CN115776724A - Sensor node layout optimization method and system for electromagnetic spectrum mapping - Google Patents

Sensor node layout optimization method and system for electromagnetic spectrum mapping Download PDF

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CN115776724A
CN115776724A CN202310091981.4A CN202310091981A CN115776724A CN 115776724 A CN115776724 A CN 115776724A CN 202310091981 A CN202310091981 A CN 202310091981A CN 115776724 A CN115776724 A CN 115776724A
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CN115776724B (en
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朱秋明
赵翼
林志鹏
王洁
黄洋
李婕
吴启晖
仲伟志
高钱豪
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Nanjing University of Aeronautics and Astronautics
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Abstract

面向电磁频谱地图测绘的传感器节点布局优化方法及系统，包括：对待测区域进行频谱数据移动式初始化采集，获得初始频谱数据；利用初始频谱数据，将采样位置两两配对，获得经验半方差值数据点；将经验半方差值数据点进行聚类分组；根据聚类分组后的半方差值数据点，确定最小采样节点数；根据最小采样节点数，基于随机优化算法进行初始采样节点位置的优化；基于克里金方差最大原则对剩下的采样节点位置进行贯序式优化，直至总采样节点数。本发明综合考虑了电波传播模型与频谱数据空间相关性，对于未知场景下的多节点传感器协同频谱地图测绘任务，可获得最少采样节点的数目和最优位置，从而达到利用最少节点数目实现最优的频谱地图测绘性能。

Figure 202310091981

The sensor node layout optimization method and system for electromagnetic spectrum map surveying and mapping, including: performing mobile initial collection of spectrum data in the area to be measured to obtain initial spectrum data; using the initial spectrum data to pair sampling positions in pairs to obtain empirical semivariance values Data points; cluster and group empirical semivariance value data points; determine the minimum number of sampling nodes according to the semivariance value data points after clustering; determine the initial sampling node position based on the random optimization algorithm according to the minimum number of sampling nodes optimization; based on the principle of maximum variance of Kriging, the remaining sampling node positions are sequentially optimized until the total number of sampling nodes is reached. The present invention comprehensively considers the spatial correlation between the radio wave propagation model and the 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 in an unknown scene, so as to realize the optimal use of the minimum number of nodes Spectrum map mapping performance.

Figure 202310091981

Description

面向电磁频谱地图测绘的传感器节点布局优化方法及系统Sensor node layout optimization method and system for electromagnetic spectrum mapping

技术领域technical field

本发明属于无线信息传输领域，具体涉及一种面向电磁频谱地图测绘的传感器节点布局优化方法及系统，特别针对多节点传感器协同感知场景下的电磁频谱地图测绘应用。The invention belongs to the field of wireless information transmission, and in particular relates to a sensor node layout optimization method and system for electromagnetic spectrum map surveying and mapping, in particular to the application of electromagnetic spectrum map surveying and mapping in multi-node sensor collaborative sensing scenarios.

背景技术Background technique

随着信息技术和无线通讯技术的迅速发展，各类无线通信网络设备的急剧增加，电磁频谱空间日益复杂。电磁频谱地图可将包括时间、频率、接收信号强度和位置在内的频谱相关信息进行定量表征与可视化，有望在非法射频信号检测、辐射源定位、频谱资源管理等多个领域发挥作用。因此，如何进行精准电磁频谱地图测绘变得越来越重要。With the rapid development of information technology and wireless communication technology, various types of wireless communication network equipment have increased dramatically, and the electromagnetic spectrum space has become increasingly complex. The electromagnetic spectrum map can quantitatively represent and visualize spectrum-related information including time, frequency, received signal strength, and location, and is expected to play a role in many fields such as illegal radio frequency signal detection, radiation source location, and spectrum resource management. Therefore, how to carry out accurate electromagnetic spectrum mapping is becoming more and more important.

针对广域的三维地理空间，电磁频谱地图测绘面临着采集节点数目有限、采集时间有限和采集环境复杂多变等挑战。此外，频谱地图的最终准确性既取决于采样节点的数量，也依赖于采样节点所处的具体位置。采样节点的数量越多，越能精确地重构待测区域的电磁频谱，但是采集工作负担也随之增加。因此，如何在给定采样节点数目的条件下，选取最优的位置进行布局和采样，是一种兼顾性能和效率的折中解决方案。For wide-area three-dimensional geographic space, electromagnetic spectrum map mapping is faced with challenges such as limited number of collection nodes, limited collection time, and complex and changeable collection environments. In addition, the final accuracy of the spectrum map depends not only on the number of sampling nodes, but also on the specific location of the sampling nodes. The greater the number of sampling nodes, the more accurately the electromagnetic spectrum of the area to be measured can be reconstructed, but the collection workload also increases. Therefore, how to select the optimal location for layout and sampling under the condition of a given number of sampling nodes is a compromise solution that takes performance and efficiency into account.

发明内容Contents of the invention

本发明针对现有技术中的不足，提供一种面向电磁频谱地图测绘的传感器节点布局优化方法及系统，其综合考虑了电波传播模型与频谱数据空间相关性，对于未知场景下的多节点传感器协同频谱地图测绘任务，可获得最少采样节点的数目和最优位置，从而达到利用最少节点数目实现最优的频谱地图测绘性能。Aiming at the deficiencies in the prior art, the present invention provides a sensor node layout optimization method and system for electromagnetic spectrum map mapping, which comprehensively considers the radio wave propagation model and the spatial correlation of spectrum data, and is suitable for multi-node sensor collaboration in unknown scenarios The task of spectrum map mapping can obtain the minimum number of sampling nodes and the optimal position, so as to achieve the optimal spectrum map mapping performance with the minimum number of nodes.

