Structural Parameter Identification with a Physics-Informed Neural Networks-Based Framework

Structural parameter identification is a critical aspect of structural health monitoring and maintenance. It belongs to inverse problems, which aim to discover mechanical parameters, such as the stiffness of the concerned system from collected measurement data. Then, the identified parameters are used to evaluate the status of the structure and detect potential structural damage in advance. As a promising machine learning method that effectively combines domain knowledge and deep neural networks, physics-informed neural networks (PINNs) have been widely applied in various fields, including structural parameter identification and structural health monitoring. In this study, we propose a novel framework based on PINNs for parameter identification in structural systems. The framework contains two main components, one is called the physical term that employs PINNs to learn the prior physical knowledge of the structural system; the other is called the discrepancy term that involves another PINNs or even a simple feedforward neural network to present the differences between the observed data and the physical term. In a nonlinear structural system, the physical term can be regarded as the linear part of the structural response, while the discrepancy term represents the nonlinear response. In the PINNs configuration, the residuals of the governing equation, which are calculated by substituting collocation points that are randomly sampled within the domain into the governing equation, are directly incorporated into the total loss function. In addition, the boundary conditions, as well as the initial conditions, are soft-embedded as essential parts in the total loss function. The measurement data is also required by an inverse problem, and the differences between the measurement data and the prediction produced by the PINNs-based physical term will be captured by the discrepancy term. Through the discrepancy term, the nonlinear structural parameter can be figured out. Finally, a two-degree of freedom mass-spring system with nonlinear spring is investigated to illustrate the ability of the proposed framework in structural parameter identification.