CN115776724B - Sensor node layout optimization method and system for electromagnetic spectrum map mapping - Google Patents
Sensor node layout optimization method and system for electromagnetic spectrum map mapping Download PDFInfo
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Abstract
Sensor node layout optimization method and system for electromagnetic spectrum map mapping comprise the following steps: carrying out mobile initialization acquisition on spectrum data of a region to be detected to obtain initial spectrum data; pairing sampling positions pairwise by using initial frequency spectrum data to obtain empirical half variance value data points; clustering and grouping the empirical half variance value data points; determining the minimum sampling node number according to the clustered half variance value data points; according to the minimum sampling node number, optimizing the initial sampling node position based on a random optimization algorithm; and (3) carrying out sequential optimization on the rest sampling node positions based on the maximum principle of the Kriging variance until the total sampling node number is reached. According to the invention, the spatial correlation between the electric wave propagation model and the spectrum data is comprehensively considered, and the number and the optimal position of the least sampling nodes can be obtained for the multi-node sensor collaborative spectrum map mapping task under an unknown scene, so that the optimal spectrum map mapping performance is realized by utilizing the least number of the nodes.
Description
Technical Field
The invention belongs to the field of wireless information transmission, and particularly relates to a sensor node layout optimization method and system for electromagnetic spectrum map mapping, which are particularly applied to electromagnetic spectrum map mapping under a multi-node sensor cooperative sensing scene.
Background
With rapid development of information technology and wireless communication technology, various wireless communication network devices have been rapidly increased, and electromagnetic spectrum space has been increasingly complex. The electromagnetic spectrum map can quantitatively characterize and visualize spectrum related information including time, frequency, received signal strength and position, and is expected to play a role in multiple fields of illegal radio frequency signal detection, radiation source positioning, spectrum resource management and the like. Therefore, how to perform accurate electromagnetic spectrum mapping becomes increasingly important.
For wide-area three-dimensional geographic space, electromagnetic spectrum mapping faces the challenges of limited acquisition node number, limited acquisition time, complex and changeable acquisition environment and the like. Furthermore, the final accuracy of the spectrum map depends on both the number of sampling nodes and the specific location where the sampling nodes are located. The more the number of sampling nodes, the more accurately the electromagnetic spectrum of the region to be measured can be reconstructed, but the acquisition workload is increased. Therefore, how to select the optimal position for layout and sampling under the condition of given sampling node number is a compromise solution for both performance and efficiency.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a sensor node layout optimization method and a system for electromagnetic spectrum map mapping, which comprehensively consider the spatial correlation between an electric wave propagation model and spectrum data, and can obtain the minimum number of sampling nodes and the optimal position for the multi-node sensor collaborative spectrum map mapping task under an unknown scene, thereby achieving the aim of realizing optimal spectrum map mapping performance by using the minimum number of nodes.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the sensor node layout optimization method for electromagnetic spectrum map mapping is characterized by comprising the following steps of:
step 1: carrying out mobile initialization acquisition on spectrum data of a region to be detected according to a random track or a uniform track by utilizing acquisition equipment to obtain initial spectrum data;
step 2: pairing sampling positions pairwise by using the obtained initial spectrum data, and calculating a half variance value to obtain an empirical half variance value data point;
step 3: clustering and grouping the empirical half variance value data points to obtain clustered half variance value data points;
step 4: fitting to obtain a space global semi-variance function according to the clustered semi-variance value data points, and determining the minimum sampling node number according to the obtained space global semi-variance function;
step 5: according to the minimum sampling node number, optimizing the initial sampling node position based on a random optimization algorithm;
step 6: and carrying out sequential optimization on the rest sampling node positions based on the maximum Kriging variance principle according to the data acquired by the optimized initial sampling node positions until the total sampling node number.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, in the step 1, the initial spectrum data M is expressed as:
in the method, in the process of the invention,
for the i-th sampling node position L i R The average received power for T time is acquired at A (L i R T) is L i R Instantaneous voltage at position t, d l And d w The transverse interval and the longitudinal interval are uniformly acquired at equal intervals respectively; l is the length of the area to be measured, W is the width of the area to be measured, N is the total number of sampling nodes, t 1 Indicating any starting moment.
