多视角地基干涉雷达监测公路边坡三维位移的联合估计方法及精度评估

Three-dimensional Displacement Estimation and Accuracy Validation on Highway Slopes Based on Multi-view Ground-based SAR

  • 摘要: 本文提出一种联合多视角地基干涉雷达观测数据的公路边坡三维形变估计方法,实现了坡向和垂直于公路走向的横向水平位移的精确提取。在边坡下方分别设置三个水平观测视角的站点,采用地基SAR轮流在每个站点观测的方式获取不同水平视角下的雷达影像,分别计算各视角下的边坡视线向形变;然后建立了多视角视线向形变在边坡坡面坐标系下三维位移(坡向、垂直向和横向水平位移)的投影函数模型,联合奇异值分解-正则化最小二乘方法实现了坡面三维位移的精确计算。通过在公路边坡实地布设的多测站开展地基SAR监测试验,并利用人工角反射器对投影函数及算法开展精度评估,结果显示本文提出的方法在试验边坡的坡向、垂直向和横向位移三个方向的形变监测精度分别为0.4mm、0.4mm和1.8mm。本文的研究可为中小型边坡工程稳定性监测与灾害预警提供新的观测技术与手段,可为边坡工程灾害防治提供参考。

     

    Abstract: Objectives: Highway slope instability poses serious threats to transportation safety and infrastructure reliability. Accurate three-dimensional (3D) deformation monitoring is essential for slope stability assessment and disaster early warning. A practical method for estimating slope-parallel horizontal displacement, transverse horizontal displacement perpendicular to the roadway, and vertical displacement is proposed in this study, using multi-view ground-based synthetic aperture radar (GBSAR). Methods: A single GBSAR system was sequentially installed at three stations respectively with different azimuth viewing angles to acquire interferometric measurements in a time-sharing mode. A projection model was established to transform multi-view line-of-sight (LOS) displacements into three independent deformation components. To address the ill-posed nature of the inversion problem, Singular Value Decomposition (SVD) combined with Tikhonov-regularized least squares method was employed to estimate the 3D displacement components, which enhanced the numerical stability and suppressed the noise amplification.A in-situ experiment on a highway slope in Changsha, China was conducted, with 4 artificial corner reflectors (CRs) installed on the slope to validate the geometry projection function and the displacement accuracy. Results: The effectiveness of the proposed method has been confirmed. The root mean square errors (RMSEs) relative to CR measurements were estimated as 0.4mm for slopeparallel displacement, 0.4mm for vertical displacement, and 1.8mm for transverse displacement, respectively. Compared with conventional least squares estimation methods, the SVD combined with Tikhonov-regularized least squares method significantly reduced the error propagation caused by rank deficiency and improved reliability under complex slope conditions. Conclusions: The proposed multiview GBSAR 3D displacement monitoring method provides a cost-effective and accurate solution for 3D slope deformation monitoring using only a single radar system. It can offer high flexibility, low hardware costs compared to multi-device systems, and ensure robust performance in complex environments. This approach has strong potential for geohazard early warning and infrastructure safety management.

     

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