Data-Driven Identification of Variational Equations for Vortex-Induced Vibration Systems

Abstract In this study, a data-driven approach using the embedded variational principle is used to identify the variational equations of vortex-induced vibration fluid–structure interaction systems, in particular the coupling term and the aerodynamic damping term. Under the data-driven paradigm, variational equation identification is primarily accomplished through five steps: collecting discrete data, setting variational functions, building the product function, solving linear equations, and evaluating errors. The explicit variational equations of the system are eventually determined automatically from the excitation and response. Gaussian white noise is added to the excitation to evaluate the method's noise robustness. The findings demonstrate that numerical estimation which stays away from higher-order derivatives significantly enhances the variational law identification's noise robustness by taking advantage of the variational law's lower-order time derivatives. Furthermore, the arbitrariness of the variational setting inherent in the variational law significantly improves the effectiveness of data utilization and lowers the necessary data volume. In addition, a system of linear equations is solved by identifying connected nonlinear equations, which significantly increases modeling efficiency. The basis for engineering modeling, optimization, and control of intricate fluid–structure interaction systems are provided by these benefits.