Parameter identification in prestressed concrete beams by incremental beam–column equation and physics-informed neural networks

This paper explores a novel methodology for identifying prestress force (and bending rigidity) from the perspective of static deflection methods and derives an incremental beam–column equation (iBCE) by elucidating the mechanisms underlying the long- and short-term behaviors, with particular emphasis on a physical system that disregards long-term deflections, including self-weight and equivalent lateral loads. It allows for the scaling of measurements from the real world to the corresponding nondimensional form of the physical system. The methodology begins by constructing the non-homogeneous terms of the equations using parameters and variables observed in the real world. Subsequently, utilizing second-order theory induced by incremental loads during step loading, the decoupling and identification of prestress force and bending rigidity are accomplished. The identification algorithm is constructed by integrating the nondimensional form of the iBCE with physics-informed neural networks. Without any additional regularization, the rationality and adaptability of this methodology are validated by nine examples that exhibit no nonlinear relations. A comprehensive series of systematic studies indicates that high accuracy can be achieved with the decoupled algorithm. This accuracy is possible when one mechanical parameter, such as bending rigidity or prestress force, is known and utilized to identify the remaining parameter. When both mechanical parameters are unknown, investing more in training costs enables the inverse identification of multiple parameters. Even with a 1% noise level, reasonable accuracy in the decoupling and identification of two mechanical parameters can be achieved. This methodology avoids the traditional limitations associated with solving the forward and inverse problems of incremental differential equations and transcendental equations.