为实现上述目的，本发明采用以下技术方案：To achieve the above object, the present invention adopts the following technical solutions:

一种面向电磁频谱地图测绘的传感器节点布局优化方法，其特征在于，包括以下步骤：A sensor node layout optimization method for electromagnetic spectrum mapping, characterized in that it comprises the following steps:

步骤1：利用采集设备对待测区域按照随机轨迹或均匀轨迹进行频谱数据移动式初始化采集，获得初始频谱数据；Step 1: Use the collection equipment to carry out mobile initialization collection of spectrum data according to the random trajectory or uniform trajectory in the area to be measured, and obtain the initial spectrum data;

步骤2：利用获得的初始频谱数据，将采样位置两两配对，计算半方差值，获得经验半方差值数据点；Step 2: Using the obtained initial spectrum data, pair the sampling positions in pairs, calculate the semivariance value, and obtain empirical semivariance value data points;

步骤3：将经验半方差值数据点进行聚类分组，获得聚类分组后的半方差值数据点；Step 3: Cluster and group the empirical semivariance value data points to obtain the semivariance value data points after clustering and grouping;

步骤4：根据聚类分组后的半方差值数据点，拟合获得空间全局半变异函数，根据获得的空间全局半变异函数，确定最小采样节点数；Step 4: According to the semivariogram data points after clustering and grouping, fit to obtain the spatial global semivariogram, and determine the minimum number of sampling nodes according to the obtained spatial global semivariogram;

步骤5：根据最小采样节点数，基于随机优化算法进行初始采样节点位置的优化；Step 5: According to the minimum number of sampling nodes, optimize the position of initial sampling nodes based on random optimization algorithm;

步骤6：根据优化后的初始采样节点位置所采集的数据，基于克里金方差最大原则对剩下的采样节点位置进行贯序式优化，直至总采样节点数。Step 6: According to the data collected at the optimized initial sampling node positions, the remaining sampling node positions are sequentially optimized based on the principle of maximum variance of Kriging until the total number of sampling nodes is reached.

为优化上述技术方案，采取的具体措施还包括：In order to optimize the above technical solutions, the specific measures taken also include:

进一步地，所述步骤1中，初始频谱数据M表示为：Further, in the step 1, the initial spectrum data M is expressed as:

Figure SMS_1
，
Figure SMS_1
,

式中，

Figure SMS_2
为第i个采样节点位置
Figure SMS_3
处采集T时间的平均接收功率，
Figure SMS_4
为
Figure SMS_5
位置处t时刻的瞬时电压，
Figure SMS_6
和
Figure SMS_7
分别为等间隔均匀采集的横向间隔与纵向间隔；L为待测区域长度，W为待测区域宽度，N为总采样节点数，t 1表示任意起始时刻。In the formula,
Figure SMS_2
is the i- th sampling node position
Figure SMS_3
The average received power collected at time T ,
Figure SMS_4
for
Figure SMS_5
The instantaneous voltage at time t at the position,
Figure SMS_6
and
Figure SMS_7
Respectively, the horizontal interval and the vertical interval of the uniform sampling at equal intervals; 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, and t 1 represents any starting time.

进一步地，所述步骤2中，经验半方差值数据点

Figure SMS_8
的计算方式如下：Further, in the step 2, the empirical semivariogram data point
Figure SMS_8
is calculated as follows:

Figure SMS_9
，
Figure SMS_9
,

式中，d表示第i个采样节点与第j个采样节点的距离，

Figure SMS_10
表示第i个采样节点与第j个采样节点的半方差值，
Figure SMS_11
表示任意两个距离为d的采样节点的半方差值，
Figure SMS_12
表示距离d的经验半方差值；将距离为d的任意两个采样节点称为距离为d的节点组，N d 为距离为d的节点组的组数。In the formula, d represents the distance between the i -th sampling node and the j -th sampling node,
Figure SMS_10
Indicates the semivariance value between the i -th sampling node and the j -th sampling node,
Figure SMS_11
Represents the semivariance value of any two sampling nodes with a distance of d ,
Figure SMS_12
Indicates the empirical semivariance value of the distance d ; any two sampling nodes with a distance of d are called a node group with a distance of d , and N d is the group number of the node group with a distance of d .

进一步地，所述步骤3具体包括以下步骤：Further, the step 3 specifically includes the following steps:

步骤3.1：选取经验半方差值数据点中的距离变量组成集合

Figure SMS_13
作为聚类分组变量，
Figure SMS_14
表示第epn个经验半方差值数据点的距离变量；随机选取K个互不重复的样本作为聚类中心
Figure SMS_15
；用
Figure SMS_16
表示第k组内半方差值数据点的数目，k的取值是1~K，每个分组集合为
Figure SMS_17
，则第k组的聚类中心
Figure SMS_18
为：Step 3.1: Select the distance variables in the empirical semivariance data points to form a set
Figure SMS_13
As a clustering grouping variable,
Figure SMS_14
Indicates the distance variable of the epnth empirical semivariance data point; randomly select K non-repeating samples as cluster centers
Figure SMS_15
;use
Figure SMS_16
Indicates the number of semi-variance value data points in the kth group, the value of k is 1~ K , and each grouping set is
Figure SMS_17
, then the cluster center of the kth group
Figure SMS_18
for:

Figure SMS_19
；
Figure SMS_19
;

步骤3.2：计算每个半方差值数据点中的距离变量

Figure SMS_20
与每个聚类中心
Figure SMS_21
的欧氏距离
Figure SMS_22
：Step 3.2: Compute the distance variable in each semivariance value data point
Figure SMS_20
with each cluster center
Figure SMS_21
Euclidean distance
Figure SMS_22
:

Figure SMS_23
，
Figure SMS_23
,

式中，ep的取值是1~epn；In the formula, the value of ep is 1~ epn ;

步骤3.3：根据计算的欧式距离，将每个样本依次划分到最近的一组，然后重新计算聚类中心

Figure SMS_24
，若
Figure SMS_25
，则将
Figure SMS_26
的值更新为聚类中心
Figure SMS_27
；Step 3.3: According to the calculated Euclidean distance, divide each sample into the nearest group in turn, and then recalculate the cluster center
Figure SMS_24
,like
Figure SMS_25
, then the
Figure SMS_26
The value of is updated as the cluster center
Figure SMS_27
;

步骤3.4：重复步骤3.2和步骤3.3，迭代至聚类中心不再改变，达到收敛后结束算法，并输出最终聚类分组结果

Figure SMS_28
；Step 3.4: Repeat step 3.2 and step 3.3, iterate until the cluster center does not change, end the algorithm after convergence, and output the final clustering and grouping results
Figure SMS_28
;

步骤3.5：将经验半方差值数据点

Figure SMS_29
根据聚类后划分的K组求取平均值，获得聚类分组后的半方差值数据点集合
Figure SMS_30
，其中
Figure SMS_31
表示聚类分组后的半方差值数据点，
Figure SMS_32
表示第K个聚类分组后的半方差值数据点的距离变量，
Figure SMS_33
是第K个聚类分组后的半方差值数据点的半方差值变量。Step 3.5: Put the empirical semivariance value data points
Figure SMS_29
Calculate the average value according to the K groups divided after clustering, and obtain the semi-variance value data point set after clustering and grouping
Figure SMS_30
,in
Figure SMS_31
Represents the semi-variance value data points after clustering and grouping,
Figure SMS_32
Indicates the distance variable of the semivariogram data points after the Kth cluster grouping,
Figure SMS_33
is the semivariogram variable of the semivariogram data points after the Kth cluster grouping.

