linearly relaxed, so that a coverage quality definition based on a credible information coverage model is obtained, and the formula is as follows:
wherein xp,ypAnd S (p) is a reconstructed neighborhood point set.
(1.2.4) constructing network connectivity such that each deployed sensor is capable of generating a flow unit when transmitting information in the network, and all flow units in the sensor network are capable of being received by the sink node;
the step (1.2.4) is specifically as follows:
utilizing network flows to construct a network connectivity problem, a sensor node can transmit flow units to neighboring nodes within its communication range, constructing the following network connectivity constraints:
fpq≤N*(yp+xp*Cpq),(p,q)∈Ψ(p)
fpq≤N*(yp+xq*Cpq),(p,q)∈Ψ(p)
where Ψ (p) is a neighboring node within communication range of the point p deployed sensor, CpqFor the adjacency matrix between the sensors disposed at points p and q, the adjacency matrix C is formed if the two sensors disposed at points p and q can communicatepq1, if two sensors cannot communicate, the adjacency matrix CpqIs 0, fpqThe number of flow units generated in the process of transmitting the collected information from the sensor of the deployment point p to the sensor of the deployment point q is N, and N is the total number of nodes of the area to be deployed. For the sink node ypAll flow units sent by the whole sensor network can be accepted, and the following network connectivity requirements are constructed:
(1.2.5) taking the sensor network coverage requirement in the step (1.2.3) and the sensor network connectivity requirement in the step (1.2.4) as constraint conditions of integer linear programming taking the deployment cost as an optimization target;
the step (1.2.5) is specifically as follows:
will deploy cost
As an optimization target, where δpIn order to deploy the deployment cost of a common sensor,
a deployment cost for deploying one sink node sensor.
And (4) obtaining a coverage constraint according to the coverage quality definition in the step (1.2.3):
wherein xp,ypRespectively, a decision variable representing whether a sensor node or a sink node is deployed at point p, ApIs the simulated air pollution concentration generated by an atmospheric diffusion simulator, apIs the simulation error generated by the simulator, tpIs the transmission error of the information transmitted between the sensors, ΛiIs the optimal interpolation weight in the kriging interpolation, and S (p) is a reconstruction neighborhood point set taking each reconstruction point CS as a central point.
Integrating the following network connectivity constraints according to the network connectivity requirements in step (1.2.4):
fpq≤N*(yp+xp*Cpq),(p,q)∈Ψ(p)
fpq≤N*(yp+xq*Cpq),(p,q)∈Ψ(p)
where Ψ (p) is a neighboring node within communication range of the point p deployed sensor, CpqFor the adjacency matrix disposed between the sensors at points p and q, fpqNumber of flow units generated during the transfer of collected information from sensors at deployment point p to sensors at deployment point qAnd N is the total number of the nodes of the area to be deployed.
(1.2.6) taking the deployment cost and the connectivity requirement of the sensor network in the step (1.2.4) as constraint conditions of integer linear programming taking the network coverage quality as an optimization target;
the step (1.2.6) is specifically as follows:
and (4) converting the integer linear programming optimization target in the step (1.2.5) from the deployment cost zeta to the maximum tolerance estimation error epsilon, and obtaining the integer linear programming with the deployment budget and the network connectivity as constraints and the network coverage quality as the optimization target.
Obtaining a deployment cost constraint according to the budget:
ζ≤F
where F is the deployment budget. And (4) combining the network connectivity constraint conditions in the step (1.2.5) to obtain an integer linear programming taking the coverage quality as a target and the deployment cost and the network connectivity as constraints.
(2) Respectively carrying out optimization solution on two integer linear plans by using a variable linear relaxation and binary search method, and comprising the following substeps:
(2.1) linearly relaxing decision variables of the integer linear programming taking the deployment cost as the optimization target in the step (1.2.5) into decimal numbers, and solving the deployment positions of the linear programming updating nodes through multiple iterations to obtain an approximate solution of the integer linear programming taking the deployment cost as the optimization target;
the step (2.1) is specifically as follows:
when the integer linear programming of the step (1.2.5) is applied to a large-scale scene, the decision variable x of the integer linear programming taking the deployment cost as the optimization target in the step (1.2.5) is usedp,ypRelaxed from {0,1} to [0,1 ]]The integer linear programming is converted into solving linear programming. The decision variable x closest to 1 in the solution for each solving of the linear programpSet to 1 as the constraint for the next linear program, repeat the operation until all decision variables xp,ypAnd changing to 0 or 1 to stop iteration so as to obtain the approximately optimal solution of the integer linear programming.
