Automated Estimation of Inverted Arch Step Distance in Construction Tunnels via Adaptive Point Cloud Segmentation and PCA‐Random Sample Consensus

ABSTRACT

The inverted arch step distance is a critical parameter for evaluating the safety and progress of tunnel construction. However, traditional manual measurements are inefficient and pose severe safety risks, while the raw point cloud data from construction sites suffer from uneven density and severe noise. To achieve automated and high‐precision measurement, this study proposes a robust point cloud processing framework. First, a dedicated large‐scale dataset, 3DTunnel, was constructed using real‐world expressway tunnel data. To address spatial heterogeneity, an adaptive sampling strategy ( n _points  = 5000, multi‐scale radii of 0.2–1.6) combined with an improved PointNet++ network was developed, achieving an mean Intersection over Union (mIoU) of 94.38% for structural component segmentation. Subsequently, to overcome the error amplification inherent in traditional perpendicularity metrics, a normal‐component‐based ( N _x ) method was proposed to extract the inverted arch vertical surface, yielding an overlap ratio of 92.98%. Furthermore, a novel principal component analysis‐constrained RANSAC algorithm was introduced to suppress the interference of residual outliers, reducing the plane fitting angular error to less than 0.5°. Finally, a mesh‐based distance calculation model was established. Field validation demonstrates that the algorithmically derived step distance achieves an absolute error of merely 0.13 m compared to laser measurements. The proposed framework achieves 94.38% mIoU, significantly outperforming PointNet++ (80.10%) and Point Transformer v3 (90.27%), while achieving comparable performance to PointNeXt (94.02%). This demonstrates a highly accurate and automated solution for digitalized tunnel construction monitoring.