﻿ 基于三维激光扫描仪的边坡形变监测研究
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 大地测量与地球动力学  2019, Vol. 39 Issue (5): 533-537  DOI: 10.14075/j.jgg.2019.05.018

### 引用本文

CHANG Ming, PAN Lijun, MENG Xiangang, et al. Research on Slope Deformation Monitoring Based on LiDAR[J]. Journal of Geodesy and Geodynamics, 2019, 39(5): 533-537.

### Foundation support

Special Fund for Earthquake Research of CEA, No. 201508009; Science and Technology Innovation Fund of the First Monitoring and Application Center, CEA, No. FMC2018006.

### Corresponding author

PAN Lijun, postgraduate, majors in data processing and analysis, E-mail:panlijun0819@163.com.

### 第一作者简介

CHANG Ming, assistant engineer, majors in data processing and analysis, E-mail:charmingxz@163.com.

### 文章历史

1. 中国地震局第一监测中心，天津市耐火路7号，300180;
2. 中国地质大学(北京)土地科学技术学院，北京市学院路29号，100083

 图 1 流程图 Fig. 1 Flow chart
1 点云数据处理 1.1 点云数据体素化

 $\left\{ \begin{array}{l} {\rm{Nu}}{{\rm{m}}_x} = {\rm{ floor }}\left( {\frac{{{x_{{\rm{max}}}} - {x_{{\rm{min}}}}}}{l}} \right)\\ {\rm{Nu}}{{\rm{m}}_y} = {\rm{ floor }}\left( {\frac{{{y_{{\rm{max}}}} - {y_{{\rm{min}}}}}}{l}} \right)\\ {\rm{Nu}}{{\rm{m}}_z} = {\rm{floor}}\left( {\frac{{{z_{{\rm{max}}}} - {z_{{\rm{min}}}}}}{l}} \right) \end{array} \right.$ (1)

 $\left\{ \begin{array}{l} {T_{ix}} = {\rm{floor}}\left( {\frac{{{p_{ix}} - {x_{\min }}}}{l}} \right)\\ {T_{iy}} = {\rm{floor}}\left( {\frac{{{p_{iy}} - {y_{\min }}}}{l}} \right)\\ {T_{iz}} = {\rm{floor}}\left( {\frac{{{p_{iz}} - {z_{\min }}}}{l}} \right) \end{array} \right.$ (2)
1.2 形变量提取

 图 2 种子生长法分类结果 Fig. 2 Result of region growing

 $ax + by + cz + d = 0$ (3)

 $\left\{ \begin{array}{l} {\xi _i} = \frac{{\left| {a{\rm{G}}{{\rm{P}}_{ix}} + b{\rm{G}}{{\rm{P}}_{iy}} + c{\rm{G}}{{\rm{P}}_{iz}} + d} \right|}}{{\sqrt {{a^2} + {b^2} + {c^2}} }}\\ {\lambda _i} = \frac{{{\xi _i} - {\xi _{i - 1}}}}{t}\\ {\mathit{\Omega }_i} = \frac{{{\lambda _i} - {\lambda _{i - 1}}}}{t} \end{array} \right.$ (4)
2 形变监测与分析

2.1 系统空间和状态向量

 $\mathit{\boldsymbol{L}} = \mathit{\boldsymbol{BX}} + \mathit{\boldsymbol{ \boldsymbol{\varDelta} }}$ (5)

 ${\mathit{\boldsymbol{X}}_{k + 1}} = {\mathit{\boldsymbol{ \boldsymbol{\varPhi} }}_{k + 1,k}}\mathit{\boldsymbol{X}}{\mathit{\boldsymbol{\xi }}_k} + {\mathit{\boldsymbol{ \boldsymbol{\varGamma} }}_{k + 1}}{\mathit{\boldsymbol{\omega }}_k}$ (6)

 $\left\{ \begin{array}{l} E\left( {{\omega _k}} \right) = 0,E\left( {{\Delta _k}} \right) = 0\\ {\mathop{\rm cov}} \left( {{\omega _k},{\omega _j}} \right) = {\mathit{\boldsymbol{D}}_k}{\xi _{kj}}\\ {\mathop{\rm cov}} \left( {{\Delta _k},{\Delta _j}} \right) = {\mathit{\boldsymbol{D}}_{{\Delta _k}}}{\xi _{kj}}\\ {\mathop{\rm cov}} \left( {{\omega _k},{\omega _j}} \right) = 0\\ E\left( {{\mathit{\boldsymbol{X}}_0}} \right) = {\mathit{\boldsymbol{\mu }}_x}\left( 0 \right) = \mathit{\boldsymbol{\hat X}}\left( {0/0} \right)\\ {\mathop{\rm var}} \left( {{\mathit{\boldsymbol{X}}_0}} \right) = {\mathit{\boldsymbol{D}}_{{x_0}}}\\ {\mathop{\rm cov}} \left( {{\mathit{\boldsymbol{X}}_0},{\omega _k}} \right) = 0,{\mathop{\rm cov}} \left( {{\mathit{\boldsymbol{X}}_0},{\Delta _k}} \right) = 0 \end{array} \right.$ (7)

 ${\dot \xi _i}\left( t \right) = {\lambda _i}\left( t \right)$ (8)
 ${\dot \lambda _i}\left( t \right) = {\mathit{\Omega }_i}\left( t \right)$ (9)

