Internal Force Identification in Prestressed Concrete Bridges via Lagrangian Interpolation and Substructural Modeling Technique

The performance of prestressed concrete bridges (PCBs) is significantly affected by the prestress loss and overloading vehicles over their service life. Structural health monitoring is critical to prevent the structural collapse and life-cycle management and cost-effective maintenance for PCBs. This paper presents an innovative dynamic equilibrium-based internal force identification (IFI) approach for evaluating structural performance of PCBs, incorporating unknown prestress and moving forces. By integrating substructural modeling and Lobatto element-based Lagrangian interpolation, a new approach is proposed for accurate and efficient IFI. This technique is structured as a two-phase process: the first focuses on an enhanced methodology for identifying prestress and vehicle-induced excitation on a PCB, while the second introduces an improved approach for IFI from the identified prestress and excitation. To solve the inverse problem of identifying external forces resulting from prestress and moving forces, an improved regularization technique based on generalized singular value decomposition (GSVD), known as the compressed GSVD (CGSVD) technique, is introduced. This improved regularization method incorporates a compression factor to mitigate the ill-posedness of the inverse problem, enabling robust and precise IFI by minimizing the ill-posedness in identifying prestress forces and vehicle-induced excitation, using only displacement responses. By substructural modeling techniques, the number of sensors can be significantly reduced while enabling the IFI at arbitrary sections of PCBs. The proposed method is validated using experimental and numerical study on a simply supported prestressed concrete box girder bridge under general excitation and experimental study on a prestressed concrete [Formula: see text]-beam under moving loads. Results validate the method’s accuracy and effectiveness in IFI and in estimating prestress forces and vehicle-induced excitation, offering clear insights into PCBs’ structural performance.