Dynamics-Guided Support Vector Machines for Response Analysis of Steel Frame Under Sine Wave Excitation

Abstract

Classical explicit and implicit time integration methods, such as the central difference method and Newmark method, are widely used for dynamic response analysis of systems. However, their computational accuracy and stability are highly sensitive to the time step size. To address this issue, a novel dynamics-guided support vector machine (DG-SVM) method is proposed, which embeds an optimization process to reduce dependence on the time step size. Unlike traditional machine learning approaches, the DG-SVM model incorporates initial conditions and dynamic equilibrium equations at each time step as physical constraints, ensuring that inertial forces, damping forces, resistance forces, and external dynamics satisfy equilibrium without relying on system dynamic response data. Furthermore, a solution algorithm combining DG-SVM with static condensation and mode decomposition methods is developed to enhance computational efficiency for the analysis of multi-degree-of-freedom systems. The superior accuracy and reliability of the proposed method are validated using a three-story steel frame structure subjected to sinusoidal excitation, where the numerical results obtained by DG-SVM are compared with those computed from classical integration methods, with analytical solutions serving as benchmarks.