Multi-Fidelity Data and Prior-Enhanced Physics-Informed Neural Networks for Multi-Parameter Identification of Prestressed Concrete Beams with Unquantifiable Noise

Although PINNs have demonstrated strong predictive capabilities in forward problems, their performance in inverse problems remains inadequate, largely due to unquantifiable noise encountered during the multi-parameter identification of prestressed concrete beams. Experimental measurements are often noisy, sparse, or asymmetric, while numerical or analytical models, although physically consistent, are typically approximate and lack regularization from well-defined multi-fidelity data. To address this limitation, this paper proposed a multi-fidelity data and prior-enhanced physics-informed neural network (MF-rPINN), which integrates multi-fidelity data with physics prior relational constraints to guide parameter identification using only sparse experimental observations. The MF-rPINN architecture is designed to enforce consistency between each training iteration and a prescribed set of experimental measurements, while embedding the second-order displacement function into the loss function. Experimental results demonstrate that the proposed MF-rPINN achieves accurate parameter identification even under noisy and incomplete observations, owing to the combined regularization effects of governing physical laws and the second-order displacement prior. The minimum relative errors of the elastic modulus are −6.49% and −9.32% under different and identical loading conditions, respectively, while the minimum relative errors of the prestress force are 0.65% and 4.51%. Compared with classical analytical approaches, MF-rPINN exhibits superior robustness and is capable of predicting continuous displacement fields of prestressed concrete beams while simultaneously identifying prestress force and elastic modulus. These advantages highlight the potential of MF-rPINN as a reliable surrogate modeling tool for practical engineering applications.