CN109922478B - Water quality sensor network optimization deployment method based on improved cuckoo algorithm - Google Patents
Water quality sensor network optimization deployment method based on improved cuckoo algorithm Download PDFInfo
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Abstract
The invention provides a water quality sensor network optimization deployment method based on an improved cuckoo algorithm. Firstly, establishing a water quality sensor network coverage model, discretizing a monitoring area into grid points, defining the proportion of the number of the grid points covered by the sensor to the total number of the grid points as coverage rate, and aiming at improving the network coverage rate as an optimization target. And secondly, the optimized deployment of the whole network is realized by utilizing an improved cuckoo algorithm. By improving the cuckoo algorithm, the water quality sensor network can achieve the optimal coverage performance through fewer iteration times.
Description
Technical Field
The invention relates to the field of environmental monitoring and sensor networks, in particular to a research of a water quality sensor network optimization deployment method based on an improved cuckoo algorithm.
Background
Water is a source of life and also a necessary resource on which humans are dependent for reproduction. However, in recent decades, with the rapid development of national economy and the continuous improvement of the living standard of people, the contradiction between water resource supply and demand becomes increasingly prominent. According to '2016 publication of environmental conditions in China', in the condition of groundwater water quality monitoring of 6124 monitoring points in 225 municipal administration districts on the national level in 2016, the proportion of monitoring points with good water quality is only 10.1%, and the proportion of observation points with worse water quality is 45.4%. For the whole surface water, the proportion of the badly polluted poor V-class water body is higher, and is about 8.6 percent nationwide.
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. Due to the high cost of water quality sensors, it is desirable to deploy more sensors in the monitoring environment in order 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 optimization deployment method based on an improved cuckoo algorithm, 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 and treatment and the like.
In order to achieve the purpose, the invention provides a water quality sensor network optimization deployment method based on an improved cuckoo algorithm, which specifically comprises two basic steps of establishing a water quality sensor network coverage model and optimizing and deploying a sensor network.
Step one, in an embodiment of the present invention, the establishing a water quality sensor network coverage model further includes:
discretizing the monitored water area into m grid points, wherein any grid point pjHas the coordinates of (x)j，yj) Randomly placing a group of sensor nodes with the same sensing radius r in a monitoring area, and setting s as { s ═ s1，s2，s3…snRepresents the set of sensor nodes, any one of which siHas the coordinates of (x)i，yi) (ii) a Calculating siTo point pjDefined as:
then a certain grid point p in the monitoring area is monitoredjThe situation covered by the sensor node is
P(si,pj) The mesh point can be covered by the sensor node as 1; for a monitored grid point, the probability that the monitored grid point is monitored by all sensor nodes in the whole monitoring area is defined as the joint monitoring probability, and the grid point pjThe joint monitoring probability is shown as the following formula:
counting the number of grids with the monitoring probability equal to 1, wherein the ratio of the number of the grids to the total number m of the grids is the coverage rate of the whole water quality monitoring network;
step two, in an embodiment of the present invention, the optimized deployment of the sensor network further includes:
and (3) uniformly deploying the network based on the improved cuckoo algorithm. The cuckoo algorithm utilizes Levy flight to carry out global search, and has good global optimization capability; the cuckoo algorithm combines a global search random walk and a local random walk, wherein the global search random walk is as follows:
wherein x isg,iRepresenting the position of each bird nest in the g-th generation;
represents the step control amount:
wherein x isbestThe current optimal solution is obtained; l (β) represents a lavi random search path, obeying a lavi probability distribution:
Lévy～u＝t-β(1≤β≤3)
beta is a parameter, and the value here is 1.5; in practice, for convenience of calculation, the lavi random number is generated by using the following formula:
that is, the location update formula of cuckoo can be expressed as follows:
wherein u and v are normally distributed,
is a constant;
it is according to the probability PaAfter discarding the partial solutions, the same number of new solutions are regenerated using local random walks:
xg+1,i＝xg,i+r(xg,j-xg,k)
where r is a scaling factor, is a uniformly distributed random number within the (0, 1) interval, xg，i，xg，kTwo random numbers representing generations g;
probability of elimination PaThe probability that the cuckoo nest is found by the host, namely the probability of generating a new solution, is a fixed value in the initial cuckoo algorithm, and P is takenaIs 0.25. In the actual optimization process, the result is more and more drawn to the optimal value along with the continuous increase of the iteration times, and at the moment, if the elimination probability still keeps the original cardinal number, a large number of high-quality solutions can be eliminated, and the optimization performance of the algorithm is damaged. Therefore, the elimination probability P is realized by introducing a variable functionaBecomes a value that varies with the number of iterations. Introducing a formula:
wherein p isa_newAs a new elimination probability, PaTo improve the prior elimination probability, P is takenaIs 0.25, N _ iter is the maximum number of iterations, N1The number of bird eggs. According to the formula, the solution quality is continuously improved as the iteration times are increased and the loop enters the later stage, and the probability that the individual is found and eliminated is lower and lower, so that the improved cuckoo algorithm has higher convergence speed and better optimization effect.