Further, in the step 2, the empirical half variance value data points (d, Γ (d)) are calculated as follows:
wherein d represents the distance Γ between the ith sampling node and the jth sampling node i,j Representing the half variance value of the i-th sampling node and the j-th sampling node,
representing the half variance value of any two sampling nodes with a distance d, and Γ (d) represents the empirical half variance value of the distance d; any two sampling nodes with the distance d are called a node group with the distance d, N d The number of groups of node groups at a distance d.
Further, the step 3 specifically includes the following steps:
step 3.1: selecting distance variable in empirical half variance value data points to form a set X= { d 1 ,d 2 ,…,d epn As a clustering grouping variable, d epn A distance variable representing an epn-th empirical half variance value data point; randomly selecting K samples which are not repeated with each other as a clustering center { u } 1 ,u 2 ,…,u K -a }; by M k Representing the number of half variance value data points in the kth group, wherein the value of K is 1-K, and each grouping set is D k ＝{d mz ∈X|mz＝1,2,...,M k Then cluster center u of k-th group k The method comprises the following steps:
step 3.2: calculating a distance variable d in each half variance value data point ep With each cluster center u k Euclidean distance dis (u) k ,d ep )：
dis(u k ,d ep )＝||u k -d ep ||2
Wherein, the value of ep is 1 to epn;
step 3.3: dividing each sample into a nearest group in turn according to the calculated Euclidean distance, and then re-calculating the clustering center u k ', if u k ′≠u k Then u is k The value of' is updated to cluster center u k ；
Step 3.4: repeating the steps 3.2 and 3.3, iterating until the clustering center is not changed, ending the algorithm after convergence, and outputting the final clustering grouping result
Step 3.5: averaging the empirical half variance value data points (d, Γ (d)) according to the clustered divided K groups to obtain a clustered half variance value data point set
Where (d, γ (d)) represents the semi-variance data points after clustering grouping, ++>
Distance variable representing half variance value data points after the kth cluster grouping, +.>
Is the half variance value variable of the half variance value data points after the kth cluster grouping.
Further, the step 4 specifically includes the following steps:
fitting to obtain a space global semi-variance function according to clustered semi-variance data points (d, gamma (d))
The optimization targets are as follows:
in the method, in the process of the invention,
represent an objective function, d k Distance variable, γ (d), representing half variance data points after the kth cluster grouping k ) Half variance variable representing half variance data points after kth cluster grouping, +.>
Is a pending parameter, c 0 Is a half variance zero offset valueC is a half variance scaling factor, α is a distance scaling factor;
will be
The distance d at which the stability tends to be achieved is referred to as the correlation distance d 0 At this time +.>
For the critical spatial variation value C, determining the minimum sampling node number P according to the following equal interval constraint formula:
where δ is the fluctuation threshold.
Further, the step 5 specifically includes the following steps:
step 5.1: initializing a solution space X, a search speed V and P initial sampling node positions:
wherein X is q For the qth solution in solution space, V q For the search rate of the q-th solution,
for the 1 st node position in the q-th solution,>
is the search speed of the 1 st node in the q-th solution, gb 1 Is the optimal initial sampling node position in the initial solution space X; the function initialization represents initialization;
step 5.2: calculating half variance value gamma of P initial sampling nodes P (d)；
Step 5.3: calculating an optimization objective function:
step 5.4: updating the solution space and obtaining a global optimum according to the following principle:
in the method, in the process of the invention,
is the search speed, pb, of the (q) th solution at the (t+1) th iteration t q Is the optimal condition of the q solution after the t iteration and Gb t Is the optimal node position after the t-th iteration, < >>
For the (q) th solution at the (t+1) th iteration, the function update represents the situation of obtaining the optimal node position from the solution space X and updating the optimal node position into Gb, w is the inertia weight, and r 1 、r 2 Is a random number obeying uniform distribution, and the function max represents taking the maximum value;
step 5.5: repeating the steps 5.2 to 5.4, iterating until convergence, ending the algorithm, and outputting the optimized initial sampling node position
Further, the step 6 specifically includes the following steps:
step 6.1: firstly, solving a weight coefficient by using the following steps:
in the method, in the process of the invention,
is the sampling node position L 1 R And the non-sampling position +.>
Is a half variance value of [ lambda ] 1 ,λ 2 ,...,λ P ,-φ] T Is the coefficient to be solved;
the Kriging variance value sigma at each unknown sampling position is then calculated using the following equation K ：
Step 6.2: taking the position with the maximum Kerling variance value
For the next sampling node position, and add the sampled node position set +.>
Updating the number of sampled nodes n=n+1;
step 6.3: and (3) repeating the step 6.1 and the step 6.2 until the total sampling node number N is reached, and outputting a final sampling node position optimization result.
