Combination of LiDAR detection and green integral method for calculating irregular cross-section geometric properties of deteriorated components in timber historic buildings

Timber components in historic buildings are susceptible to deterioration due to the complex external environment. The loss of material in these components and changes in their cross-section geometry significantly impact the stability and load-bearing capacity of historic buildings. A portable LiDAR device is utilized to acquire the cross-section geometry of the deteriorated components. The irregular cross-section profiles are extracted using point cloud slicing and the Alpha-Shape algorithm. Geometric characteristics such as cross-section area, moment of inertia, and moment of resistance are calculated using Green's integral method. The performance of this method is evaluated by measuring eight groups of deteriorated components with different cross-section characteristics and comparing it with five traditional methods. The results demonstrate that the proposed method improves the calculation accuracy by 1%–21% relative to traditional methods, thereby enhancing reliability by 9%–54%. Additionally, it reduces manual calculation workload and human error, while promoting calculation efficiency. The method exhibits excellent applicability and high efficiency, with an error below 3% when compared to the true value. This method proves valuable in evaluating the extent of deterioration in historic timber components and provides essential data for preventive conservation and restoration of historic timber buildings.