进一步地，所述步骤4具体如下：Further, the step 4 is specifically as follows:

根据聚类分组后的半方差值数据点

Figure SMS_34
，拟合获得空间全局半变异函数
Figure SMS_35
，其优化目标为：Semivariance value data points grouped by cluster
Figure SMS_34
, fitting to obtain the spatial global semivariogram
Figure SMS_35
, and its optimization objective is:

Figure SMS_36
，
Figure SMS_36
,

式中，

Figure SMS_37
表示目标函数，
Figure SMS_38
表示第k个聚类分组后的半方差值数据点的距离变量，
Figure SMS_39
表示第k个聚类分组后的半方差值数据点的半方差值变量，
Figure SMS_40
是待定参数，c 0是半方差零点偏移值，c是半方差缩放系数，
Figure SMS_41
为距离缩放系数；In the formula,
Figure SMS_37
represents the objective function,
Figure SMS_38
Indicates the distance variable of the semivariogram data points after the kth cluster grouping,
Figure SMS_39
Represents the semivariogram variable of the semivariogram data points after the kth cluster grouping,
Figure SMS_40
is an undetermined parameter, c 0 is the semivariance zero offset value, c is the semivariance scaling coefficient,
Figure SMS_41
is the distance scaling factor;

将

Figure SMS_42
趋于稳定时的距离d记作相关距离d 0，此时的
Figure SMS_43
为临界空间变异值C，根据如下等间隔约束公式确定最小采样节点数P：Will
Figure SMS_42
The distance d when it tends to be stable is recorded as the correlation distance d 0 , at this time
Figure SMS_43
As the critical spatial variation value C , the minimum number of sampling nodes P is determined according to the following equal interval constraint formula:

Figure SMS_44
，
Figure SMS_44
,

式中，

Figure SMS_45
为波动阈值。In the formula,
Figure SMS_45
is the fluctuation threshold.

进一步地，所述步骤5具体包括如下步骤：Further, the step 5 specifically includes the following steps:

步骤5.1：初始化解空间X、搜索速度V与P个初始采样节点位置：Step 5.1: Initialize the solution space X, search speed V and P initial sampling node positions:

Figure SMS_46
，
Figure SMS_46
,

式中，

Figure SMS_47
为解空间中的第q个解，
Figure SMS_48
为第q个解的搜索速度，
Figure SMS_49
为第q个解中的第1个节点位置，
Figure SMS_50
是第q个解中第1个节点的搜索速度，
Figure SMS_51
是初始解空间X中的最优初始采样节点位置；函数initialize表示初始化；In the formula,
Figure SMS_47
is the qth solution in the solution space,
Figure SMS_48
is the search speed of the qth solution,
Figure SMS_49
is the first node position in the qth solution,
Figure SMS_50
is the search speed of the first node in the qth solution,
Figure SMS_51
is the optimal initial sampling node position in the initial solution space X; the function initialize represents initialization;

步骤5.2：计算P个初始采样节点的半方差值

Figure SMS_52
；Step 5.2: Calculate the semivariance value of P initial sampling nodes
Figure SMS_52
;

步骤5.3：计算优化目标函数：Step 5.3: Calculate the optimization objective function:

Figure SMS_53
；
Figure SMS_53
;

步骤5.4：依据如下原则更新解空间并获得全局最优情况：Step 5.4: Update the solution space and obtain the global optimal situation according to the following principles:

Figure SMS_54
，
Figure SMS_54
,

式中，

Figure SMS_55
是第t+1次迭代时第q个解的搜索速度，
Figure SMS_56
是第t次迭代后第q个解的最优情况，
Figure SMS_57
是第t次迭代后最优节点位置情况，
Figure SMS_58
为第t+1次迭代时的第q个解，函数update表示从解空间X中取得最优节点位置情况，并更新到Gb中，w是惯性权重，r 1、r 2是服从均匀分布的随机数，函数max表示取最大值；In the formula,
Figure SMS_55
is the search speed of the qth solution at the t +1th iteration,
Figure SMS_56
is the optimal case of the qth solution after the tth iteration,
Figure SMS_57
is the optimal node position after the tth iteration,
Figure SMS_58
is the qth solution at the t +1th iteration, the function update means to obtain the optimal node position from the solution space X, and update it to Gb, w is the inertia weight, r 1 and r 2 are uniformly distributed Random number, the function max means to take the maximum value;

步骤5.5：重复步骤5.2至步骤5.4，迭代至收敛后结束算法，并输出优化后的初始采样节点位置

Figure SMS_59
。Step 5.5: Repeat steps 5.2 to 5.4, iterate until convergence and end the algorithm, and output the optimized initial sampling node position
Figure SMS_59
.