The invention also provides a sensor node layout optimization system for electromagnetic spectrum mapping, which is characterized by comprising the following steps:
the acquisition equipment is used for carrying out mobile initialization acquisition on the frequency spectrum data of the region to be detected according to a random track or a uniform track to obtain initial frequency spectrum data;
the calculation module is used for pairing sampling positions one by utilizing the obtained initial frequency spectrum data, calculating a half variance value and obtaining an empirical half variance value data point; clustering and grouping the empirical half variance value data points to obtain clustered half variance value data points; fitting to obtain a space global semi-variance function according to the clustered semi-variance value data points, and determining the minimum sampling node number according to the obtained space global semi-variance function;
the optimization module is used for optimizing the initial sampling node positions based on a random optimization algorithm according to the minimum sampling node number; and carrying out sequential optimization on the rest sampling node positions based on the maximum Kriging variance principle according to the data acquired by the optimized initial sampling node positions until the total sampling node number.
The beneficial effects of the invention are as follows:
1) According to the sensor node layout optimization method and system for electromagnetic spectrum map mapping, provided by the invention, the spatial correlation between the electric wave propagation model and spectrum data is comprehensively considered, and the accurate electromagnetic spectrum map can be obtained by using the minimum number of sensors;
2) According to the sensor node layout optimization scheme provided by the invention, the sampling node layout optimization and the sequential node optimization are combined based on the frequency spectrum data spatial correlation model and the Kerling covariance model which are built in a mixed mode, so that the calculation complexity is effectively reduced.
Drawings
FIG. 1 is a flow chart of a sensor node layout optimization method for electromagnetic spectrum mapping.
Fig. 2 is a global spectrum map of an embodiment.
Fig. 3 is a schematic diagram of spectrum data collected by equal interval initialization according to an embodiment.
Fig. 4 is a graph showing the result of the calculation of the empirical half variance value of the embodiment.
Fig. 5 is a schematic diagram of a cluster center of an embodiment.
Fig. 6 is a graph of the calculation result of the fitting global spatial half-variance function according to the embodiment.
Fig. 7a to 7d are graphs showing the results of initial sampling node optimization according to an embodiment, fig. 7a shows the initialized 25 node positions, fig. 7b shows the 25 node positions after 10 iterations, fig. 7c shows the 25 node positions after 20 iterations, and fig. 7d shows the final optimized 25 node positions.
Fig. 8a to 8d are graphs showing the result of optimizing the final output of the sampling node according to the embodiment, fig. 8a shows the optimized positions of 50 nodes, fig. 8b shows the optimized positions of 100 nodes, fig. 8c shows the optimized positions of 150 nodes, and fig. 8d shows the optimized positions of 256 nodes.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings of the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
In an embodiment, as shown in fig. 1, the present invention proposes a sensor node layout optimization method for electromagnetic spectrum mapping. The global spectrum map of this embodiment is shown in fig. 2, where there are 8 transmitters in the scene to be measured. Position parameters of corresponding transmitters
Transmission frequency f and transmission power->
As shown in table 1.
Table 1 transmitter configuration parameters
The specific implementation steps are as follows:
the first step: the user sets the length L=500m and the width W=500m of the region to be measured, and the frequency band f=2450Mhz to be measured; the user sets the total number of sampling nodes n=256. The present embodiment adopts a scheme of uniform and equally spaced arrangement. Equidistant acquisition is carried out according to the constraint condition of the formula (1), and the transverse interval d l =30m and longitudinal spacing d w =30m, resulting in the initial acquired spectral data M, as shown in fig. 3.
In the method, in the process of the invention,
for the i-th sampling node position L i R The average received power for T time is acquired at A (L i R T) is L i R Instantaneous voltage at position t; t is t 1 Indicating any starting moment.
And a second step of: according to the spectrum data M after initial acquisition, every sampling node is paired in pairs, and an empirical half variance value data point (d, Γ (d)) is calculated by using a formula (2), as shown in fig. 4.
