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单根电力线分割指将跨越多档的同一条电力线点云分为一类,将不同电力线的点云分为不同的类,单根电力线分割是提取电力线悬挂点的基础。一般情况下,同一条电力线上相邻点云间距离较小且紧密,不同电力线点云间距离较大。但由于激光雷达系统数据采集的随机性、激光扫描系统自身的误差和环境因素等,所采集的电力线点云很有可能存在电力线缺失情况。对于这种情况,常见的使用距离聚类分割电力线的方法鲁棒性较低,聚类中距离阈值若过小,则聚类不完整,同一条电力线因为点云缺失而被聚类为多条电力线; 若过大,则不同电力线被聚类为同一条电力线。因此,对电力线点云的空间特征进行描述,形成电力线空间约束条件,以此作为生长准则进行区域生长分割,实现电力线点云缺失情况下单根电力线的准确分割。
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通过研究发现,同一条电力线中点云即使存在缺失时,仍然表现出独特的空间特征,主要可概括为以下两点:(1)空间特征1。在x-y-z 3维空间,同一条电力线上相邻点云之间高程变化较小,即使电力线点云出现缺失情况,即两相邻点云间距离较大时,高差仍然较小,如图 1所示,同层电力线中相邻点云高差dz1远远小于不同层电力线间点云高差dz2; (2)空间特征2。在x-O-y 2维平面,同一条电力线上所有点云大致在同一直线上,具体可通过点到直线的距离dP来判定表征,如图 2所示。
同一条电力线中点云具备以上2个空间特征,不同电力线点云则不具备。根据空间特征1,可以实现电力线分层提取; 根据空间特征2,可以实现电力线同层分离。因此,将上述两个空间特征进行公式化表达,作为单根电力线点云分割的空间约束条件,详细定义如表 1所示。
Table 1. Spatial constraints of power line point cloud
serial
numbercoordinate
systemspatial constraint
conditionformulaic
expression1 x-y-z 3-D space height difference specific formula (1) 2 x-O-y 2-D plane distance from
point to linespecific formula (2) $ \Delta z = {z_i} - {z_0} < {T_1} $
(1) $ {d_p} = \frac{{\left| {A{x_i} + B{y_i} + C} \right|}}{{\sqrt {{A^2} + {B^2}} }} < {T_2} $
(2) 式中,zi, z0分别表示未分类点Pi与种子点P0的高程值,Δz表示未分类点Pi与种子点P0之间的高程差,T1表示高程差阈值,取经验值1.00m;(2)式中dP表示P点到直线的距离,(xi,yi)表示未分类点Pi的平面坐标,A, B和C为平面直线方程系数,T2表示点到直线距离阈值,取经验值1.00m。
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对电力线点云2个空间约束条件进行公式化表达后,以此作为生长准则对电力线点云进行区域生长,实现单根电力线分割,具体步骤在下面阐述。
(1) 建立K-D树(K-dimension tree)。为加快搜索速度,采用K-D树结构分割散乱点云,K-D树的维度为3。
(2) 选取初始种子点。选取电力线点云中最小坐标值的激光点云数据作为初始种子点P0。
(3) 基于K-D树索引的邻域点搜索。借助K-D树查找该种子点半径为R的邻域内所有电力线点云,并存入邻域点集Φ{P1, P2, …, Pi}。本文中半径R设为10.00m。
(4) 基于空间约束的区域生长。种子点作为生长的起点,将邻域点与种子点进行对比,将符合电力线空间约束条件的邻域点合并起来继续向外生长,具体包括如下两个层次的生长过程:(a)电力线点云分层提取。计算邻域点集Φ中各点云与种子点P0的高程差值Δz,高程差小于阈值T1的点云视为与该种子点同层的电力线点云,并保存在相应同层电力线点云数组Φs中,完成第一层次生长; (b)电力线点云同层分离。利用最小二乘线性拟合对同层电力线点云数组Φs中点云进行x-O-y平面内的直线拟合,并选取与种子点P0距离最近的直线作为基准电力线,计算Φs中点云到该电力线距离dP,距离小于阈值T2的点云视为同层电力线中同一根电力线上点云,并保存在相应同一根电力线点云数组Φline中,完成第二层次生长。
(5) 更新种子点。将数组Φline中点云的质心点作为下次生长的种子点。
(6) 重复执行步骤(3)~步骤(5),直到不存在符合生长准则的电力线点则停止生长,至此,完成一条电力线分割。
(7) 对于未处理的点云数据,重复执行步骤(2)~步骤(6),完成所有电力线的分割。
跨越多档电力线原始点云(存在电力线中间点云缺失及悬挂点附近点云缺失情况)如图 3所示,最终单根电力线分割效果如图 4所示。
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对杆塔点云数据进行基于密度的聚类,分割出每基杆塔相对应的点云数据Ct, i(i=1, 2, …, n,其中i表示杆塔序号,n表示杆塔数量),将聚类分割后的每基杆塔点云Ct, i投影到x-O-y平面,提取各投影后的杆塔点云质心坐标Pt, i(x, y),作为该基杆塔中心的x-O-y平面坐标; 将各杆塔中心平面点Pt, i(x, y)依次连线,计算各点的角平分线Li(x, y)(首尾两个点的角平分线为垂直于电力线点云的垂线),如图 5所示,图中T1,T2,…,T5表示杆塔序号。