进一步地，所述步骤6具体包括如下步骤：Further, the step 6 specifically includes the following steps:

步骤6.1：首先利用下式求解权重系数：Step 6.1: First use the following formula to solve the weight coefficient:

Figure SMS_60
，
Figure SMS_60
,

式中，

Figure SMS_61
是采样节点位置
Figure SMS_62
和未采样位置
Figure SMS_63
的半方差值，
Figure SMS_64
是待求解系数；In the formula,
Figure SMS_61
is the sampling node position
Figure SMS_62
and the unsampled position
Figure SMS_63
The semivariance value of ,
Figure SMS_64
is the coefficient to be solved;

然后利用下式计算每个未知采样位置处的克里金方差值

Figure SMS_65
：The kriging variance value at each unknown sampling location is then calculated using
Figure SMS_65
:

Figure SMS_66
；
Figure SMS_66
;

步骤6.2：取克里金方差值最大的位置

Figure SMS_67
为下一个采样节点位置，并加入已采样节点位置集合
Figure SMS_68
，更新已采样节点数n =n+1；Step 6.2: Take the position with the largest kriging variance value
Figure SMS_67
For the next sampling node position, and join the set of sampled node positions
Figure SMS_68
, update the number of sampled nodes n = n +1;

步骤6.3：重复步骤6.1与步骤6.2，直至达到总采样节点数N，输出最终采样节点位置优化结果。Step 6.3: Repeat steps 6.1 and 6.2 until the total number of sampling nodes N is reached, and output the final optimization results of sampling node positions.

本发明还提出了一种面向电磁频谱地图测绘的传感器节点布局优化系统，其特征在于，包括：The present invention also proposes a sensor node layout optimization system oriented to electromagnetic spectrum map surveying and mapping, which is characterized in that it includes:

采集设备，用于对待测区域按照随机轨迹或均匀轨迹进行频谱数据移动式初始化采集，获得初始频谱数据；Acquisition equipment, which is used to perform mobile initial collection of spectrum data in accordance with random or uniform trajectories in the area to be measured to obtain initial spectrum data;

计算模块，用于利用获得的初始频谱数据，将采样位置两两配对，计算半方差值，获得经验半方差值数据点；将经验半方差值数据点进行聚类分组，获得聚类分组后的半方差值数据点；根据聚类分组后的半方差值数据点，拟合获得空间全局半变异函数，根据获得的空间全局半变异函数，确定最小采样节点数；The calculation module is used to use the obtained initial spectrum data to pair the sampling positions in pairs, calculate the semivariance value, and obtain the empirical semivariance value data points; cluster and group the empirical semivariance value data points to obtain the clustering The semivariogram data points after grouping; according to the semivariogram data points after clustering and grouping, the spatial global semivariogram is obtained by fitting, and the minimum number of sampling nodes is determined according to the obtained spatial global semivariogram;

优化模块，用于根据最小采样节点数，基于随机优化算法进行初始采样节点位置的优化；根据优化后的初始采样节点位置所采集的数据，基于克里金方差最大原则对剩下的采样节点位置进行贯序式优化，直至总采样节点数。The optimization module is used to optimize the initial sampling node position based on the random optimization algorithm according to the minimum number of sampling nodes; according to the data collected at the optimized initial sampling node position, the remaining sampling node positions are calculated based on the principle of maximum kriging variance Perform sequential optimization up to the total number of sampled nodes.

本发明的有益效果是：The beneficial effects of the present invention are:

1）本发明提出的面向电磁频谱地图测绘的传感器节点布局优化方法及系统，综合考虑了电波传播模型与频谱数据空间相关性，能利用最少的传感器数目获取精确的电磁频谱地图；1) The sensor node layout optimization method and system for electromagnetic spectrum map surveying and mapping proposed by the present invention comprehensively consider the radio wave propagation model and the spatial correlation of spectrum data, and can obtain accurate electromagnetic spectrum maps with the least number of sensors;

2）本发明提出的传感器节点布局优化方案，基于混合构建的频谱数据空间相关性模型与克里金方差模型，将采样节点布局优化与贯序式节点优化相结合，有效降低了计算复杂度。2) The sensor node layout optimization scheme proposed by the present invention is based on the hybrid construction of the spectral data spatial correlation model and the kriging variance model, and combines the sampling node layout optimization with the sequential node optimization, which effectively reduces the computational complexity.

附图说明Description of drawings

图1为本发明面向电磁频谱地图测绘的传感器节点布局优化方法流程图。FIG. 1 is a flowchart of a sensor node layout optimization method for electromagnetic spectrum map mapping according to the present invention.

图2为实施例的全局频谱地图。Fig. 2 is a global spectrum map of an embodiment.

图3为实施例的等间隔初始化采集的频谱数据示意图。Fig. 3 is a schematic diagram of spectrum data collected by initialization at equal intervals according to an embodiment.

图4为实施例的经验半方差值的计算结果图。Fig. 4 is a diagram of the calculation result of the empirical semivariance value of the embodiment.

图5为实施例的聚类中心示意图。Fig. 5 is a schematic diagram of the cluster center of the embodiment.

图6为实施例的拟合全局空间半变异函数的计算结果图。Fig. 6 is a diagram of the calculation result of fitting the global spatial semivariogram of the embodiment.

图7a到图7d为实施例的初始采样节点优化的结果图，图7a表示初始化的25个节点位置，图7b表示迭代10次后25个节点位置，图7c表示迭代20次后25个节点位置，图7d表示最终优化后25个节点位置。Fig. 7a to Fig. 7d are the result graphs of the initial sampling node optimization of the embodiment, Fig. 7a represents the 25 node positions of initialization, Fig. 7b represents the 25 node positions after 10 iterations, and Fig. 7c represents the 25 node positions after 20 iterations , Figure 7d shows the 25 node positions after final optimization.

图8a到图8d为实施例的采样节点优化最终输出的结果图，图8a表示50个节点的优化位置，图8b表示100个节点的优化位置，图8c表示150个节点的优化位置，图8d表示256个节点的优化位置。Fig. 8 a to Fig. 8 d are the result figure of the final output of sampling node optimization of the embodiment, Fig. 8 a represents the optimized position of 50 nodes, Fig. 8 b represents the optimized position of 100 nodes, Fig. 8 c represents the optimized position of 150 nodes, Fig. 8 d Indicates the optimal placement of 256 nodes.

实施方式Implementation

下面将结合本申请实施例中的附图，对本申请实施例中的技术方案进行清楚、完整的描述，显然，所描述的实施例仅仅是本申请一部分实施例，而不是全部的实施例。基于本申请中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本申请保护的范围。The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all of them. Based on the embodiments in this application, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the scope of protection of this application.