Wherein d represents the distance Γ between the ith sampling node and the jth sampling node i,j Representing the half variance value of the i-th sampling node and the j-th sampling node,
representing the half variance value of any two sampling nodes with a distance d, and Γ (d) represents the empirical half variance value of the distance d; any two sampling nodes with the distance d are called a node group with the distance d, N d The number of groups of node groups at a distance d.
And a third step of: clustering grouping is carried out on the obtained empirical half variance value Γ (d), and the clustering grouping number k=12. And calculating the distance vector of each group by using a formula (3), measuring the distance by using a formula (4) until convergence is finished, and calculating the half variance mean value of each group according to the clustering result, as shown in fig. 5.
dis(u k ,d ep )＝||u k -d ep || 2 (4)
Where the distance variables in the empirical half variance value data points form the set x= { d 1 ,d 2 ,…,d epn As a clustering grouping variable, d epn A distance variable representing an epn-th empirical half variance value data point; randomly selecting K samples which are not repeated with each other as a clustering center { u } 1 ,u 2 ,…,u K -a }; by M k Representing the number of half variance value data points in the kth group, wherein the value of K is 1-K, and each grouping set is D k ＝{d mz ∈X|mz＝1,2,...,M k }，u k The clustering center of the k-th group is represented, and the ep value is 1 to epn.
Fourth step: fitting to obtain a global space semi-variation function according to the clustered semi-variance mean value
As shown in fig. 6, the optimization targets are: />
In the method, in the process of the invention,
represent an objective function, d k Distance variable, γ (d), representing half variance data points after the kth cluster grouping k ) Half variance variable representing half variance data points after kth cluster grouping, +.>
Is a pending parameter, c 0 Is a half variance zero offset value, c is a half variance scaling factor, and α is a distance scaling factor.
Will be
The distance d at which the stability tends to be achieved is referred to as the correlation distance d 0 At this time +.>
For the critical spatial variation value C, d is determined according to equation (6) 0 10m, the minimum initial layout point number p=25.
Where δ is the fluctuation threshold.
Fifth step: and solving and obtaining an initial sampling node optimization position based on a random optimization algorithm. The specific implementation steps are as follows:
s5.1: initializing the solution space, the search speed and the optimal node position by using a formula (7):
wherein X is q For the qth solution in solution space, V q For the search rate of the q-th solution,
for the 1 st node position in the q-th solution,>
is the search speed of the 1 st node in the q-th solution, gb 1 Is the optimal initial sampling node position in the initial solution space X, and the function initial represents initialization.
S5.2: calculating half variance values gamma of P initial sampling nodes according to the methods of the second step and the third step P (d)。
S5.3: calculating an objective function value using formula (8):
s5.4: updating the solution space, the search speed and the optimal initial node position by using the formula (9):
in the method, in the process of the invention,
is the search speed, pb, of the (q) th solution at the (t+1) th iteration t q Is the optimal condition of the q solution after the t iteration and Gb t Is the optimal node position after the t-th iteration, < >>
For the (q) th solution at the (t+1) th iteration, the function update represents the situation of obtaining the optimal node position from the solution space X and updating the optimal node position into Gb, w is the inertia weight, and r 1 、r 2 Is a random number subject to uniform distribution, and the function max represents taking the maximum value.
S5.5: repeating S5.2 to S5.4, iterating until convergence, ending the algorithm, and outputting the optimal sampling node position
As shown in fig. 7a to 7d, the detailed sampling coordinates are shown in table 2.
Table 2 detailed sampling coordinates
| Sampling point sequence number | Coordinates of sampling points | Sampling point sequence number | Coordinates of sampling points |
| 1 | (130,460,30) | 13 | (250,70,30) |
| 2 | (250,130,30) | 14 | (100,280,30) |
| 3 | (370,460,30) | 15 | (400,460,30) |
| 4 | (40,340,30) | 16 | (310,40,30) |
| 5 | (460,310,30) | 17 | (130,310,30) |
| 6 | (460,370,30) | 18 | (490,340,30) |
| 7 | (460,130,30) | 19 | (400,220,30) |
| 8 | (280,130,30) | 20 | (220,40,30) |
| 9 | (340,280,30) | 21 | (340,460,30) |
| 10 | (310,490,30) | 22 | (280,220,30) |
| 11 | (160,430,30) | 23 | (490,430,30) |
| 12 | (100,160,30) | 24 | (490,70,30) |
| 25 | (310,40,30) |
Sixth step: initializing the number n=p=25 of sampled nodes, and performing sequential optimization on the remaining nodes based on the maximum cricket variance principle until the total number n=256 of sampled nodes is reached. The specific implementation steps are as follows:
s6.1: the kriging variance value for each non-sampled position is calculated using equation (10) and equation (11):
in the method, in the process of the invention,
is the sampling node position L 1 R And the non-sampling position +.>
Is a half variance value of [ lambda ] 1 ,λ 2 ,...,λ P ,-φ] T Is the coefficient to be solved.