过各角平分线Li(x, y)作垂直于x-O-y平面的空间平面Si(x, y, z)面,并将空间平面Si(x, y, z)作为分割该基杆塔左右两档各单根电力线的空间分割平面,如图 6a和图 6b所示,图中白色为杆塔点云,绿色为以杆塔连线的角平分线为基准的空间分割平面。根据杆塔与电力线悬挂点的位置关系可知,悬挂点在空间分割平面附近或在空间分割平面内。
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分别提取空间分割平面Si(x, y, z)两侧距离该平面10.00m之内的电力线点云并存入集合Cr, i和Cl, i,分别对Cr, i和Cl, i中点云进行空间多项式拟合,并延长至20.00m长,进行间隔为0.05m的等距采样,得到电力线悬挂点附近局部3维重建后的电力线点云集合CCR, i和CCL, i,空间多项式拟合方程如下式所示:
$ z = a({x^2} + {y^2}) + b\sqrt {{x^2} + {y^2}} + c $
(3) 式中,a, b, c是多项式方程参量,为了获得多项式模型系数,采用最小二乘方法进行拟合求解。根据最小二乘原理,其局部拟合过程可转化为以下极值问题:
$ \begin{array}{l} W = \sum {[{z_i} - (a(x_i^2 + y_i^2) + } \\ b\sqrt {x_i^2 + y_i^2} + c){]^2} \to \min \end{array} $
(4) 即:
$ \left\{ \begin{array}{l} \frac{{\partial W}}{{\partial a}} = - 2\sum {\{ {z_i} - [a(x_i^2 + y_i^2) + } \\ b{(x_i^2 + y_i^2)^{1/2}} + c]{\} ^2} = 0\\ \frac{{\partial W}}{{\partial b}} = - 2{\sum {\{ {z_i}{{(x_i^2 + y_i^2)}^{1/2}} - [a(x_i^2 + y_i^2)} ^{3/2}} + \\ b(x_i^2 + y_i^2) + c{(x_i^2 + y_i^2)^{1/2}}]{\} ^2} = 0\\ \frac{{\partial W}}{{\partial c}} = - 2{\sum {\{ {z_i}(x_i^2 + y_i^2) - [a(x_i^2 + y_i^2)} ^2} + \\ b{(x_i^2 + y_i^2)^{3/2}} + c(x_i^2 + y_i^2)]{\} ^2} = 0 \end{array} \right. $
(5) 式中,xi, yi, zi分别表示待拟合点云的3维空间坐标; W表示3维空间中高程zi的真实值与计算值之间的误差平方和,∂W/∂a, ∂W/∂b, ∂W/∂c分别表示误差平方和W对a, b, c系数的1阶偏导数。
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根据电力线悬挂点的定义可知,局部3维重建后的电力线CCR, i和CCL, i相交点即为电力线悬挂点,采用以下方法快速搜索两电力线交点(即悬挂点)。
(1) 分别提取CCR, i和CCL, i中距离分割平面Si(x, y, z)0.10m之内的电力线点集合C1, i,C2, i。
(2) 分别计算点集合C1, i,C2, i中平均坐标P1, i,P2, i,若P1, i和P2, i坐标值相同,则P1, i即为电力线悬挂点,停止搜索; 否则,计算点P1, i,P2, i之间的距离d。
(3) 将空间分割平面Si(x, y, z)沿d递减的电力线方向以一定步长进行平移,直到搜索到d=0.00m或者为最小值时则停止平移,此时两电力线交点(即电力线悬挂点)位于停止平移时的空间分割平面Si(x, y, z)上或其附近,提取CCR, i和CCL, i中距离停止平移时的空间分割平面Si(x, y, z)0.10m之内的点云于一个集合中,计算该集合中点坐标的平均值即为电力线悬挂点空间坐标。
其中,将空间分割平面Si(x, y, z)沿d递减的电力线方向进行平移方法具体为:设置平移步长为0.10m,将分割平面沿某侧电力线方向进行平移,若平移后的d值大于平移前的d值(即d递增),则将分割平面沿反方向进行平移,若平移后的d值小于平移前的d值(即d递减),则继续沿该方向平移。
(4) 对于首尾两基杆塔上的悬挂点,若只有一侧存在电力线点云,则将该侧电力线点云局部3维重建结果与空间分割平面Si(x, y, z)的交点作为悬挂点。
电力线悬挂点定位结果如图 7所示,图中红色点为定位到的电力线悬挂点。其中第三基杆塔为悬挂点处电力线点云缺失(误分类)情况,其余为悬挂点处电力线点云完整情况。
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为验证算法的有效性,本文中以实际输电线路点云数据为准,采集某电网运检公司所辖3种常见电压等级输电线路部分档的激光点云作为算法测试的数据源,线路点云数据如图 8所示,具体信息如表 2所示。
Table 2. Test line information
