Identification of the Flexural Stiffness of Prestressed Concrete Beams Under Multi-Point Source Force Loading Based on Physics-Informed Neural Networks

Flexural stiffness identification of prestressed concrete beams plays an important role in evaluating the mechanical performance and damage condition of bridge structures and has become a critical research direction in bridge health monitoring. Accordingly, this paper presented a Physics-Informed Neural Network (PINN)-based method for flexural stiffness identification. In the physical modeling framework, point source forces in the beam-column equation (BCE) were represented by approximating the Dirac delta function with Gaussian functions. This strategy alleviated the convergence issue of the loss function caused by singular behavior and enabled the formulation of a unified governing equation for multi-point loading scenarios. To eliminate the long-term deflection caused by non-load-related factors and self-weight, the BCE was expressed in incremental form. The resulting nondimensional equation was adopted as the target constraint for PINN training to alleviate multi-scale challenges. Furthermore, the residual-based adaptive refinement (RAR) strategy was incorporated during network training to improve computational efficiency and identification accuracy. The proposed method was validated through nine numerical cases without linear relationships and three experimental cases. The results indicate that, even with limited measurement data and under the tested noise levels, the proposed framework can achieve satisfactory flexural stiffness identification under the tested loading conditions. This suggests that the proposed method has promising potential for flexural stiffness identification and may be useful in bridge structural health monitoring under sparse-data conditions.