S6.2: let the non-sampling position with maximum Kriging variance value be the next sampling node position
And add the position to the sampled node set +.>
The sampled node number n=n+1 is updated.
S6.3: repeating S6.1 and S6.2 until the total sampling node number n=256 is reached, and outputting the final sampling node position optimization result, as shown in fig. 8a to 8 d.
In another embodiment, the present invention further provides a system corresponding to the sensor node layout optimization method for electromagnetic spectrum map mapping provided in the first embodiment, that is, a sensor node layout optimization system for electromagnetic spectrum map mapping, specifically including:
the acquisition equipment is used for carrying out mobile initialization acquisition on the frequency spectrum data of the region to be detected according to a random track or a uniform track to obtain initial frequency spectrum data;
the calculation module is used for pairing sampling positions one by utilizing the obtained initial frequency spectrum data, calculating a half variance value and obtaining an empirical half variance value data point; clustering and grouping the empirical half variance value data points to obtain clustered half variance value data points; fitting to obtain a space global semi-variance function according to the clustered semi-variance value data points, and determining the minimum sampling node number according to the obtained space global semi-variance function;
the optimization module is used for optimizing the initial sampling node positions based on a random optimization algorithm according to the minimum sampling node number; and carrying out sequential optimization on the rest sampling node positions based on the maximum Kriging variance principle according to the data acquired by the optimized initial sampling node positions until the total sampling node number.
In the sensor node layout optimization system for electromagnetic spectrum map mapping, the specific working mode and implementation steps of each device/module are the same as those of the sensor node layout optimization method for electromagnetic spectrum map mapping, so that the description is not repeated.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above examples, and all technical solutions belonging to the concept of the present invention belong to the protection scope of the present invention. It should be noted that modifications and adaptations to the invention without departing from the principles thereof are intended to be within the scope of the invention as set forth in the following claims.
Claims (1)
1. The sensor node layout optimization method for electromagnetic spectrum map mapping is characterized by comprising the following steps of:
step 1: carrying out mobile initialization acquisition on spectrum data of a region to be detected according to a random track or a uniform track by utilizing acquisition equipment to obtain initial spectrum data;
step 2: pairing sampling positions pairwise by using the obtained initial spectrum data, and calculating a half variance value to obtain an empirical half variance value data point;
step 3: clustering and grouping the empirical half variance value data points to obtain clustered half variance value data points;
step 4: fitting to obtain a space global semi-variance function according to the clustered semi-variance value data points, and determining the minimum sampling node number according to the obtained space global semi-variance function;
step 5: according to the minimum sampling node number, optimizing the initial sampling node position based on a random optimization algorithm;
step 6: according to the data acquired by the optimized initial sampling node positions, performing sequential optimization on the rest sampling node positions based on the maximum Kriging variance principle until the total sampling node number is reached;
in the step 1, the initial spectrum data M is expressed as:
in the method, in the process of the invention,
for the i-th sampling node position L i R The average received power for T time is acquired at A (L i R T) is L i R Instantaneous voltage at position t, d l And d w The transverse interval and the longitudinal interval are uniformly acquired at equal intervals respectively; l is the length of the area to be measured, W is the width of the area to be measured, N is the total number of sampling nodes, t 1 Representing an arbitrary starting time;
in the step 2, the empirical half variance value data points (d, Γ (d)) are calculated as follows:
wherein d represents the distance Γ between the ith sampling node and the jth sampling node i,j Representing the half variance value of the i-th sampling node and the j-th sampling node,
representing the half variance value Γ (d) of any two sampling nodes at a distance dAn empirical half variance value representing the distance d; any two sampling nodes with the distance d are called a node group with the distance d, N d The number of node groups with a distance d;
the step 3 specifically comprises the following steps:
