﻿ 基于HVCE-RBFNN的矿区地表三维形变监测研究
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 大地测量与地球动力学  2022, Vol. 42 Issue (5): 520-525  DOI: 10.14075/j.jgg.2022.05.015

### 引用本文

ZHOU Wentao, ZHANG Wenjun, MIAO Junyi, et al. 3D Surface Deformation Monitoring of Mining Areas Based on HVCE-RBFNN Method[J]. Journal of Geodesy and Geodynamics, 2022, 42(5): 520-525.

### Foundation support

National Key Research and Development Program of China, No.2018YFC150540202; National Natural Science Foundation of China, No.41871174.

### Corresponding author

ZHANG Wenjun, professor, majors in remote sensing information technology, E-mail: 113999066@qq.com.

### 第一作者简介

ZHOU Wentao, postgraduate, majors in 3D surface deformation monitoring of mining area, E-mail: 269026354@qq.com.

### 文章历史

1. 西南科技大学环境与资源学院, 四川省绵阳市青龙大道中段59号, 621010;
2. 国家遥感中心绵阳科技城分部, 四川省绵阳市青龙大道中段59号, 621010;
3. 四川航遥智测科技有限公司, 四川省绵阳市涪金路389号, 621010

1 HVCE-RBFNN模型建立 1.1 InSAR三维几何分解原理

 $D_{\mathrm{LOS}}=-D_{E} \sin \theta \cos \alpha+D_{N} \sin \theta \sin \alpha+D_{U} \cos \theta$ (1)
 图 1 InSAR三维几何分解原理 Fig. 1 3D geometric decomposition schematic of InSAR

1.2 HVCE-RBFNN模型

 $\boldsymbol{V}_{i}=\boldsymbol{B}_{i} \hat{\boldsymbol{x}}-\boldsymbol{l}_{i}, i=1,2, \cdots, n$ (2)

 $\hat{\boldsymbol{x}}=\boldsymbol{N}^{-1} \boldsymbol{W}$ (3)
 $\boldsymbol{N}=\sum\limits_{i=1}^{n} \boldsymbol{B}_{i}^{\mathrm{T}} \boldsymbol{P}_{i} \boldsymbol{B}_{i}=\sum\limits_{i=1}^{n} \boldsymbol{N}_{i}$ (4)
 $\boldsymbol{W}=\sum\limits_{i=1}^{3} \boldsymbol{B}_{i}^{\mathrm{T}} \boldsymbol{P}_{i} \boldsymbol{l}_{i}=\sum\limits_{i=1}^{3} \boldsymbol{W}_{i}$ (5)

 $\hat{\boldsymbol{\theta}}=\boldsymbol{A}^{-1} \boldsymbol{W}_{\theta}$ (6)
 $\hat{\boldsymbol{\theta}}=\left[\begin{array}{llll} \hat{\sigma}_{01}^{2} & \hat{\sigma}_{02}^{2} & \cdots & \hat{\sigma}_{0 n}^{2} \end{array}\right]^{\mathrm{T}}$ (7)
 $\boldsymbol{W}_{\theta}=\left[\begin{array}{llll} \boldsymbol{V}_{1}^{\mathrm{T}} \boldsymbol{P}_{1} \boldsymbol{V}_{1} & \boldsymbol{V}_{2}^{\mathrm{T}} \boldsymbol{P}_{2} \boldsymbol{V}_{2} & \cdots & \boldsymbol{V}_{n}^{\mathrm{T}} \boldsymbol{P}_{n} \boldsymbol{V}_{n} \end{array}\right]^{\mathrm{T}}$ (8)
 $\boldsymbol{A}=\left[\begin{array}{ccc} a_{1}-2 \operatorname{tr}\left(\boldsymbol{N}^{-1} \boldsymbol{N}_{1}\right)+\operatorname{tr}\left(\boldsymbol{N}^{-1} \boldsymbol{N}_{1}\right)^{2} & \cdots & \operatorname{tr}\left(\boldsymbol{N}^{-1} \boldsymbol{N}_{1} \boldsymbol{N}^{-1} \boldsymbol{N}_{n}\right) \\ \vdots & \ddots & \vdots \\ \operatorname{tr}\left(\boldsymbol{N}^{-1} \boldsymbol{N}_{1} \boldsymbol{N}^{-1} \boldsymbol{N}_{n}\right) & \cdots & a_{n}-2 \operatorname{tr}\left(\boldsymbol{N}^{-1} \boldsymbol{N}_{n}\right)+\operatorname{tr}\left(\boldsymbol{N}^{-1} \boldsymbol{N}_{n}\right)^{2} \end{array}\right]$ (9)

 $\hat{\boldsymbol{P}}_{i}=\frac{c}{\hat{\sigma}_{0 i}^{2} \boldsymbol{P}_{i}^{-1}}$ (10)

 $\hat{\sigma}_{01}^{2} \approx \hat{\sigma}_{02}^{2} \approx \cdots \approx \hat{\sigma}_{0 n}^{2}$ (11)

RBFNN具有自主学习、自主组合和自主适应等特点，可对差异较大的数据进行训练，从而达到数据融合的目的，不仅解决了计算效率的问题，还可完整地表达各组数据在融合中的贡献[14]。RBFNN由3层前向网络构成，第1层为输入层，第2层为隐含层，第3层为输出层，其数学模型表示为：