(2.2) subdividing the integer linear plan of the given deployment budget in the step (1.2.6) by utilizing binary search to tolerate estimation errors in a given threshold range, and obtaining an approximate solution of the integer linear plan of the given deployment budget when the error range reaches the given threshold range;
the step (2.2) is specifically as follows:
when the integer linear programming of step (1.2.6) is applied to a large-scale scene, the binary search is carried out on [ Low, Upp ]]And (3) taking the binary value V ═ Low + Upp)/2 as the deployment cost xi of the solution corresponding to the maximum tolerance estimation error in the step (2.1)v. The deployment cost xi of the step (2.1) under the two-point value V is divided into xivXi, compared to the budget FvIf > F, the new dichotomy value Vnew(V + Low)/2, whereas VnewRepeat the binary operation until the maximum tolerated estimation error range [ V, V ] is 2 (V + Upp)/2new]Size of | V-VnewStopping when | is less than our given threshold TH, obtaining the approximate maximum tolerated estimation error epsilon for the deployment cost J calculated using step (2.1), where Low is 0, Upp ≦ ap+2*ap。
Fig. 2 is a comparison effect diagram of credible information coverage and disk coverage in the invention, and it can be seen that six spatial positions P1, P2, P3, P4, P5 and P6 in the CR can be cooperatively sensed by four sensor nodes S1, S2, S3 and S4. When the disc covering model is used, S2 and S4 can only cover P2 and P6, respectively. Compared with a disc model, the credible information coverage model utilizes the cooperation between adjacent nodes, explores the spatial correlation of the physical characteristics of the perception object, and improves the coverage efficiency.
Fig. 3 and 4 are both deployment effect graphs of the method of the present invention in an air pollution to-be-deployed area, black dots represent sensor nodes, triangles represent sink nodes, and the darker the color in the graphs, the higher the air pollution concentration. Experiments prove that the method has good deployment effect.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A wireless sensor network node credible coverage deployment optimization method based on integer programming is characterized by comprising the following steps:
(1) the method for formulating the air pollution sensor deployment optimization model by combining the credible information coverage and integer linear programming comprises the following substeps:
(1.1) taking given urban air pollution map data as input, carrying out grid discretization on the map to obtain a group of region point sets P to be deployed, taking each discrete point P belonging to P as a region point to be deployed, and taking a decision variable xpAnd ypTo respectively specify whether to deploy a sensor node or a sink node at a point p, and only one sensor node or sink node can be deployed at the same point x to be deployedp+yp≤1,p∈P；
(1.2) constructing an air pollution sensor deployment optimization model based on trusted information coverage, designing estimation errors and interpolation by using the urban air pollution data set in the step (1.1), defining air pollution sensor coverage constraints and network connectivity constraints by combining air pollution specific scene parameters, and formulating the deployment optimization model of air pollution deployment by using an integer linear programming method;
(1.2.1) inputting the urban air pollution data into an atmospheric diffusion simulator to obtain the simulated air pollution concentration A of the deployment areapThe meteorological physical parameters and the pollutant discharge parameters directly influence the magnitude of the simulated air concentration, and the simulated air pollution concentration ApWith true air pollution concentration RpAnalog error of (A)p-Rp∈[-ap,ap]Combined with measurement of air pollution concentration McpWith true air pollution concentration RpSensor transmission error Mcp-Rp∈[-tp,tp]To obtain the simulated air pollution concentration ApAnd measuring air pollution concentration McpError range of (Mc)p-Ap∈[-tp-ap,tp+ap]；
(1.2.2) obtaining the covering quality of the air pollution sensor according to tolerance estimation errors, obtaining a variation function under an air pollution scene after considering the wind speed and the wind direction, combining a kriging interpolation, and constructing a linear kriging system by using a Lagrange multiplier method according to the linear unbiased characteristic of the kriging interpolation;
(1.2.3) dividing the deployment area into a plurality of representative reconstruction neighborhoods according to the variation, obtaining an interpolation weight value of an estimation error of the undeployed sensor area by using the Kriging linear system in the step (1.2.2), obtaining an estimation concentration of the undeployed area by using the interpolation weight value, and establishing the coverage quality of the sensor network under multiple scenes by using a credible information coverage model as a basic coverage model;
