Physical embedded neural network model and method for dynamic load identification

To address the ill-posedness caused by the inversion of the frequency response function matrix in traditional dynamic load identification methods, as well as the lack of physical interpretability in deep learning methods, a novel Physical Embedded Neural Network (PENN) for dynamic load identification is proposed. By embedding structural dynamic parameters, such as modal mass, modal stiffness, and modal damping, directly into the neural network, the PENN model is constructed to offer physical interpretability. The PENN model can directly identify the power spectral density of dynamic loads through a forward computational process, avoiding the need for inverting the frequency response function matrix as in traditional methods. Additionally, this model can adaptively adjust internal physical parameters, ensuring high-precision identification of dynamic loads even when prior physical parameters are inaccurate. The paper provides a detailed explanation of the method's mechanism, the construction rules of the PENN model, parameter settings, and the training process. Numerical simulations and experimental validations were conducted under various conditions The results show that even when the prior dynamic system parameters are inaccurate and only one training sample is available, the Pearson correlation coefficient of dynamic load identification was consistently above 95%, demonstrating strong robustness and potential for engineering applications.