Estimation of pre-existing deformations in historical masonry vaults from contemporary point clouds

Vaults in historical masonry structures often feature geometric distortions whose deformation history remains unknown. Understanding these deformations can support damage assessment and residual load-carrying capacity evaluation. This study presents a methodology to estimate pre-existing deformations through non-rigid registration of a reference template to surveyed point clouds. A physics-informed iterative closest point algorithm (π-ICP) which minimises normal distances while constraining elastic strain energy is developed. The template is a triangular three-noded finite element mesh; the optimal nodal displacement field is sought as a linear optimization problem solved using least-squares approach. This enables a flexible representation of undeformed geometries, allowing imposed displacements and discontinuities such as cracks. The method is evaluated on synthetic data generated through FEM simulations of a barrel vault under differential support movement and on real data of a viaduct damaged during piling works. Both applications show accurate displacements recovery and the ability to detect pre-existing and ongoing distortions.