在一实施例中，如图1所示，本发明提出了一种面向电磁频谱地图测绘的传感器节点布局优化方法。本实施例的全局频谱地图如图2所示，待测场景中存在有发射机数目8个。对应发射机的位置参数

Figure SMS_69
、发射频率f和发射功率
Figure SMS_70
如表1所示。In one 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 , and there are 8 transmitters in the scene to be tested. Corresponding to the location parameters of the transmitter
Figure SMS_69
, transmit frequency f and transmit power
Figure SMS_70
As shown in Table 1.

表1 发射机配置参数Table 1 Transmitter Configuration Parameters

Figure SMS_71
。
Figure SMS_71
.

具体实施步骤如下：The specific implementation steps are as follows:

第一步：用户设置待测区域长度L = 500m和宽度W = 500m，待测频段f =2450Mhz；用户设置总采样节点数N = 256。本实施例采用均匀等间隔布置的方案。根据公式（1）的约束条件进行等间隔采集，横向间隔

Figure SMS_72
= 30m和纵向间隔
Figure SMS_73
= 30m，得到初始采集后的频谱数据M，如图3所示。Step 1: The user sets the length L = 500m and width W = 500m of the area to be tested, and the frequency band to be tested f = 2450Mhz; the user sets the total number of sampling nodes N = 256. This embodiment adopts the scheme of uniform and equidistant arrangement. According to the constraints of formula (1), the acquisition is performed at equal intervals, and the horizontal interval
Figure SMS_72
= 30 m and longitudinal separation
Figure SMS_73
= 30 m , get the spectrum data M after the initial acquisition, as shown in Fig. 3.

Figure SMS_74
（1）
Figure SMS_74
(1)

式中，

Figure SMS_75
为第i个采样节点位置
Figure SMS_76
处采集T时间的平均接收功率，
Figure SMS_77
为
Figure SMS_78
位置处t时刻的瞬时电压；t 1表示任意起始时刻。In the formula,
Figure SMS_75
is the i- th sampling node position
Figure SMS_76
The average received power collected at time T ,
Figure SMS_77
for
Figure SMS_78
The instantaneous voltage at time t at the position; t 1 represents an arbitrary starting time.

第二步：根据初始采集后的频谱数据M，将每个采样节点两两配对，利用公式（2）计算得到经验半方差值数据点

Figure SMS_79
，如图4所示。Step 2: According to the spectrum data M after the initial collection, pair each sampling node in pairs, and use the formula (2) to calculate the empirical semivariance value data points
Figure SMS_79
,As shown in Figure 4.

Figure SMS_80
（2）
Figure SMS_80
(2)

式中，d表示第i个采样节点与第j个采样节点的距离，

Figure SMS_81
表示第i个采样节点与第j个采样节点的半方差值，
Figure SMS_82
表示任意两个距离为d的采样节点的半方差值，
Figure SMS_83
表示距离d的经验半方差值；将距离为d的任意两个采样节点称为距离为d的节点组，N d 为距离为d的节点组的组数。In the formula, d represents the distance between the i -th sampling node and the j -th sampling node,
Figure SMS_81
Indicates the semivariance value between the i- th sampling node and the j -th sampling node,
Figure SMS_82
Represents the semivariance value of any two sampling nodes with a distance of d ,
Figure SMS_83
Indicates the empirical semivariance value of the distance d ; any two sampling nodes with a distance of d are called a node group with a distance of d , and N d is the group number of the node group with a distance of d .

对得到的经验半方差值

Figure SMS_84
进行聚类分组，聚类分组数K=12。利用公式（3）计算每组的距离向量，利用公式（4）进行距离度量，直至收敛后结束，并根据聚类结果计算每类的半方差均值，如图5所示。For the obtained empirical semivariance value
Figure SMS_84
Carry out clustering and grouping, the number of clustering groups K =12. Use the formula (3) to calculate the distance vector of each group, use the formula (4) to measure the distance until it converges, and calculate the semivariance mean of each class according to the clustering results, as shown in Figure 5.

Figure SMS_85
（3）
Figure SMS_85
(3)

Figure SMS_86
（4）
Figure SMS_86
(4)

式中，经验半方差值数据点中的距离变量组成集合

Figure SMS_87
作为聚类分组变量，
Figure SMS_88
表示第epn个经验半方差值数据点的距离变量；随机选取K个互不重复的样本作为聚类中心
Figure SMS_89
；用
Figure SMS_90
表示第k组内半方差值数据点的数目，k的取值是1~K，每个分组集合为
Figure SMS_91
，
Figure SMS_92
表示第k组的聚类中心，ep的取值是1~epn。In the formula, the distance variables in the empirical semivariance value data points form the set
Figure SMS_87
As a clustering grouping variable,
Figure SMS_88
Indicates the distance variable of the epnth empirical semivariance data point; randomly select K non-repeating samples as cluster centers
Figure SMS_89
;use
Figure SMS_90
Indicates the number of semi-variance value data points in the kth group, the value of k is 1~ K , and each grouping set is
Figure SMS_91
,
Figure SMS_92
Indicates the cluster center of the kth group, and the value of ep is 1~ epn .

第四步：根据聚类分组后的半方差均值，拟合获得全局空间半变异函数

Figure SMS_93
，如图6所示，其优化目标为：Step 4: According to the mean value of semivariance after clustering and grouping, fit to obtain the global spatial semivariogram
Figure SMS_93
, as shown in Figure 6, its optimization objective is:

Figure SMS_94
（5）
Figure SMS_94
(5)

式中，

Figure SMS_95
表示目标函数，
Figure SMS_96
表示第k个聚类分组后的半方差值数据点的距离变量，
Figure SMS_97
表示第k个聚类分组后的半方差值数据点的半方差值变量，
Figure SMS_98
是待定参数，c 0是半方差零点偏移值，c是半方差缩放系数，
Figure SMS_99
为距离缩放系数。In the formula,
Figure SMS_95
represents the objective function,
Figure SMS_96
Indicates the distance variable of the semivariogram data points after the kth cluster grouping,
Figure SMS_97
Represents the semivariogram variable of the semivariogram data points after the kth cluster grouping,
Figure SMS_98
is an undetermined parameter, c 0 is the semivariance zero offset value, c is the semivariance scaling coefficient,
Figure SMS_99
is the distance scaling factor.