line serial number 1 2 3 voltage level/kV 110 220 500 line length/km 2.56 1.16 4.88 number of power lines 6 5 4 number of towers 9 4 14 number of suspension points 54 20 56 -
利用本文中的方法分别对上述3条不同电压等级的架空输电线路点云数据进行分析处理,定位电力线悬挂点,定位效果图如图 9所示,详细结果如表 3所示。其中110kV架空线路的整体最大定位偏差为0.12m,最小定位偏差为0.03m,x, y, z平均偏差和整体平均偏差分别为0.07m, 0.07m, 0.05m, 0.063m;220kV架空线路的整体最大定位偏差为0.16m,最小定位偏差为0.04m,x, y, z平均偏差和整体偏差分别为0.07m, 0.06m, 0.07m, 0.067m;500kV架空线路的整体最大定位偏差为0.21m,最小定位偏差为0.05m,x, y, z平均偏差和整体偏差分别为0.09m, 0.09m, 0.08m, 0.087m,3种不同电压等级的整体定位偏差均保持在0.09m以下,偏差在允许范围内。
Figure 9. Location result of power line suspension point(the red point in the figure is the power line suspension point that is located)
Table 3. Analysis of test results
line serial
numbervoltage
level/kVmaximum positioning
deviation/mminimum positioning
deviation/maverage positioning deviation/m Δx Δy Δz whole 1 110 0.12 0.03 0.07 0.07 0.05 0.063 2 220 0.16 0.04 0.07 0.06 0.07 0.067 3 500 0.21 0.05 0.09 0.09 0.08 0.087 -
算法提出的目的是从输电线路点云数据中精确的提取电力线悬挂点空间坐标,以实现精准的各工况下电力线模拟,以便及时发现输电通道潜在缺陷,实现潜在危险区域的自动化监测。因此,将本文中的方法与已有的其它悬挂点定位方法进行测试对比,客观分析方法的准确性及鲁棒性,方法1为以局部极大值点作为悬挂点,方法2为以2阶导数显著变化的位置作为悬挂点。
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将本文中方法与其它已有方法分别对悬挂点附近电力线点云完整且分类正确情况下(数据类型1),以及悬挂点附近电力线点云缺失或分类错误情况下(数据类型2)两种数据质量情况的悬挂点空间坐标提取进行测试对比,计算平均定位偏差如表 4所示。
Table 4. Robustness comparison of positioning methods
data type method 1/m method 2/m this paper method/m 1 0.51 0.31 0.06 2 2.14 1.85 0.07 由表 4可知,对于数据质量较好的数据类型1,方法1、方法2均基本能定位悬挂点位置,但方法1因易受粗差点和噪点的影响定位偏差较大; 对于数据质量较差的数据类型2,因两种方法对于数据质量的依赖性较大,均存在应用局限性,导致悬挂点定位偏差都较大,达到2.00m左右; 相比于方法1、方法2,本文中的方法对于这两种质量数据均能较为准确的定位悬挂点,表现出了更高的鲁棒性。
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对同一基杆塔上6个悬挂点提取的详细实验结果对比如表 5所示。表中悬挂点5为悬挂点附近电力线点云被自动分类为杆塔点云情况。
Table 5. Comparison of the accuracy of positioning methods
suspension
pointactual position/m positioning deviation/m method one method two this paper method x y z Δx Δy Δz Δx Δy Δz Δx Δy Δz 1 722634 2954542.25 1147.82 0.49 0.41 0.45 0.29 0.31 0.39 0.07 0.04 0.05 2 722646.38 2954562 1147.82 0.55 0.45 0.56 0.34 0.35 0.35 0.05 0.06 0.05 3 722634.11 2954542.19 1164.35 0.57 0.52 0.51 0.39 0.41 0.34 0.06 0.05 0.07 4 722646.31 2954562.05 1164.34 0.37 0.48 0.45 0.32 0.45 0.46 0.05 0.07 0.06 5 722633.94 2954542.22 1174.44 2.1 1.98 2.09 1.98 1.81 1.94 0.08 0.07 0.06 6 722646.4 2954562.19 1174.42 0.42 0.5 0.48 0.49 0.51 0.41 0.04 0.06 0.06 由表 5可知,方法1平均定位偏差为0.50m左右,方法2平均定位偏差为0.40m左右,而本文中的方法平均偏差在0.06m左右,相比于方法1和方法2,本文中方法更能较为精确地提取电力线悬挂点坐标。