 $y_{j}=\sum\limits_{i=1}^{n} w_{i j} \varphi\left(\left\|\boldsymbol{X}-\boldsymbol{x}_{i}\right\|^{2}\right), j=1, \cdots, k$ (12)

RBF函数中心确定的方法不同，RBFNN的学习策略也不同。根据各组观测数据的特点，采用随机选取固定中心的学习策略，使基函数中心和标准差恒定不变。当各组数据比较典型、具有代表性时，这种策略的学习效率会大幅提升。传递函数选择高斯分布函数：

 $\varphi_{i}(r)=\mathrm{e}^{-\frac{r^{2}}{\sigma_{i}^{2}}}$ (13)

 $\sigma_{i}=\frac{d_{\max }}{\sqrt{2 n}}$ (14)

 \begin{aligned} \varphi\left(\left\|\boldsymbol{X}-\boldsymbol{x}_{i}\right\|\right) &=\exp \left(-\frac{n}{d_{\max }^{2}}\left\|\boldsymbol{X}-\boldsymbol{x}_{i}\right\|^{2}\right), \\ i &=1,2, \cdots, n \end{aligned} (15)

 $\omega_{i j}=\varphi\left(\left\|\boldsymbol{X}-\boldsymbol{x}_{i}\right\|^{2}\right) d_{k j}$ (16)

2 实验分析 2.1 研究区概况及数据介绍

 (a)矿区地理位置;(b)实验SAR 影像覆盖情况;(c)监测点位分布;(d)地面监测桩 图 2 研究区概况 Fig. 2 Overview of the study area

 $\left\{\begin{array}{l} D_{\mathrm{LOS}}^{\text {升 }}=-0.657\ 89 D_{E}- \\ \quad 0.154\ 83 D_{N}+0.737\ 03 D_{U} \\ D_{\mathrm{LOS}}^{\text {降 }}=0.674\ 72 D_{E}-0.159\ 92 D_{N}+ \\ \quad 0.720\ 53 D_{U} \end{array}\right.$ (17)

2.2 实验过程与分析

 图 3 Kriging插值的GNSS三维形变场 Fig. 3 GNSS 3D deformation fields with Kriging interpolation

 图 4 升降轨InSAR LOS向形变场 Fig. 4 InSAR LOS direction deformation fields of ascending and descending

 $\begin{array}{c} \left[\begin{array}{l} V_{1} \\ V_{2} \\ V_{3} \\ V_{4} \\ V_{5} \end{array}\right]=\left[\begin{array}{cccc} 1 & 0 & 0 & \\ 0 & 1 & 0 & \\ 0 & 0 & 1 & \\ -0.657\ 9 & -0.154\ 8 & 0.737\ 0 \\ \ \ \ 0.674\ 7 & -0.159\ 9 & 0.720\ 5 \end{array}\right] \cdot\\ \left[\begin{array}{c} D_{E} \\ D_{N} \\ D_{U} \end{array}\right]-\left[\begin{array}{c} D_{E}^{\mathrm{GNSS}} \\ D_{N}^{\mathrm{GNSS}} \\ D_{U}^{\mathrm{GNSS}} \\ D_{\mathrm{LOS}}^{\text {升 }} \\ D_{\mathrm{LOS}}^{\text {降 }} \end{array}\right] \end{array}$ (18)

2.3 地表三维形变结果及分析

 图 5 GNSS与HVCE-RBFNN法的三维形变结果对比 Fig. 5 Comparison of 3D deformation results between GNSS and HVCE-RBFNN method

 图 6 基于HVCE-RBFNN法的三维形变场 Fig. 6 3D deformation fields based on HVCE-RBFNN method

3 结语

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3D Surface Deformation Monitoring of Mining Areas Based on HVCE-RBFNN Method
ZHOU Wentao1,2,3     ZHANG Wenjun1,2,3     MIAO Junyi1,2     SHEN Rui1,2     ZI Yingkun1,2
1. School of Environment and Resource, Southwest University of Science and Technology, 59 Mid-Qinglong Road, Mianyang 621010, China;
2. Mianyang Science and Technology City Division, National Remote Sensing Center of China, 59 Mid-Qinglong Road, Mianyang 621010, China;
3. Sichuan Space Remote Sensing and Smart Mapping Technology Co Ltd, 389 Fujin Road, Mianyang 621010, China
Abstract: We propose a 3D deformation fusion method based on Helmert variance component estimation(HVCE) and radial basis function neural network(RBFNN), and fuse the data of GNSS and InSAR monitoring to obtain the 3D surface deformation field of Jinchuan West Second mining area in Jinchang, Gansu. The results show that the accuracy of 3D deformation fields obtained by HVCE-RBFNN method are higher than that obtained by traditional methods, and the RMSE of east-west direction, north-south direction and vertical direction is 20.85 mm, 7.41 mm and 34.47 mm, respectively. The maximum deformation values in three directions are 228 mm, 300 mm and 193 mm, respectively. The spatial distribution of goaf deformation conforms to the law of mining subsidence.
Key words: GNSS; InSAR; HVCE-RBFNN; 3D deformation; mining subsidence