(1.2.4) constructing network connectivity such that each deployed sensor is capable of generating a flow unit when transmitting information in the network, and all flow units in the sensor network are capable of being received by the sink node;
(1.2.5) taking the sensor network coverage requirement in the step (1.2.3) and the sensor network connectivity requirement in the step (1.2.4) as constraint conditions of integer linear programming taking the deployment cost as an optimization target;
(1.2.6) taking the deployment cost and the connectivity requirement of the sensor network in the step (1.2.4) as constraint conditions of integer linear programming taking the network coverage quality as an optimization target;
(2) respectively carrying out optimization solution on two integer linear plans by using a variable linear relaxation and binary search method, and comprising the following substeps:
(2.1) linearly relaxing decision variables of the integer linear programming taking the deployment cost as the optimization target in the step (1.2.5) into decimal numbers, and solving the deployment positions of the linear programming updating nodes through multiple iterations to obtain an approximate solution of the integer linear programming taking the deployment cost as the optimization target;
(2.2) subdividing the integer linear plan of the given deployment budget in the step (1.2.6) by utilizing binary search to tolerate estimation errors in a given threshold range, and obtaining an approximate solution of the integer linear plan of the given deployment budget when the error range reaches the given threshold range.
2. The integer programming-based wireless sensor network node trusted coverage deployment optimization method of claim 1, wherein the step (1.2.2) is specifically:
maximum tolerance estimation error phi for deploying air pollution sensors to cover qualitypThe construction is carried out, and the calculation formula is as follows:
Φp＝UB(|Mcp-Ecp|)
estimated error EcpCan be expressed as a weighted average, Ec, of the measured values of the nodes in the reconstructed neighborhood point set S in the region to be deployed according to the Krigin interpolationpThe calculation formula is as follows:
wherein, ΛiRefers to the interpolation weight value, and the weight lambada in the formula is based on the linear unbiased condition of common krigingiThe sum being equal to 1, i.e.
In order to obtain the optimal weight coefficient, the Lagrange multiplier method is used for converting the weight coefficient lambdaiMinimizing, for n +1 unknowns, a linear kriging system consisting of n +1 equations can be obtained, the expression being as follows:
wherein n is the number n ═ S (p) of points to be deployed in the reconstruction neighborhood, γ is a Gaussian variation function combined with an air pollution coefficient w, and the air pollution coefficient w is determined by the wind speed
At an angle to the wind direction
Calculated, the formula is as follows:
wherein d represents the Euclidean distance between two sensors, C0+ C is called the base value and a is the range.
3. The integer programming-based wireless sensor network node trusted coverage deployment optimization method of claim 1 or 2, wherein the step (1.2.3) is specifically:
dividing a square of a deployment region with variable range a as side length to obtain a group of representative reconstruction point sets CS, and obtaining a plurality of reconstruction neighborhood point sets S (p) with each reconstruction point as a center, wherein the variable range a is twice of the communication range of the air pollution sensor, and the minimum weight coefficient Lambda obtained by a Kriging system in the step (1.2.2)iCalculating the estimation error EcpThe quality of coverage is defined using a trusted information coverage model from the point of view of information reconstruction and estimation, i.e. the estimation error is less than or equal to a given threshold epsilon for a given kriging interpolationpIs considered to be covered by the trust, the coverage quality constraint based on the trust information coverage model is defined as:
|Mcp-Rp|≤εp
by simulating the air pollution concentration ApSensor transmission error tpAnd simulation error a of atmosphere simulatorpThe measured value of the air pollution concentration is represented, and then the maximum tolerance error is linearly relaxed, so that a coverage quality definition based on a credible information coverage model is obtained, and the formula is as follows:
wherein xp,ypAnd S (p) is a reconstructed neighborhood point set.