基于激光点云的电力线悬挂点定位方法
Power line suspension point location method based on laser point cloud
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摘要: 为了解决目前电力线悬挂点定位方法鲁棒性低、定位不精确的问题,采用基于激光点云的结合局部3维重建与迭代搜索的方法对电力线悬挂点定位进行了研究。首先,对电力线点云空间特征进行分析进而推导电力线空间约束条件,以此作为生长准则进行基于空间约束的区域生长,实现跨越多档的单根电力线分割; 然后,对杆塔点云聚类提取杆塔中心点,以杆塔中心点连线的角平分线为基准划定每档电力线的空间分割平面; 之后,对各分割平面附近电力线点云进行空间多项式局部3维重建; 最后,结合分割平面迭代搜索计算重建电力线的交点,实现电力线悬挂点空间位置定位。结果表明,对于3种电压等级线路点云及2种数据质量点云,电力线悬挂点定位平均偏差均在0.09m以内,最小偏差为0.03m。该方法鲁棒性高,可以精确地实现各电压等级及各质量点云数据中的电力线悬挂点定位,为后续基于悬挂点的电力线模拟工况安全分析提供了基础。Abstract: In order to solve the problems of low robustness and inaccurate location of power line suspension point location methods, a power line suspension point location method based on laser point cloud combined with local 3-D reconstruction and iterative search was used to study the location of power line suspension point. The spatial characteristics of power line point clouds were analyzed and the spatial constraints of power lines were deduced, which is used as a growth criterion for region growth based on spatial constraints to realize single power line segmentation across multiple stages. Then, the center point of the tower was extracted by clustering the point cloud of the tower, and the spatial segmentation plane of each power line was delineated on the basis of the angular bisector of the connection line of the center point of the tower. After that, the spatial polynomial local 3-D reconstruction of the power line point cloud near each segmentation plane was carried out; Finally, combined with the iterative search of the segmentation plane, the intersection point of the power line was reconstructed, and the spatial location of the power line suspension point was realized. The results show that for three kinds of voltage grade line point clouds and two kinds of data quality point clouds, the average location deviation is less than 0.09m, and the minimum deviation is 0.03m. This method has high robustness and can accurately locate the power line suspension point in each voltage level and mass point cloud data with high robustness and accuracy, which provides a basis for the subsequent safety analysis of power line simulation based on the suspension point.