Fig. 2 shows an initial random distribution diagram of a water quality sensor network, wherein circles in the diagram represent water quality sensor nodes, the outermost square frame is an area to be monitored, and grids in the square frame are discretized grid points. Through multiple iterations and optimization of the cuckoo algorithm, the sensor nodes can be deployed at the position where the network coverage rate is maximum, as shown in fig. 3. Fig. 4 shows a comparison of the number of iterations required to achieve maximum network coverage for the improved cuckoo algorithm and the particle swarm algorithm proposed herein under the same initial conditions. In the figure, PSO represents a particle swarm algorithm, IMCS represents an improved cuckoo algorithm, and it can be known from the figure that the improved cuckoo algorithm finds an optimal solution after the number of iterations reaches 65, while the particle swarm algorithm needs to iterate up to 145 times to reach an optimal optimization result. It can be seen that the improved cuckoo algorithm has a search speed stronger than that of the particle swarm algorithm. In addition, the particle swarm algorithm in the graph has several smooth curves before reaching the optimal state, which shows that the particle swarm algorithm is easy to fall into the local optimal solution. Therefore, the improved cuckoo algorithm can be used for improving the deployment effect of the water quality sensor network with higher efficiency.
The uniform deployment of the water quality sensor network is realized, on the basis, the water quality data of a monitored water area can be acquired, all factors are analyzed by using a principal component analysis method aiming at the acquired water area monitoring data, the water quality parameters are subjected to dimensionality reduction treatment, representative components for water quality evaluation are extracted, and the mathematical model is as follows:
wherein i is the number of samples; j is the number of factors; n is the number of principal components after principal component analysis; a is1j，a2j，…，anjIs the load of the original variable matrix on each principal component; xi1，Xi2，…，XijIs the value of the original variable matrix after standardization; z is a radical ofi1，zi2，……，zinRepresenting the value of each principal component after principal component analysis;
principal component z of each sample obtained by principal component analysisinValue of which the corresponding principal component evaluation function Z can be obtainediAnd as a data basis for judging key monitoring points:
wherein Z isiIs the principal component evaluation score value corresponding to each sample; lambda [ alpha ]i1,λi2…λinIs a matrix [ X ]i1，Xi2，……，Xij]Variance contribution rate corresponding to the initial characteristic value;
the analysis of the water quality parameters of a certain area through principal component analysis can obtain the time variation of the areaComprehensive water quality evaluation score ZiAnd similarly, the variance values of the comprehensive water quality evaluation scores of all the water areas can be obtained, the variance values of all the water areas are compared, the monitoring point with the maximum variance value is taken as a key monitoring area, the monitoring point with the minimum variance value is taken as a non-key monitoring area, then the sensor of the non-key monitoring area is moved to the key monitoring area, the key monitoring water area is redeployed, and the monitoring efficiency of the network is effectively improved.