4. The integer programming-based wireless sensor network node trusted coverage deployment optimization method of claim 1 or 2, wherein the step (1.2.4) is specifically:
utilizing network flows to construct a network connectivity problem, a sensor node can transmit flow units to neighboring nodes within its communication range, constructing the following network connectivity constraints:
fpq≤N*(yp+xp*Cpq),(p,q)∈Ψ(p)
fpq≤N*(yp+xq*Cpq),(p,q)∈Ψ(p)
where Ψ (p) is a neighboring node within communication range of the point p deployed sensor, CpqFor the adjacency matrix between the sensors disposed at points p and q, the adjacency matrix C is formed if the two sensors disposed at points p and q can communicatepq1, if two sensors cannot communicate, the adjacency matrix CpqIs 0, fpqThe number of flow units generated in the process of transmitting the collected information from the sensor of the deployment point p to the sensor of the deployment point q, N is the total number of the nodes of the area to be deployed, and is used for converging the node ypAll flow units sent by the whole sensor network can be accepted, and the following network connectivity requirements are constructed:
5. the integer programming-based wireless sensor network node trusted coverage deployment optimization method of claim 1 or 2, wherein the step (1.2.5) is specifically:
will deploy cost
As an optimization target, where δpIn order to deploy the deployment cost of a common sensor,
a deployment cost for deploying one sink node sensor;
and (4) obtaining a coverage constraint according to the coverage quality definition in the step (1.2.3):
wherein xp,ypRespectively, a decision variable representing whether a sensor node or a sink node is deployed at point p, ApIs the simulated air pollution concentration generated by an atmospheric diffusion simulator, apIs the simulation error generated by the simulator, tpIs the transmission error of the information transmitted between the sensors, ΛiIs the optimal interpolation weight in the kriging interpolation, and S (p) is a reconstruction neighborhood point set taking each reconstruction point CS as a central point;
integrating the following network connectivity constraints according to the network connectivity requirements in step (1.2.4):
fpq≤N*(yp+xp*Cpq),(p,q)∈Ψ(p)
fpq≤N*(yp+xq*Cpq),(p,q)∈Ψ(p)
where Ψ (p) is a neighboring node within communication range of the point p deployed sensor, CpqFor the adjacency matrix disposed between the sensors at points p and q, fpqThe number of flow units generated in the process of transmitting the collected information from the sensor of the deployment point p to the sensor of the deployment point q is N, and N is the total number of nodes of the area to be deployed.
6. The integer programming-based wireless sensor network node trusted coverage deployment optimization method of claim 1 or 2, wherein the step (1.2.6) is specifically:
converting the integer linear programming optimization target in the step (1.2.5) from the deployment cost zeta to the maximum tolerance estimation error epsilon, and obtaining the integer linear programming with the deployment budget and the network connectivity as constraints and the network coverage quality as the optimization target;
obtaining a deployment cost constraint according to the budget:
ζ≤F
and F is a deployment budget, and an integer linear programming which takes the coverage quality as a target and takes the deployment cost and the network connectivity as constraints is obtained by combining the network connectivity constraint conditions in the step (1.2.5).
7. The integer programming-based wireless sensor network node trusted coverage deployment optimization method of claim 1 or 2, wherein the step (2.1) is specifically:
when the integer linear programming of the step (1.2.5) is applied to a large-scale scene, the decision variable x of the integer linear programming taking the deployment cost as the optimization target in the step (1.2.5) is usedp,ypRelaxed from {0,1} to [0,1 ]]Converting the integer linear programming into solving linear programming, and solving the decision variable x closest to 1 in the solution of the linear programming each timepSet to 1 as the constraint for the next linear program, repeat the operation until all decision variables xp,ypAnd changing to 0 or 1 to stop iteration so as to obtain the approximately optimal solution of the integer linear programming.
8. The integer programming-based wireless sensor network node trusted coverage deployment optimization method of claim 1 or 2, wherein the step (2.2) is specifically:
when the integer linear programming of step (1.2.6) is applied to a large-scale scene, the binary search is carried out on [ Low, Upp ]]And (3) taking the binary value V ═ Low + Upp)/2 as the deployment cost xi of the solution corresponding to the maximum tolerance estimation error in the step (2.1)vThe deployment cost xi of the step (2.1) under the two-point value V isvXi, compared to the budget FvIf > F, the new dichotomy value Vnew(V + Low)/2, whereas VnewRepeat the binary operation until the maximum tolerated estimation error range [ V, V ] is 2 (V + Upp)/2new]Size of | V-VnewStopping when | is less than our given threshold TH, obtaining the approximate maximum tolerated estimation error epsilon for the deployment cost J calculated using step (2.1), where Low is 0, Upp ≦ ap+2*ap。
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