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Figure 9. Location result of power line suspension point(the red point in the figure is the power line suspension point that is located)
a—positioning results of suspension point of a 110kV line b—positioning results of suspension point of a 220kV line c—positioning results of suspension point of a 500kV line
Table 1. Spatial constraints of power line point cloud
serial
numbercoordinate
systemspatial constraint
conditionformulaic
expression1 x-y-z 3-D space height difference specific formula (1) 2 x-O-y 2-D plane distance from
point to linespecific formula (2) Table 2. Test line information
line serial number 1 2 3 voltage level/kV 110 220 500 line length/km 2.56 1.16 4.88 number of power lines 6 5 4 number of towers 9 4 14 number of suspension points 54 20 56 Table 3. Analysis of test results
line serial
numbervoltage
level/kVmaximum positioning
deviation/mminimum positioning
deviation/maverage positioning deviation/m Δx Δy Δz whole 1 110 0.12 0.03 0.07 0.07 0.05 0.063 2 220 0.16 0.04 0.07 0.06 0.07 0.067 3 500 0.21 0.05 0.09 0.09 0.08 0.087 Table 4. Robustness comparison of positioning methods
data type method 1/m method 2/m this paper method/m 1 0.51 0.31 0.06 2 2.14 1.85 0.07 Table 5. Comparison of the accuracy of positioning methods
suspension
pointactual position/m positioning deviation/m method one method two this paper method x y z Δx Δy Δz Δx Δy Δz Δx Δy Δz 1 722634 2954542.25 1147.82 0.49 0.41 0.45 0.29 0.31 0.39 0.07 0.04 0.05 2 722646.38 2954562 1147.82 0.55 0.45 0.56 0.34 0.35 0.35 0.05 0.06 0.05 3 722634.11 2954542.19 1164.35 0.57 0.52 0.51 0.39 0.41 0.34 0.06 0.05 0.07 4 722646.31 2954562.05 1164.34 0.37 0.48 0.45 0.32 0.45 0.46 0.05 0.07 0.06 5 722633.94 2954542.22 1174.44 2.1 1.98 2.09 1.98 1.81 1.94 0.08 0.07 0.06 6 722646.4 2954562.19 1174.42 0.42 0.5 0.48 0.49 0.51 0.41 0.04 0.06 0.06 -
[1] SHI L, GUO T, PENG Ch, et al. Segmentation of laser point cloud and safety detection of power lines[J]. Laser Technology, 2019, 43(3): 341-346(in Chinese). [2] WU J J, LI L, FANG P k, et al. Effective organization and visualization of helicopter-based laser scanning data in power line inspection[J]. Laser Technology, 2019, 43(3): 318-323(in Chinese). [3] WU J J, CHEN L, LI L, et al. Power line extraction and reconstruction from airborne LiDAR point cloud[J]. Laser Technology, 2019, 43(4): 500-500(in Chinese). [4] YANG J, ZENG X J, WANG J Y, et al. Research on power equipment damage based on laser detection and big data analysis [J]. Laser Journal, 2018, 39 (12): 78-82(in Chinese). [5] POULIOT N, RICHARD P, MONTAMBAULT S. LineScout power line robot: Characterization of a UTM-30LX LIDAR system for obstacle detection[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). New York, USA: IEEE, 2012: 25-46. [6] WANG S B, LI M X, LI H R, et al. Research on obstacle detection of transmission line corridor based on 3-D laser radar technology[J]. Electronic Technology, 