The water quality sensor network optimization deployment method based on the improved cuckoo algorithm can realize effective monitoring of key monitoring water areas and provide a full theoretical basis for effective monitoring and comprehensive treatment of water environment.
Drawings
Fig. 1 is a flow chart of a water quality sensor network optimization deployment method based on an improved cuckoo algorithm according to an embodiment of the present invention;
FIG. 2 is an initial random distribution diagram of a water quality sensor network according to an embodiment of the present invention;
FIG. 3 is a diagram of an optimized deployment result of a water quality sensor network according to an embodiment of the invention;
FIG. 4 is a comparison graph of iteration times of the method of the present invention and the network optimization deployment based on the particle swarm optimization.
Detailed Description
Reference will now be made in detail to the 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 meanings throughout. The following examples are illustrative only and are not to be construed as limiting the invention.
The invention provides a water quality sensor network optimization deployment method based on an improved cuckoo algorithm, aiming at complex water area environments in a water environment monitoring process.
In order that the invention may be more clearly understood, it is briefly described herein. The invention comprises two basic steps: step one, establishing a water quality sensor network coverage model; and step two, optimizing and deploying the sensor network.
Specifically, fig. 1 is a flowchart of a water quality sensor network optimization deployment method based on an improved cuckoo algorithm according to an embodiment of the present invention, and the method includes the following steps:
and step S101, establishing a water quality sensor network coverage model.
In one embodiment of the invention, discretization processing is carried out on the monitored water area, and the water area is discretized into m grid points, wherein any grid point pjHas the coordinates of (x)j，yj) Randomly placing a group of sensor nodes with the same sensing radius r in a monitoring area, and setting s as { s ═ s1，s2，s3…snRepresents the set of sensor nodes, any one of which siHas the coordinates of (x)i，yi) (ii) a Calculating siTo point pjDefined as:
then a certain grid point p in the monitoring area is monitoredjThe case of being covered by a sensor node is:
P(si,pj) The mesh point can be covered by the sensor node as 1; for a monitored grid point, the probability that the monitored grid point is monitored by all sensor nodes in the whole monitoring area is defined as the joint monitoring probability, and the grid point pjThe joint monitoring probability is shown as the following formula:
counting the number of grids with the monitoring probability equal to 1, wherein the ratio of the number of the grids to the total number of the grids m multiplied by n is the coverage rate of the whole water quality monitoring network;
and S102, uniformly deploying the network based on the improved cuckoo algorithm.
The cuckoo algorithm utilizes Levy flight to carry out global search, and has good global optimization capability; the cuckoo algorithm combines a global search random walk and a local random walk, wherein the global search random walk is shown in formula (4):
wherein x isg,iRepresenting the position of each bird nest in the g-th generation;
represents the step control amount:
wherein x isbestThe current optimal solution is obtained; l (β) represents a lavi random search path, obeying a lavi probability distribution:
Lévy～u＝t-β(1≤β≤3) (6)
beta is a parameter, and the value here is 1.5; in practice, for convenience of calculation, the lavi random number is generated by using the following formula:
that is, the location update formula of cuckoo can be expressed as follows:
wherein u and v are normally distributed,
is a constant;
it is according to the probability PaAfter discarding the partial solutions, the same number of new solutions are regenerated using local random walks:
xg+1,i＝xg,i+r(xg,j-xg,k) (10)
where r is a scaling factor, is a uniformly distributed random number within the (0, 1) interval, xg，i，xg，kTwo random numbers representing generations g;
probability of elimination PaThe probability that the cuckoo nest is found by the host, namely the probability of generating a new solution, is a fixed value in the initial cuckoo algorithm, and P is takenaIs 0.25. In the actual optimization process, the result is more and more drawn to the optimal value along with the continuous increase of the iteration times, and at the moment, if the elimination probability still keeps the original cardinal number, a large number of high-quality solutions can be eliminated, and the optimization performance of the algorithm is damaged. Therefore, the elimination probability P is realized by introducing a variable functionaBecomes a value that varies with the number of iterations. Introducing a formula:
wherein p isa_newAs a new elimination probability, PaTo improve the prior elimination probability, P is takenaIs 0.25, N _ iter is the maximum number of iterations, N1The number of bird eggs. As can be seen from the formula (11), the solution quality is continuously improved as the iteration number increases and the loop enters the later stage, and the probability that the individual is found and eliminated is lower and lower, so that the improved cuckoo algorithm has higher convergence rate and better optimization effect.