将

Figure SMS_100
趋于稳定时的距离d记作相关距离d 0，此时的
Figure SMS_101
为临界空间变异值C，根据公式（6）确定d 0为10m，最小初始布局点数P =25。Will
Figure SMS_100
The distance d when it tends to be stable is recorded as the correlation distance d 0 , at this time
Figure SMS_101
is the critical spatial variation value C , according to formula (6), determine that d 0 is 10m, and the minimum number of initial layout points P =25.

Figure SMS_102
（6）
Figure SMS_102
(6)

式中，

Figure SMS_103
为波动阈值。In the formula,
Figure SMS_103
is the fluctuation threshold.

第五步：基于随机优化算法求解获得初始采样节点优化位置。具体实现步骤如下：Step 5: Obtain the optimal position of the initial sampling node based on the stochastic optimization algorithm. The specific implementation steps are as follows:

S5.1：利用公式（7）对解空间、搜索速度和最优节点位置进行初始化：S5.1: Use formula (7) to initialize the solution space, search speed and optimal node position:

Figure SMS_104
（7）
Figure SMS_104
(7)

式中，

Figure SMS_105
为解空间中的第q个解，
Figure SMS_106
为第q个解的搜索速度，
Figure SMS_107
为第q个解中的第1个节点位置，
Figure SMS_108
是第q个解中第1个节点的搜索速度，
Figure SMS_109
是初始解空间X中的最优初始采样节点位置，函数initialize表示初始化。In the formula,
Figure SMS_105
is the qth solution in the solution space,
Figure SMS_106
is the search speed of the qth solution,
Figure SMS_107
is the first node position in the qth solution,
Figure SMS_108
is the search speed of the first node in the qth solution,
Figure SMS_109
is the optimal initial sampling node position in the initial solution space X, and the function initialize represents initialization.

S5.2：根据第二步、第三步的方法计算P个初始采样节点的半方差值

Figure SMS_110
。S5.2: Calculate the semivariance value of P initial sampling nodes according to the second and third steps
Figure SMS_110
.

S5.3：利用公式（8）计算目标函数值：S5.3: Use formula (8) to calculate the objective function value:

Figure SMS_111
（8）
Figure SMS_111
(8)

S5.4：利用公式（9）更新解空间、搜索速度与最优初始节点位置：S5.4: Use formula (9) to update the solution space, search speed and optimal initial node position:

Figure SMS_112
（9）
Figure SMS_112
(9)

式中，

Figure SMS_113
是第t+1次迭代时第q个解的搜索速度，
Figure SMS_114
是第t次迭代后第q个解的最优情况，
Figure SMS_115
是第t次迭代后最优节点位置情况，
Figure SMS_116
为第t+1次迭代时的第q个解，函数update表示从解空间X中取得最优节点位置情况，并更新到Gb中，w是惯性权重，r 1、r 2是服从均匀分布的随机数，函数max表示取最大值。In the formula,
Figure SMS_113
is the search speed of the qth solution at the t +1th iteration,
Figure SMS_114
is the optimal case of the qth solution after the tth iteration,
Figure SMS_115
is the optimal node position after the tth iteration,
Figure SMS_116
is the qth solution at the t +1th iteration, the function update means to obtain the optimal node position from the solution space X, and update it to Gb, w is the inertia weight, r 1 and r 2 are uniformly distributed Random number, the function max means to take the maximum value.

重复S5.2至S5.4，迭代至收敛后结束算法，并输出最优采样节点位置

Figure SMS_117
如图7a到图7d所示，详细采样坐标如表2所示。Repeat S5.2 to S5.4, iterate until convergence and end the algorithm, and output the optimal sampling node position
Figure SMS_117
As shown in Figure 7a to Figure 7d, the detailed sampling coordinates are shown in Table 2.

表2 详细采样坐标Table 2 Detailed sampling coordinates

Figure SMS_118
。
Figure SMS_118
.

第六步：初始化已采样节点数n=P=25，基于克里金方差最大原则对剩余节点进行贯序式优化，直至达到总采样节点数N=256。具体实现步骤如下：Step 6: Initialize the number of sampled nodes n = P = 25, and perform sequential optimization on the remaining nodes based on the principle of maximum variance of Kriging until the total number of sampled nodes N = 256. The specific implementation steps are as follows:

S6.1：利用公式（10）和公式（11）计算每个未采样位置的克里金方差值：S6.1: Calculate the kriging variance value for each unsampled location using Equation (10) and Equation (11):

Figure SMS_119
（10）
Figure SMS_119
(10)

Figure SMS_120
（11）
Figure SMS_120
(11)

式中，

Figure SMS_121
是采样节点位置
Figure SMS_122
和未采样位置
Figure SMS_123
的半方差值，
Figure SMS_124
是待求解系数。In the formula,
Figure SMS_121
is the sampling node position
Figure SMS_122
and the unsampled position
Figure SMS_123
The semivariance value of ,
Figure SMS_124
is the coefficient to be solved.

S6.2：令克里金方差值最大的未采样位置为下一个采样节点位置

Figure SMS_125
，并将该位置加入已采样节点集合
Figure SMS_126
。更新已采样节点数n=n+1。S6.2: Let the unsampled position with the largest kriging variance value be the next sampling node position
Figure SMS_125
, and add the position to the set of sampled nodes
Figure SMS_126
. Update the number of sampled nodes n = n +1.

S6.3：重复S6.1与S6.2直至达到总采样节点数N=256，输出最终采样节点位置优化结果，如图8a到图8d所示。S6.3: Repeat S6.1 and S6.2 until the total number of sampling nodes N = 256, and output the final sampling node position optimization results, as shown in Fig. 8a to Fig. 8d.

