CN111263369B - Water quality sensor network coverage optimization method - Google Patents

Water quality sensor network coverage optimization method Download PDF

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CN111263369B
CN111263369B CN202010089596.2A CN202010089596A CN111263369B CN 111263369 B CN111263369 B CN 111263369B CN 202010089596 A CN202010089596 A CN 202010089596A CN 111263369 B CN111263369 B CN 111263369B
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孙茜
王小艺
许继平
张慧妍
王立
于家斌
申志平
羊峰波
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Beijing Technology and Business University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention provides a water quality sensor network coverage optimization method. Firstly, a water quality sensor network coverage model is established, a monitoring area is discretized into grid points, the ratio of the number of the grid points covered by the sensor to the total grid number is defined as coverage rate, and the network coverage rate is improved as an optimization target. Secondly, an optimization process of the cuckoo algorithm is improved based on the Adam optimization algorithm, and the elimination probability of the cuckoo algorithm is improved by using a learning rate attenuation method. By improving the cuckoo algorithm, the water quality sensor network can achieve better coverage performance through fewer iteration times.

Description

Water quality sensor network coverage optimization method
Technical Field
The invention relates to the field of environment monitoring and sensor networks, in particular to a study of a water quality sensor network coverage optimization method.
Background
Water is a source of life and is also an essential resource for human reproduction. However, in recent decades, with rapid development of national economy and continuous improvement of living standard of people, the contradiction between supply and demand of water resources is increasingly prominent. According to the 2016 Chinese environmental condition publication, in the condition of groundwater quality monitoring of 6124 monitoring points in 225 land-level municipal areas in 2016, the proportion of the monitoring points with good quality is only 10.1%, and the proportion of the observation points with bad quality is up to 45.4%. For the whole surface water, the proportion of the poor V-shaped water body which is severely polluted is higher, which is about 8.6 percent of the whole country.
In recent years, scientific monitoring of water environments has received increasing attention. In the process of monitoring the water environment, the sensor network occupies a very important position. Because the water quality sensor has higher cost, more sensors are hoped to be deployed in key areas in the monitoring environment so as to improve the monitoring quality and save the cost. Therefore, an area needing to be monitored in a water area to be monitored is required to be found, the deployment of the sensor network is realized through an effective sensor deployment strategy, and a full theoretical basis is provided for accurate water environment monitoring.
Disclosure of Invention
The invention aims to provide a water quality sensor network coverage optimization method which can provide a theoretical basis for the deployment of a water quality sensor network and can be widely applied to the fields of water environment monitoring, water pollution prediction, water pollution treatment and the like.
In order to achieve the above purpose, the invention provides a water quality sensor network coverage optimization method, which specifically comprises two basic steps of establishing a water quality sensor network coverage model and optimizing and deploying a sensor network.
In one embodiment of the present invention, the establishing the water quality sensor network coverage model further includes:
discretizing the monitored water area into m grid points, wherein any grid point p j Is (x) j ，y j ) Randomly placing a group of sensor nodes with the same sensing radius r in a monitoring area, and setting s= { s 1 ，s 2 ，s 3 …s n And represents the set of sensor nodes, any one of which is s i Is (x) i ，y i ) The method comprises the steps of carrying out a first treatment on the surface of the Calculation s i To point p j The euclidean distance of (2) is defined as:
Figure BDA0002382200000000021
then a certain grid point p in the area is monitored j The cases covered by the sensor nodes are:
Figure BDA0002382200000000022
P(s i ,p j ) =1 indicates that the grid point can be covered by a sensor node; for a monitored grid point, the probability that it is monitored by all sensor nodes in the whole monitored area is defined as joint monitoring probability, and grid point p j The joint monitoring probability of (2) is shown in the following formula:
Figure BDA0002382200000000023
counting the number of grids with the monitoring probability equal to 1, wherein the ratio of the number of grids to the total grid number m is the coverage rate of the whole water quality monitoring network;
in a second embodiment of the present invention, the optimizing deployment of the sensor network further includes:
the step size is improved based on an Adam optimization algorithm. The cuckoo algorithm utilizes the Lewy flight to perform global search, and has good global optimizing capability; the cuckoo algorithm combines a globally searched random walk with a local random walk, where the globally searched random walk is represented by the following formula:
Figure BDA0002382200000000024
wherein ,xg,i Indicating the position of the bird nest of the g generation;
Figure BDA0002382200000000025
the step control amount is represented:
Figure BDA0002382200000000026
wherein ,
Figure BDA0002382200000000027
is constant, x best Is the current optimal solution; l (ψ) represents the lewye random search path, which obeys the lewye probability distribution:
Lévy～σ 2 ＝t -ψ (1≤ψ≤3)
psi is a parameter, here a value of 1.5; in practice, for the sake of convenient calculation, the following formula is used to generate the Lev random number:
Figure BDA0002382200000000028
i.e. the position update formula of cuckoo can be expressed as follows:
Figure BDA0002382200000000029
wherein u, v are all subject to normal distribution;
Figure BDA00023822000000000210
which is based on probability P a After discarding part of the solution, the same number of new solutions are regenerated using local random walks:
x g+1,i ＝x g,i +r(x g,j -x g,k )
where r is a scaling factor, is a uniformly distributed random number within the (0, 1) interval, x g，i ，x g，k Two random numbers representing g generation;
the Adam optimization algorithm combines a momentum gradient descent method and a root mean square algorithm, and adopts the idea of the Adam optimization algorithm for updating the Lewy flight step length in the cuckoo algorithm, and the idea is shown in the following formula:
Δl x ＝β 1 Δl x,t-1 +(1-β 1 )Δl x,t Δl y ＝β 1 Δl y,t-1 +(1-β 1 )Δl y,t
S dx ＝β 2 S dx +(1-β 2 )d 2 x S dy ＝β 2 S dy +(1-β 2 )d 2 y
Figure BDA0002382200000000031
/>
Figure BDA0002382200000000032
in the formula ,Δlx Is the size of the x-direction step update, Δl y Is the size of the step update in the y-direction, Δl x,t 、Δl y,t The step sizes of the time t in the x direction and the y direction are respectively Deltal x,t-1 ，Δl y,t-1 The time step sizes in the x and y directions t-1 are respectively, S dx For velocity variation in x direction, S dy For velocity change in the y-direction, beta 1 、β 2 Is the weight, ω is the learning rate, ε is a very small positive integer that prevents the denominator from being zero; the advantage of adopting a momentum gradient descent method in an Adam optimization algorithm can be seen from a formula, so that a local optimal solution can be jumped out in the optimizing process, the advantage of a root mean square algorithm is absorbed, the searching step length in the optimizing direction is quickened, and the influence of adverse disturbance on the optimizing process is reduced.
Improved elimination probability P a . Probability of elimination P a The probability that a cuckoo nest is found by a host, i.e., the probability of generating a new solution, is shown as a fixed value in the initial cuckoo algorithm; in the actual optimizing process, as the iteration times are continuously increased, the results are more and more closed towards the optimal value, and at the moment, if the elimination probability still keeps the original base number, a large number of high-quality solutions are eliminated, so that the optimizing performance of an algorithm is destroyed; thus, by learning rate decaySubtracting, updating the elimination probability by the following formula to enable the elimination probability P a Becomes a value that varies with the number of iterations:
Pa＝0.95 iteration Pa 0
wherein, the iteration is iteration number, pa 0 Taking the initial elimination probability as 0.25;
through multiple iterations of the cuckoo algorithm and optimization, the water quality sensor network can be optimally covered.
FIG. 2 shows an initial random distribution diagram of a water quality sensor network, and sensor nodes can be redeployed through multiple iterations and optimization of a cuckoo algorithm, as shown in FIG. 3. The coverage rate is improved from 59.64% to 86.48%, so that the deployment of the water quality sensor nodes is optimized, and the monitoring performance of the sensor network can be effectively improved.
The coverage optimization method of the water quality sensor network provided by the invention can realize effective monitoring of the monitored water area, and provides a full theoretical basis for effective monitoring and comprehensive treatment of the water environment.
Drawings
FIG. 1 is a flow chart of a method for optimizing coverage of a water quality sensor network according to an embodiment of the invention;
FIG. 2 is a graph showing an initial random deployment profile of a water quality sensor network according to an embodiment of the present invention;
FIG. 3 is a graph of the results of an optimized deployment of a water quality sensor network according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the like or similar elements throughout. The following described embodiments are illustrative only and are not to be construed as limiting the invention.
The invention provides a water quality sensor network coverage optimization method aiming at complex water area environments in the water environment monitoring process.
In order that the invention may be more clearly understood, a brief description is provided herein. The invention comprises two basic steps: step one, establishing a water quality sensor network coverage model; and step two, optimizing deployment of the sensor network.
Specifically, fig. 1 is a flowchart of a coverage optimization method of a water quality sensor network according to an embodiment of the present invention, including the following steps:
and step S101, establishing a water quality sensor network coverage model.