Through multiple iterations and optimization of the cuckoo algorithm, the sensor nodes can be deployed at the position where the network coverage rate is maximum.
And step S103, realizing effective coverage on the important monitoring area.
Aiming at the collected water area monitoring data, analyzing each factor by using a principal component analysis method, performing dimensionality reduction on water quality parameters, and extracting representative components of water quality evaluation, wherein a mathematical model of the method is as follows:
wherein i is the number of samples; j is the number of factors; n is the number of principal components after principal component analysis; a is1j，a2j，…，anjIs the load of the original variable matrix on each principal component; xi1，Xi2，…，XijIs the value of the original variable matrix after standardization; z is a radical ofi1，zi2，……，zinRepresenting the value of each principal component after principal component analysis;
principal component z of each sample obtained by principal component analysisinValue of which the corresponding principal component evaluation function Z can be obtainediAnd as a data basis for judging key monitoring points:
wherein Z isiIs the principal component evaluation score value corresponding to each sample; lambda [ alpha ]i1,λi2…λinIs a matrix [ X ]i1，Xi2，……，Xij]Variance contribution rate corresponding to the initial eigenvalue.
The analysis of the water quality parameters of a certain area through principal component analysis can obtain the comprehensive water quality evaluation score Z of the area on the time changeiThe variance value of the scores is obtained to evaluate the stability or fluctuation of the water quality data of the water area, and similarly, the variance value of the comprehensive water quality evaluation score of each water area is obtained to compare the variance value of each water area, and the monitoring point with the largest variance value is used as the key monitoring pointAnd measuring the area, taking the monitoring point with the minimum variance as a non-key monitoring area, and then moving the sensor of the non-key monitoring area to a key monitoring area, so that the key monitoring water area is redeployed, and the monitoring efficiency of the network is effectively improved.
By the water quality sensor network optimal deployment method based on the improved cuckoo algorithm, optimal deployment of the water quality sensor network can be realized, and a full theoretical basis is provided for effective monitoring and comprehensive treatment of a water environment.
Finally, it should be noted that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Those of ordinary skill in the art will understand that: it is to be understood that modifications may be made to the above-described embodiments, or equivalents may be substituted for elements thereof without departing from the spirit and scope of the present invention as defined by the appended claims and their equivalents.