2019, 32 (4): 81-84(in Chinese). [7] DING W, HUANG X Y, TAN X Y, et al. Detecting danger vegetation in powerline corridors using airborne laser points [J]. Surveying and Mapping and Spatial Geographic Information, 2018, 41 (11): 125-128(in Chinese). [8] CHEN L M, ZHANG W, YU H, et al. Application of UAV-based LiDAR system for power line surveys [J]. Surveying and Mapping Bulletin, 2017(s1): 176-178(in Chinese). [9] PU Sh, WU X Q, YAN Zh L, et al. Automatic recognition of defects on transmission lines from UAV-borne laser scanning data [J]. Remote Sensing Information, 2017, 32 (4): 52-57(in Chinese). [10] RICHARD P L, POULIOT N, MONTAMBAULT S. Introduction of a LIDAR-based obstacle detection system on the Line Scout power line robot[C]//IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM).New York, USA: IEEE, 2014: 3533-3538. [11] CHEN Ch, PENG X Y, SONG Sh, et al. Safety distance diagnosis of large scale transmission line corridor inspection based on LiDAR point cloud collected with UAV [J]. Power Grid Technology, 2017, 41(8): 2723-2730(in Chinese). [12] GUO B, LI Q, HUANG X, et al. An improved method for power line reconstruction from point cloud data[J]. Remote Sensing, 2016, 8(1): 36. doi: 10.3390/rs8010036 [13] YANG Y, CHEN F X, GUO T, et al. Power line extraction using airborne LiDAR point clouds characteristics and model fitting method [J]. Journal of Chinese Academy of Sciences, 2018, 35(5): 612-616(in Chinese). [14] SHEN X J, QIN Ch, DU Y, et al. An automatic power line extraction method from airborne light detection and ranging point cloud in complex terrain [J]. Journal of Tongji University (Natural Science Edition), 2018, 46 (7): 982-987(in Chinese). [15] LIN X G, NING X G, XIA Sh B. A method for power line LiDAR point cloud segmentation using K-means clustering of a feature space [J]. Surveying and Mapping Science, 2016, 41(5): 60-63(in Chinese). [16] WANG Y, CHEN Q, LIU L, et al. Supervised classification of power lines from airborne LiDAR data in urban areas[J]. Remote Sensing, 2017, 9(8):771. doi: 10.3390/rs9080771 [17] XU B, LIU Zh J, WANG J. Extraction and security detection of power line based on laser point cloud data [J]. Laser Journal, 2017, 38 (7): 48-51(in Chinese). [18] DUAN M Y. 3-D power line reconstruction from airborne LiDAR point cloud [J]. Journal of Surveying and Mapping, 2016, 45 (12): 1495(in Chinese). [19] YU J, MU Ch, FENG Y M, et al.Powerlines extraction techniques from airborne LiDAR data [J]. Journal of Wuhan University (Information Science Edition), 2011, 36(11): 1275-1279(in Chinese). [20] YIN H Z, SUN X, NIE Zh G. An automated extraction algorithm of power lines based on airborne laser scanning data[J]. Geography and Geographic Information Science, 2012, 28 (2): 31-34(in Chinese). [21] LIN X G, DUAN M Y, ZHANG J X, et al. A method of reconstructing 3-D powerlines from airborne LiDAR point clouds [J]. Surveying and Mapping Science, 2016, 41(1): 109-114(in Chinese).