在另一实施例中，本发明还提出了与第一实施例所提出的面向电磁频谱地图测绘的传感器节点布局优化方法相对应的系统，即一种面向电磁频谱地图测绘的传感器节点布局优化系统，具体包括：In another embodiment, the present invention also proposes a system corresponding to the sensor node layout optimization method for electromagnetic spectrum map mapping proposed in the first embodiment, that is, a sensor node layout optimization system for electromagnetic spectrum map mapping , including:

采集设备，用于对待测区域按照随机轨迹或均匀轨迹进行频谱数据移动式初始化采集，获得初始频谱数据；Acquisition equipment, which is used to perform mobile initial collection of spectrum data in accordance with random or uniform trajectories in the area to be measured to obtain initial spectrum data;

计算模块，用于利用获得的初始频谱数据，将采样位置两两配对，计算半方差值，获得经验半方差值数据点；将经验半方差值数据点进行聚类分组，获得聚类分组后的半方差值数据点；根据聚类分组后的半方差值数据点，拟合获得空间全局半变异函数，根据获得的空间全局半变异函数，确定最小采样节点数；The calculation module is used to use the obtained initial spectrum data to pair the sampling positions in pairs, calculate the semivariance value, and obtain the empirical semivariance value data points; cluster and group the empirical semivariance value data points to obtain the clustering The semivariogram data points after grouping; according to the semivariogram data points after clustering and grouping, the spatial global semivariogram is obtained by fitting, and the minimum number of sampling nodes is determined according to the obtained spatial global semivariogram;

优化模块，用于根据最小采样节点数，基于随机优化算法进行初始采样节点位置的优化；根据优化后的初始采样节点位置所采集的数据，基于克里金方差最大原则对剩下的采样节点位置进行贯序式优化，直至总采样节点数。The optimization module is used to optimize the initial sampling node position based on the random optimization algorithm according to the minimum number of sampling nodes; according to the data collected at the optimized initial sampling node position, the remaining sampling node positions are calculated based on the principle of maximum kriging variance Perform sequential optimization up to the total number of sampled nodes.

在面向电磁频谱地图测绘的传感器节点布局优化系统中，各设备/模块的具体工作方式及实施步骤与面向电磁频谱地图测绘的传感器节点布局优化方法相同，故不再重复描述。In the sensor node layout optimization system for electromagnetic spectrum map mapping, the specific working methods and implementation steps of each device/module are the same as the sensor node layout optimization method for electromagnetic spectrum map mapping, so the description will not be repeated.

以上仅是本发明的优选实施方式，本发明的保护范围并不仅局限于上述实施例，凡属于本发明思路下的技术方案均属于本发明的保护范围。应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理前提下的若干改进和润饰，应视为本发明的保护范围。The above are only preferred implementations of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions under the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (8)