Claims (1)
1. A water quality sensor network optimization deployment method based on an improved cuckoo algorithm is characterized by comprising the following steps: the method comprises the two basic steps of establishing a water quality sensor network coverage model and optimizing and deploying a sensor network;
the establishing of the water quality sensor network coverage model comprises the following steps: discretizing the monitored water area into m grid points, wherein any grid point pjHas the coordinates of (x)j，yj) Randomly placing a group of sensor nodes with the same sensing radius r in a monitoring area, and setting s as { s ═ s1，s2，s3…snRepresents the set of sensor nodes, any one of which siHas the coordinates of (x)i，yi) (ii) a Calculating siTo point pjDefined as:
then a certain grid point p in the monitoring area is monitoredjThe case of being covered by a sensor node is:
P(si,pj) The mesh point can be covered by the sensor node as 1; for a monitored grid point, the probability that the monitored grid point is monitored by all sensor nodes in the whole monitoring area is defined as the joint monitoring probability, and the grid point pjThe joint monitoring probability is shown as the following formula:
counting the number of grids with the monitoring probability equal to 1, wherein the ratio of the number of the grids to the total number m of the grids is the coverage rate of the whole water quality monitoring network;
the optimized deployment of the sensor network comprises the following steps:
(1) network uniform deployment based on improved cuckoo algorithm
The cuckoo algorithm utilizes Levy flight to carry out global search, and has good global optimization capability; the cuckoo algorithm combines a global search random walk and a local random walk, wherein the global search random walk is shown in formula (4):
wherein x isg,iRepresenting the position of each bird nest in the g-th generation;
represents the step control amount:
wherein x isbestThe current optimal solution is obtained; l (β) represents a lavi random search path, obeying a lavi probability distribution:
Lévy～u＝t-β(1≤β≤3) (6)
beta is a parameter, and the value here is 1.5; in practice, for convenience of calculation, the lavi random number is generated by using the following formula:
that is, the location update formula of cuckoo can be expressed as follows:
wherein u and v are normally distributed,
is a constant;
it is according to the probability PaAfter discarding the partial solutions, the same number of new solutions are regenerated using local random walks:
xg+1,i＝xg,i+r(xg,j-xg,k) (10)
where r is a scaling factor, is a uniformly distributed random number within the (0, 1) interval, xg,i，xg,kTwo random numbers representing generations g;
probability of elimination PaThe probability that the cuckoo nest is found by the host, namely the probability of generating a new solution, is a fixed value in the initial cuckoo algorithm, and P is takenaIs 0.25; in the actual optimization process, the result is more and more drawn to the optimal value along with the continuous increase of the iteration times, and if the elimination probability still keeps the original cardinal number, a large number of high-quality solutions can be eliminated, so that the optimization performance of the algorithm is damaged; therefore, the elimination probability P is realized by introducing a variable functionaBecomes a value that varies with the number of iterations; introducing a formula:
wherein p isa_newAs a new elimination probability, PaTo improve the prior elimination probability, P is takenaIs 0.25, N _ iter is the maximum number of iterations, N1For the number of the bird eggs, the formula (11) shows that the solution quality is continuously improved and the probability that the individual is found and eliminated is lower and lower as the iteration times increase and the cycle enters the later stage, so that the improved cuckoo algorithm has higher convergence speed and better optimization effect;
through multiple iterations and optimization of the cuckoo algorithm, the sensor nodes can be deployed at the position where the network coverage rate is maximum;
(2) realizing effective coverage of key monitoring area
Above realized the even deployment of water quality sensor network, on this basis, to the waters monitoring data that gathers, utilize principal component analysis to carry out the analysis to each factor, carry out the dimensionality reduction to the quality of water parameter and handle, extract the representative composition of water quality evaluation, its mathematical model is:
wherein i is the number of samples; j is the number of factors; n is the number of principal components after principal component analysis; a is1j，a2j，…，anjIs the load of the original variable matrix on each principal component; xi1，Xi2，…，XijIs a primary variableThe normalized values of the matrix; z is a radical ofi1，zi2，……，zinRepresenting the value of each principal component after principal component analysis;
principal component z of each sample obtained by principal component analysisinValue of which the corresponding principal component evaluation function Z can be obtainediAnd as a data basis for judging key monitoring points:
wherein Z isiIs the principal component evaluation score value corresponding to each sample; lambda [ alpha ]i1,λi2…λinIs a matrix [ X ]i1，Xi2，……，Xij]Variance contribution rate corresponding to the initial characteristic value;
the analysis of the water quality parameters of a certain area through principal component analysis can obtain the comprehensive water quality evaluation score Z of the area on the time changeiAnd similarly, the variance values of the comprehensive water quality evaluation scores of all the water areas can be obtained, the variance values of all the water areas are compared, the monitoring point with the maximum variance value is taken as a key monitoring area, the monitoring point with the minimum variance value is taken as a non-key monitoring area, then the sensor of the non-key monitoring area is moved to the key monitoring area, the key monitoring water area is redeployed, and the monitoring efficiency of the network is effectively improved.
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