Study of a Virtual Assembly Algorithm for Precast T-Beams Using a Two-Stage Principal Component Analysis and Lie Algebra-Based Iterative Closest Point Registration Strategy

An intelligent pre-assembly framework integrating three-dimensional (3D) laser scanning with hierarchical point-cloud registration is presented to improve digital assembly accuracy of precast concrete T-beams. First, point cloud data of individual beam segments are acquired. Coarse registration is performed using principal component analysis (PCA) and refined through an enhanced Lie algebra-based iterative closest point (Lie-ICP) algorithm for high-precision alignment. In the Hezhou Expressway project, a discrepancy of less than 2.0 mm between the registered point cloud and total station measurements is observed. Following the fine registration, the residual error is further reduced to 1.83 mm, and the maximum assembly misalignment remains within 2.9 mm. Precision and reliability of 3D digital assembly for precast T-beams are effectively enhanced, providing a robust technical foundation for quality-controlled assembly of bridge precast components.