1. A sensor node layout optimization method for electromagnetic spectrum mapping is characterized by comprising the following steps:
step 1: carrying out mobile initialization collection on the frequency spectrum data of the area to be detected according to a random track or a uniform track by utilizing collection equipment to obtain initial frequency spectrum data;
step 2: pairing the sampling positions pairwise by using the obtained initial frequency spectrum data, calculating a half variance value, and obtaining an empirical half variance value data point;
and 3, step 3: clustering and grouping the empirical half-variance value data points to obtain clustered and grouped half-variance value data points;
and 4, step 4: according to the clustered and grouped half variance value data points, fitting to obtain a spatial global half-variation function, and according to the obtained spatial global half-variation function, determining the minimum number of sampling nodes;
and 5: optimizing the position of the initial sampling node based on a random optimization algorithm according to the minimum number of the sampling nodes;
and 6: and performing sequential optimization on the positions of the rest sampling nodes based on the principle of maximum kriging variance according to the data acquired from the optimized initial sampling node position until the total number of the sampling nodes.
2. The method for optimizing the layout of the sensor nodes for electromagnetic spectrum mapping as claimed in claim 1, wherein: in step 1, the initial spectrum data M is represented as:
Figure QLYQS_1
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_3
is as follows
Figure QLYQS_8
Sampling node position
Figure QLYQS_13
Department collection
Figure QLYQS_5
The average received power over time is determined by,
Figure QLYQS_9
is composed of
Figure QLYQS_11
At the position
Figure QLYQS_14
Instantaneous electricity of time of dayThe pressure is applied to the inner wall of the cylinder,
Figure QLYQS_2
and
Figure QLYQS_6
respectively are uniformly collected at equal intervals in the transverse direction and the longitudinal direction;
Figure QLYQS_10
is the length of the region to be measured,
Figure QLYQS_12
is the width of the region to be measured,
Figure QLYQS_4
for the total number of sampling nodes to be counted,
Figure QLYQS_7
indicating an arbitrary starting moment.
3. The method for optimizing the layout of the sensor nodes for electromagnetic spectrum mapping as claimed in claim 2, wherein: in the step 2, empirical half-variance data points
Figure QLYQS_15
The calculation method of (c) is as follows:
Figure QLYQS_16
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_18
is shown as
Figure QLYQS_22
A sampling node and the second
Figure QLYQS_28
The distance of the individual sampling nodes,
Figure QLYQS_20
is shown as
Figure QLYQS_23
A sampling node and the second
Figure QLYQS_27
The half variance value of each sampling node,
Figure QLYQS_30
means any two distances of
Figure QLYQS_17
The value of the half-variance of the sampling node of (a),
Figure QLYQS_21
indicating distance
Figure QLYQS_25
The empirical half variance value of; will be at a distance of
Figure QLYQS_29
Any two sampling nodes of are referred to as a distance of
Figure QLYQS_19
The group of nodes of (a) is,
Figure QLYQS_24
is a distance of
Figure QLYQS_26
The number of groups of node groups.
4. The method for optimizing the layout of sensor nodes for electromagnetic spectrum mapping as claimed in claim 3, wherein: the step 3 specifically comprises the following steps:
step 3.1: selecting a set of distance variables from empirical half-variance data points
Figure QLYQS_33
As a variable of the clustering group, there is,
Figure QLYQS_37
is shown as
Figure QLYQS_39
Distance variables for the empirical half variance value data points; random selection
Figure QLYQS_34
Using non-repetitive samples as clustering center
Figure QLYQS_36
(ii) a By using
Figure QLYQS_40
Is shown as
Figure QLYQS_42
The number of points of the semi-variance data values within the group,
Figure QLYQS_31
is taken as
Figure QLYQS_35
Each group is aggregated into
Figure QLYQS_38
Then it is first
Figure QLYQS_41
Cluster center of group
Figure QLYQS_32
Comprises the following steps:
Figure QLYQS_43
；
step 3.2: calculating each half variance valueDistance variables in data points
Figure QLYQS_44
With each cluster center
Figure QLYQS_45
Euclidean distance of
Figure QLYQS_46
：
Figure QLYQS_47
，
In the formula (I), the compound is shown in the specification,
Figure QLYQS_48
is taken as
Figure QLYQS_49
；
Step 3.3: according to the calculated Euclidean distance, dividing each sample into a group with the nearest one in turn, and then recalculating the clustering center
Figure QLYQS_50
If, if
Figure QLYQS_51
Then will be
Figure QLYQS_52
Update the value of (2) to cluster center
Figure QLYQS_53
；
Step 3.4: repeating the step 3.2 and the step 3.3, iterating until the clustering center is not changed, ending the algorithm after convergence is reached, and outputting the final clustering grouping result
Figure QLYQS_54
；
Step 3.5: empirical half-variance valuesData points
Figure QLYQS_57
According to post-clustering partitioning
Figure QLYQS_59
The groups are averaged to obtain a semi-variance data point set after clustering grouping
Figure QLYQS_60
Wherein
Figure QLYQS_56
Representing the semi-variance value data points after clustering grouping,
Figure QLYQS_58
is shown as
Figure QLYQS_61
Distance variables for the grouped half variance value data points,
Figure QLYQS_62
is the first
Figure QLYQS_55
And the variance value of the grouped half variance value data points is variable.
5. The method for optimizing the layout of the sensor nodes for electromagnetic spectrum mapping as claimed in claim 4, wherein: the step 4 is specifically as follows:
grouping the data points according to the clustering
Figure QLYQS_63
Fitting to obtain a spatial global semi-variogram
Figure QLYQS_64
The optimization target is as follows:
Figure QLYQS_65
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_67
the representation of the objective function is shown as,
Figure QLYQS_70
is shown as
Figure QLYQS_72
The distance variable of the grouped half variance value data points of each cluster,
Figure QLYQS_68
denotes the first
Figure QLYQS_71
The variance of the grouped half variance value data points,
Figure QLYQS_73
is the parameter to be determined and is,
Figure QLYQS_74
is the value of the half-variance zero offset,
Figure QLYQS_66
is the half-variance scaling factor and is,
Figure QLYQS_69
is a distance scaling factor;
will be provided with
Figure QLYQS_75
Distance at which stability tends to occur
Figure QLYQS_76
Record as the correlation distance
Figure QLYQS_77
At this time
Figure QLYQS_78
Is the critical space variation value
Figure QLYQS_79
Determining the minimum number of sampling nodes according to the following equal interval constraint formula
Figure QLYQS_80
：
Figure QLYQS_81
，
In the formula (I), the compound is shown in the specification,
Figure QLYQS_82
is the fluctuation threshold.
6. The method for optimizing the layout of sensor nodes for electromagnetic spectrum mapping as claimed in claim 5, wherein: the step 5 specifically comprises the following steps:
step 5.1: initializing solution space X, search speed V and
Figure QLYQS_83
initial sampling node location:
Figure QLYQS_84
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_86
is the first in solution space
Figure QLYQS_89
The number of the solutions is one,
Figure QLYQS_91
is as follows
Figure QLYQS_87
The speed of the search of the individual solutions,
Figure QLYQS_90
is as follows
Figure QLYQS_92
The 1 st node position in the solution,
Figure QLYQS_93
is the first
Figure QLYQS_85
The search speed of the 1 st node in the solution,
Figure QLYQS_88
the position of the optimal initial sampling node in the initial solution space X is shown, and the initialization is represented by the function initialization;
step 5.2: computingPHalf-variance value of initial sampling node
Figure QLYQS_94
；
Step 5.3: calculating an optimization objective function:
Figure QLYQS_95
；
step 5.4: the solution space is updated and the global optimum is obtained according to the following principle:
Figure QLYQS_96
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_97
is the firstt+1 iteration timeqThe speed of the search of the individual solutions,
Figure QLYQS_98
is the firsttAfter the second iterationqThe optimal situation of the individual solutions is,
Figure QLYQS_99
is the firsttThe optimal node position situation after the sub-iteration,
Figure QLYQS_100
is as followstThe first of +1 iterationsqThe solution, function update, indicates the situation of obtaining the optimal node position from the solution space X and updating into Gb,
Figure QLYQS_101
it is the weight of the inertia that,
Figure QLYQS_102
、
Figure QLYQS_103
is a random number subject to uniform distribution, and the function max represents taking the maximum value;
step 5.5: repeating the step 5.2 to the step 5.4, iterating until the algorithm is finished after convergence, and outputting the optimized initial sampling node position
Figure QLYQS_104
。
7. The method for optimizing the layout of sensor nodes based on electromagnetic spectrum mapping as claimed in claim 6, wherein: the step 6 specifically comprises the following steps:
step 6.1: first, the weight coefficients are solved using the following formula:
Figure QLYQS_105
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_106
is the sampling node position
Figure QLYQS_107
And a non-sampled position
Figure QLYQS_108
The value of the half-variance of (c),
Figure QLYQS_109
is the coefficient to be solved;
and then calculating the kriging variance value at each unknown sampling position by using the following formula
Figure QLYQS_110
：
Figure QLYQS_111
；
Step 6.2: taking the position with the maximum Kriging variance value
Figure QLYQS_112
For the next sampled node location, and add the sampled node location set
Figure QLYQS_113
Updating the number of sampled nodes
Figure QLYQS_114
；
Step 6.3: repeating the step 6.1 and the step 6.2 until the total number of sampling nodes is reachedNAnd outputting the final sampling node position optimization result.
8. A sensor node layout optimization system oriented to electromagnetic spectrum mapping is characterized by comprising:
the acquisition equipment is used for carrying out mobile initialization acquisition on the frequency spectrum data of the area 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 the sampling positions pairwise by using the obtained initial 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 and grouped half-variance value data points; according to the clustered and grouped half variance value data points, fitting to obtain a spatial global half-variation function, and according to the obtained spatial global half-variation function, determining the minimum number of sampling nodes;
the optimization module is used for optimizing the position of the initial sampling node based on a random optimization algorithm according to the minimum number of the sampling nodes; and performing sequential optimization on the positions of the rest sampling nodes based on the principle of maximum kriging variance according to the data acquired from the optimized initial sampling node position until the total number of the sampling nodes.
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