引用本文: 江克贵, 王磊, 滕超群. 融合单视线D-InSAR和BK模型的煤矿地表三维变形动态监测方法[J]. 武汉大学学报 ( 信息科学版), 2023, 48(4): 620-630.
JIANG Kegui, WANG Lei, TENG Chaoqun. A Dynamic Monitoring Method of Surface 3D Deformation of Coal Mine Based on Fusion of Single Sight D-InSAR and BK Model[J]. Geomatics and Information Science of Wuhan University, 2023, 48(4): 620-630.
 Citation: JIANG Kegui, WANG Lei, TENG Chaoqun. A Dynamic Monitoring Method of Surface 3D Deformation of Coal Mine Based on Fusion of Single Sight D-InSAR and BK Model[J]. Geomatics and Information Science of Wuhan University, 2023, 48(4): 620-630.

## A Dynamic Monitoring Method of Surface 3D Deformation of Coal Mine Based on Fusion of Single Sight D-InSAR and BK Model

• 摘要: 合成孔径雷达差分干涉测量（differential interferometric synthetic aperture radar, D-InSAR）在获取地表形变的过程中有其特有的监测手段，针对D-InSAR矿区地表三维变形监测的难点，首先，顾及D-InSAR难以获取快速大梯度变形的特性，选取边界拟合度较好的Boltzmann函数模型，结合Knothe时间函数，构建一种BK（Boltzmann-Knothe）模型；然后，由于D-InSAR仅能获取地表沿视线向（line of sight, LOS）的短时段一维变形量，依据地表三维移动变形和LOS向变形的投影关系，结合目标区域地质采矿条件，构建适应短时段单视线向变形的适应度函数；最后，引入烟花算法（fireworks algorithm, FWA），提出了融合单视线D-InSAR和BK模型的煤矿地表三维变形动态监测方法。模拟实验表明，所提方法能够可靠准确地反演出全部开采沉陷动态预计参数，求参相对误差为0.11%~7.51%；在大变形区域，该方法监测的下沉和水平移动与真实值一致。抗差求参实验结果表明，在观测误差或模型参数误差的影响下，该方法反演参数的总体效果较好，在一定程度上表现出了抗差的能力。将该方法应用于安徽省淮南市顾北煤矿13121工作面，对2019-10-25—2019-12-12的煤矿地表三维变形进行监测，实现了矿区地表短时段D-InSAR监测向三维变形动态监测转化，且监测结果与地表移动观测站实测变形量较吻合，验证了D-InSAR矿区地表三维变形动态监测方法的可靠性与科学性。

Abstract:
Objectives  Differential interferometric synthetic aperture radar (D-InSAR) has its own unique monitoring methods in acquiring surface deformation. In view of the difficulties in the application of D-InSAR technology in three-dimensional (3D) deformation monitoring of coal mine surface, this paper proposes a dynamic monitoring method based on fusion of single sight D-InSAR and Boltzmann-Knothe (BK) model.
Methods  First, taking into account the characteristics of D-InSAR that it is difficult to obtain large gradient deformations, the Boltzmann function model with good boundary fit was selected, and BK model was constructed by the fusion of the Knothe time function. Second, due to the decoherence of the time-space baseline and the limitation of D-InSAR principle, it can often only obtain the short-term, one-dimensional deformation of the surface in line of sight (LOS). Therefore, based on the projection relationship between the 3D deformation and the LOS deformation, combined with the geological mining conditions of the target area, the fitness function with non-cumulative deformation was constructed. Finally, a dynamic monitoring method of surface 3D deformation of coal mine based on fusion of single sight D-InSAR and BK model was proposed by introducing the fireworks algorithm (FWA).
Results and Conclusions  Simulation experiments show that the proposed method can reliably and accurately inverted all dynamic prediction parameters of mining subsidence, and the relative error of the solved parameters was between 0.11% and 7.51%. The subsidence and horizontal movement monitored by this proposed method were consistent with the real values, and the monitoring effect of the PIM-Knothe method was distorted. The results of the anti-error experiment show that under the influence of observation error or model parameter error, the overall effect of the solved parameters by the method in this paper was better, and the ability to resist errors was shown to a certain extent. The proposed method was applied to the 13121 working face of Gubei Mine in Huainan, and the surface 3D deformation of the coal mine from 2019-10-25 to 2019-12-12 was obtained. The conversion of short-term D-InSAR observation to 3D deformation dynamic monitoring based on the proposed method was realized, and the monitoring results were more consistent with the surface movement and deformation measured by the observation station. The reliability and scientificity of the dynamic prediction method for solving the surface 3D deformation of coal seam based on D-InSAR technology has been verified.

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