 ${\mathit{\boldsymbol{X}}_k}\left( t \right) = \left[ {\begin{array}{*{20}{c}} {{\xi _k}\left( t \right)}\\ {{\lambda _k}\left( t \right)}\\ {{\mathit{\Omega }_k}\left( t \right)} \end{array}} \right],\mathit{\boldsymbol{X}}\left( t \right) = \left[ {\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{X}}_1}\left( t \right)}\\ {{\mathit{\boldsymbol{X}}_2}\left( t \right)}\\ \vdots \\ {{\mathit{\boldsymbol{X}}_k}\left( t \right)} \end{array}} \right]$ (10)
2.2 预测更新

 $\left\{ \begin{array}{l} {{\mathit{\boldsymbol{\bar X}}}_{k + 1,k}} = {\mathit{\boldsymbol{\varphi }}_{k + 1,k}}{\mathit{\boldsymbol{X}}_k} + {\mathit{\boldsymbol{\omega }}_{k + 1}} = \\ \left[ {\begin{array}{*{20}{c}} \mathit{\boldsymbol{I}}&{\Delta {t_k}\mathit{\boldsymbol{I}}}&{\frac{1}{2}\Delta {t_k}\mathit{\boldsymbol{I}}}\\ 0&\mathit{\boldsymbol{I}}&{\Delta {t_k}\mathit{\boldsymbol{I}}}\\ 0&0&\mathit{\boldsymbol{I}} \end{array}} \right]{\mathit{\boldsymbol{X}}_k} + {\mathit{\boldsymbol{\omega }}_{k + 1}}\\ {\mathit{\boldsymbol{L}}_{k + 1}} = {\mathit{\boldsymbol{B}}_{k + 1,k}}{\mathit{\boldsymbol{X}}_{k + 1}} + \Delta {\mathit{\boldsymbol{v}}_{k + 1}} \end{array} \right.$ (11)

 ${\mathit{\boldsymbol{D}}_{k + 1,k}} = {\mathit{\boldsymbol{\varphi }}_{k + 1,k}}{\mathit{\boldsymbol{D}}_k}\mathit{\boldsymbol{\varphi }}_{k + 1,k}^{\rm{T}} + {\mathit{\boldsymbol{R}}_k}$ (12)

2.3 状态更新

 $\begin{array}{*{20}{c}} {{\mathit{\boldsymbol{J}}_{k + 1}} = }\\ {{\mathit{\boldsymbol{D}}_{k + 1,k}}\mathit{\boldsymbol{B}}_{k + 1}^{\rm{T}}{{\left[ {{\mathit{\boldsymbol{B}}_{k + 1}}{\mathit{\boldsymbol{D}}_{k + 1,k}}\mathit{\boldsymbol{B}}_{k + 1}^{\rm{T}} + {\mathit{\boldsymbol{D}}_{\Delta \left( {k + 1} \right)}}} \right]}^{ - 1}}} \end{array}$ (13)

 $\left\{ \begin{array}{l} {\mathit{\boldsymbol{X}}_{k + 1}} = {\left[ {\mathit{\boldsymbol{D}}_{k + 1,k}^{ - 1} + \mathit{\boldsymbol{B}}_{k + 1}^{\rm{T}}\mathit{\boldsymbol{D}}_{{\Delta _{\left( {k + 1} \right)}}}^{ - 1}{\mathit{\boldsymbol{B}}_{k + 1}}} \right]^{ - 1}}\\ \left[ {\mathit{\boldsymbol{D}}_{k + 1,k}^{ - 1}{{\mathit{\boldsymbol{\bar X}}}_{k + 1,k}} + \mathit{\boldsymbol{B}}_{k + 1}^{\rm{T}}\mathit{\boldsymbol{D}}_{{\Delta _{\left( {k + 1} \right)}}}^{ - 1}{\mathit{\boldsymbol{L}}_{k + 1}}} \right]\\ {\mathit{\boldsymbol{D}}_{k + 1}} = {\left[ {\mathit{\boldsymbol{D}}_{k + 1,k}^{ - 1} + \mathit{\boldsymbol{B}}_{k + 1}^{\rm{T}}\mathit{\boldsymbol{D}}_{{\Delta _{\left( {k + 1} \right)}}}^{ - 1}{\mathit{\boldsymbol{B}}_{k + 1}}} \right]^{ - 1}} \end{array} \right.$ (14)

3 边坡实验

 图 3 实验场地全景 Fig. 3 Experimental site panorama

 图 4 点云配准结果 Fig. 4 Results ofregistration

 图 5 观测结果 Fig. 5 Observation results

 图 6 第6次观测数据全景图及局部放大图 Fig. 6 The 6thpanorama and the magnification of the segment
4 结语

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Research on Slope Deformation Monitoring Based on LiDAR
CHANG Ming1     PAN Lijun2     MENG Xiangang1     XU Yujian1     XU Kai1
1. The First Monitoring and Application Center, CEA, 7 Naihuo Road, Tianjin 300180, China;
2. School of Land Science and Technology, China University of Geosciences, 29 Xueyuan Road, Beijing 100083, China
Abstract: For deformation monitoring of railway slopes, three-dimensional laser scanners are used for data acquisition and voxelization. The seed growth method is used to classify the voxelized data, and its spatial parameters are fitted. By observing the distance between the point cloud data and the fitting plane of the target data classification result, the specific value of the slope deformation is obtained. Using Kalman filter to analyze multi-period data, the rate and acceleration of slope deformation is obtained, and the deformation of slope is predicted.
Key words: point cloud; region growing; voxelization; deformation monitoring; extended Kalman filter