In one embodiment of the invention, the monitored water area is discretized into m grid points, any one of which is p j Is (x) j ，y j ) Randomly placing a group of sensor nodes with the same sensing radius r in a monitoring area, and setting s= { s 1 ，s 2 ，s 3 …s n And represents the set of sensor nodes, any one of which is s i Is (x) i ，y i ) The method comprises the steps of carrying out a first treatment on the surface of the Calculation s i To point p j The euclidean distance of (2) is defined as:
Figure BDA0002382200000000041
then a certain grid point p in the area is monitored j The cases covered by the sensor nodes are:
Figure BDA0002382200000000042
P(s i ,p j ) =1 indicates that the grid point can be covered by a sensor node; for a monitored grid point, the probability that it is monitored by all sensor nodes in the whole monitored area is defined as joint monitoring probability, and grid point p j The joint monitoring probability of (2) is shown in the following formula:
Figure BDA0002382200000000043
counting the number of grids with the monitoring probability equal to 1, wherein the ratio of the number of grids to the total grid number m multiplied by n is the coverage rate of the whole water quality monitoring network;
step S102, step length is improved based on an Adam optimization algorithm.
The cuckoo algorithm utilizes the Lewy flight to perform global search, and has good global optimizing capability; the cuckoo algorithm combines a globally searched random walk with a local random walk, where the globally searched random walk is shown in equation (4):
Figure BDA0002382200000000051
wherein ,xg,i Indicating the position of the bird nest of the g generation;
Figure BDA0002382200000000052
the step control amount is represented:
Figure BDA0002382200000000053
wherein ,
Figure BDA0002382200000000054
is constant, x best Is the current optimal solution; l (ψ) represents the lewye random search path, which obeys the lewye probability distribution:
Lévy～σ 2 ＝t -ψ (1≤ψ≤3) (6)
psi is a parameter, here a value of 1.5; in practice, for the sake of convenient calculation, the following formula is used to generate the Lev random number:
Figure BDA0002382200000000055
i.e. the position update formula of cuckoo can be expressed as follows:
Figure BDA0002382200000000056
wherein u, v are all subject to normal distribution;
Figure BDA0002382200000000057
which is based on probability P a After discarding part of the solution, the same number of new solutions are regenerated using local random walks:
x g+1,i ＝x g , i +r(x g,j -x g , k ) (10)
where r is a scaling factor, is a uniformly distributed random number within the (0, 1) interval, x g，i ，x g，k Two random numbers representing g generation;
the Adam optimization algorithm combines a momentum gradient descent method and a root mean square algorithm, and adopts the idea of the Adam optimization algorithm for updating the Lewy flight step length in the cuckoo algorithm, as shown in a formula (11):
Figure BDA0002382200000000058
in the formula ,Δlx Is the size of the x-direction step update, Δl y Is the size of the step update in the y-direction, Δl x,t 、Δl y,t The step sizes of the time t in the x direction and the y direction are respectively Deltal x,t-1 ，Δl y,t-1 The time step sizes in the x and y directions t-1 are respectively, S dx For velocity variation in x direction, S dy For velocity change in the y-direction, beta 1 、β 2 Is the weight, ω is the learning rate, ε is a very small positive integer that prevents the denominator from being zero; the advantage of adopting a momentum gradient descent method in an Adam optimization algorithm can be seen from a formula, so that a local optimal solution can be jumped out in the optimizing process, and meanwhile, the advantage of a root mean square algorithm is absorbed, the searching step length in the optimizing direction is quickened, and the influence of adverse disturbance on the optimizing process is reduced;
step S103, improving the elimination probability P a
Probability of elimination P a The probability of bird nest being found by the host, i.e., the probability of generating a new solution, is shown as a fixed value in the initial bird's brook algorithm. In the actual optimizing process, as the iteration times are continuously increased, the results are more and more closed towards the optimal value, and at the moment, if the elimination probability still keeps the original base number, a large number of high-quality solutions are eliminated, so that the optimizing performance of an algorithm is destroyed; therefore, the elimination probability is updated by the learning rate attenuation method by using the formula (12), so that the elimination probability P a Becomes a value that varies with the number of iterations:
Pa＝0.95 iteration Pa 0 (12)
wherein, the iteration is iteration number, pa 0 The initial elimination probability was taken as 0.25.
Through multiple iterations of the cuckoo algorithm and optimization, the sensor nodes can be deployed at the position which optimizes the network coverage rate.
The water quality sensor network coverage optimization method provided by the invention can realize the optimized deployment of the water quality sensor network, and provides a full theoretical basis for the effective monitoring and comprehensive treatment of the water environment.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting. Those of ordinary skill in the art will appreciate that: it is still possible to modify the technical solutions described in the foregoing embodiments or to make equivalent substitutions for some technical features thereof, without departing from the spirit and scope of the technical solutions of the respective embodiments of the present invention, the scope of which is defined by the appended claims and equivalents thereof.