step 3.1: selecting distance variable in empirical half variance value data points to form a set X= { d 1 ,d 2 ,…,d epn As a clustering grouping variable, d epn A distance variable representing an epn-th empirical half variance value data point; randomly selecting K samples which are not repeated with each other as a clustering center { u } 1 ,u 2 ,…,u K -a }; by M k Representing the number of half variance value data points in the kth group, wherein the value of K is 1-K, and each grouping set is D k ＝{d mz ∈X|mz＝1,2,...,M k Then cluster center u of k-th group k The method comprises the following steps:
step 3.2: calculating a distance variable d in each half variance value data point ep With each cluster center u k Euclidean distance dis (u) k ,d ep )：
dis(u k ,d ep )＝||u k -d ep || 2
Wherein, the value of ep is 1 to epn;
step 3.3: dividing each sample into a nearest group in turn according to the calculated Euclidean distance, and then re-calculating the clustering center u k ', if u k ′≠u k Then u is k The value of' is updated to cluster center u k ；
Step 3.4: repeating the steps 3.2 and 3.3, iterating until the clustering center is not changed, ending the algorithm after convergence, and outputting the final clustering grouping result
Step 3.5: will experienceThe half variance value data points (d, Γ (d)) are averaged according to the K groups divided after clustering to obtain a half variance value data point set after clustering
Where (d, γ (d)) represents the semi-variance data points after clustering grouping, ++>
Distance variable representing half variance value data points after the kth cluster grouping, +.>
Is the half variance value variable of the half variance value data points after the K clustering grouping;
the step 4 specifically comprises the following steps:
fitting to obtain a space global semi-variance function according to clustered semi-variance data points (d, gamma (d))
The optimization targets are as follows:
in the method, in the process of the invention,
represent an objective function, d k Distance variable, γ (d), representing half variance data points after the kth cluster grouping k ) Half variance variable representing half variance data points after kth cluster grouping, +.>
Is a pending parameter, c 0 Is a half variance zero offset value, c is a half variance scaling factor, α is a distance scaling factor;
will be
The distance d at which the stability tends to be achieved is referred to as the correlation distance d 0 At this time +.>
For the critical spatial variation value C, determining the minimum sampling node number P according to the following equal interval constraint formula:
wherein, delta is a fluctuation threshold;
the step 5 specifically comprises the following steps:
step 5.1: initializing a solution space X, a search speed V and P initial sampling node positions:
wherein X is q For the qth solution in solution space, V q For the search rate of the q-th solution,
for the 1 st node position in the q-th solution,>
is the search speed of the 1 st node in the q-th solution, gb 1 Is the optimal initial sampling node position in the initial solution space X; the function initialization represents initialization;
step 5.2: calculating half variance value gamma of P initial sampling nodes P (d)；
Step 5.3: calculating an optimization objective function:
step 5.4: updating the solution space and obtaining a global optimum according to the following principle:
in the method, in the process of the invention,
is the search speed, pb, of the (q) th solution at the (t+1) th iteration t q Is the optimal condition of the q solution after the t iteration and Gb t Is the optimal node position after the t-th iteration, < >>
For the (q) th solution at the (t+1) th iteration, the function update represents the situation of obtaining the optimal node position from the solution space X and updating the optimal node position into Gb, w is the inertia weight, and r 1 、r 2 Is a random number obeying uniform distribution, and the function max represents taking the maximum value;
step 5.5: repeating the steps 5.2 to 5.4, iterating until convergence, ending the algorithm, and outputting the optimized initial sampling node position
The step 6 specifically comprises the following steps:
step 6.1: firstly, solving a weight coefficient by using the following steps:
in the method, in the process of the invention,
is the sampling node position +.>
And the non-sampling position +.>
Is a half variance value of [ lambda ] 1 ,λ 2 ,...,λ P ,-φ] T Is the coefficient to be solved;
the Kriging variance value sigma at each unknown sampling position is then calculated using the following equation K ：
Step 6.2: taking the position with the maximum Kerling variance value
For the next sampling node position, and add the sampled node position set +.>
Updating the number of sampled nodes n=n+1;
step 6.3: and (3) repeating the step 6.1 and the step 6.2 until the total sampling node number N is reached, and outputting a final sampling node position optimization result.
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