Physical Embedded Neural Network (PENN): A new modeling paradigm for structural inverse dynamics models

This work proposed an interpretable neural network specifically designed for structural inverse dynamic modeling, termed the Physical Embedded Neural Network (PENN). Distinguished from the Physics-Informed Neural Network (PINN), the PENN does not use the traditional perceptron as its basic neuron unit; instead, it employs newly designed neurons; instead, it uses newly designed neurons embedded with physical parameters as its fundamental units, enabling a convex optimization-based training through a dual-driven technique combining knowledge and data. Through simulation case studies, we apply the PENN to the inverse dynamics modeling of an 8-degree-of-freedom discrete system and a fixed-supported beam structure, both achieving high modeling accuracy. The dynamic parameter errors of the trained PENN are all less than 1 %. Furthermore, we apply the PENN to the inverse dynamics modeling of a fixed-supported beam structure, and a hybrid glass–carbon laminate experimentally. The results show that the errors of dynamic parameters embedded in the trained PENN for the fixed-supported beam are all less than 1 %, and for the laminate are all less than 10 %. The current study indicates that the proposed PENN can combine the rigor and interpretability of physical models with the flexibility of data-driven modeling methodology to establish analytical mapping relationships, creating a new paradigm for structural inverse dynamics modeling.