Claims (1)

1. A water quality sensor network coverage optimization method is characterized in that: the method comprises the basic steps of establishing a water quality sensor network coverage model and optimizing and deploying a sensor network;
the establishing the water quality sensor network coverage model comprises the following steps: to monitor water areaDiscretizing process of discretizing it into m grid points, any one of which is p j Is (x) j ，y j ) Randomly placing a group of sensor nodes with the same sensing radius r in a monitoring area, and setting s= { s 1 ，s 2 ，s 3 …s n And represents the set of sensor nodes, any one of which is s i Is (x) i ，y i ) The method comprises the steps of carrying out a first treatment on the surface of the Calculation s i To point p j The euclidean distance of (2) is defined as:
Figure FDA0002382199990000011
then a certain grid point p in the area is monitored j The cases covered by the sensor nodes are:
Figure FDA0002382199990000012
P(s i ,p j ) =1 indicates that the grid point can be covered by a sensor node; for a monitored grid point, the probability that it is monitored by all sensor nodes in the whole monitored area is defined as joint monitoring probability, and grid point p j The joint monitoring probability of (2) is shown in the following formula:
Figure FDA0002382199990000013
counting the number of grids with the monitoring probability equal to 1, wherein the ratio of the number of grids to the total grid number m is the coverage rate of the whole water quality monitoring network;
the optimal deployment of the sensor network comprises the following steps:
(1) Adam optimization algorithm-based step length improvement
The cuckoo algorithm utilizes the Lewy flight to perform global search, and has good global optimizing capability; the cuckoo algorithm combines a globally searched random walk with a local random walk, where the globally searched random walk is shown in equation (4):
Figure FDA0002382199990000014
wherein ,xg,i Indicating the position of the bird nest of the g generation;
Figure FDA0002382199990000015
the step control amount is represented:
Figure FDA0002382199990000016
wherein ,
Figure FDA0002382199990000017
is constant, x best Is the current optimal solution; l (ψ) represents the lewye random search path, which obeys the lewye probability distribution:
Figure FDA0002382199990000018
psi is a parameter, here a value of 1.5; in practice, for the sake of convenient calculation, the following formula is used to generate the Lev random number:
Figure FDA0002382199990000021
i.e. the position update formula of cuckoo can be expressed as follows:
Figure FDA0002382199990000022
wherein u, v are all subject to normal distribution;
Figure FDA0002382199990000023
which is based on probability P a After discarding part of the solution, the same number of new solutions are regenerated using local random walks:
x g+1,i ＝x g,i +r(x g,j -x g,k ) (10)
where r is a scaling factor, is a uniformly distributed random number within the (0, 1) interval, x g，i ，x g，k Two random numbers representing g generation;
the Adam optimization algorithm combines a momentum gradient descent method and a root mean square algorithm, and adopts the idea of the Adam optimization algorithm for updating the Lewy flight step length in the cuckoo algorithm, as shown in a formula (11):
Figure FDA0002382199990000024
in the formula ,Δlx Is the size of the x-direction step update, Δl y Is the size of the step update in the y-direction, Δl x,t 、Δl y,t The step sizes of the time t in the x direction and the y direction are respectively Deltal x,t-1 ，Δl y,t-1 The time step sizes in the x and y directions t-1 are respectively, S dx For velocity variation in x direction, S dy For velocity change in the y-direction, beta 1 、β 2 Is the weight, ω is the learning rate, ε is a very small positive integer that prevents the denominator from being zero; the advantage of adopting a momentum gradient descent method in an Adam optimization algorithm can be seen from a formula, so that a local optimal solution can be jumped out in the optimizing process, and meanwhile, the advantage of a root mean square algorithm is absorbed, the searching step length in the optimizing direction is quickened, and the influence of adverse disturbance on the optimizing process is reduced;
(2) Improved elimination probability P a
Probability of elimination P a The probability that a cuckoo nest is found by a host, i.e., the probability of generating a new solution, is shown as a fixed value in the initial cuckoo algorithm; in practiceIn the optimizing process, as the iteration times are continuously increased, the results are more and more close to the optimal values, and at the moment, if the elimination probability still keeps the original cardinality, a large number of high-quality solutions are eliminated, so that the optimizing performance of an algorithm is destroyed; therefore, the elimination probability is updated by the learning rate attenuation method by using the formula (12), so that the elimination probability P a Becomes a value that varies with the number of iterations:
Pa＝0.95 iteration Pa 0 (12)
wherein, the iteration is iteration number, pa 0 Taking the initial elimination probability as 0.25;
through multiple iterations of the cuckoo algorithm and optimization, the water quality sensor network can be optimally covered.
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