Strengthening Structural Dynamics for Upcoming Eurocode 8 Seismic Standards Using Physics-Informed Machine Learning

Structural dynamics analysis is essential for predicting the behavior of engineering systems under dynamic forces. This study presents a hybrid framework that combines analytical modeling, machine learning, and optimization techniques to enhance the accuracy and efficiency of dynamic response predictions for Single-Degree-of-Freedom (SDOF) systems subjected to harmonic excitation. Utilizing a classical spring–mass–damper model, Fourier decomposition is applied to derive transient and steady-state responses, highlighting the effects of damping, resonance, and excitation frequency. To overcome the uncertainties and limitations of traditional models, Extended Kalman Filters (EKFs) and Physics-Informed Neural Networks (PINNs) are incorporated, enabling precise parameter estimation even with sparse and noisy measurements. We use Adam followed by L-BFGS to improve accuracy while limiting runtime. Numerical experiments using 1000 time samples with a 0.01 s sampling interval demonstrate that the proposed PINN model achieves a displacement MSE of 0.0328, while the Eurocode 8 response-spectrum estimation yields 0.047, illustrating improved predictive performance under noisy conditions and biased initial guesses. Although the present study focuses on a linear SDOF system under harmonic excitation, it establishes a conceptual foundation for adaptive dynamic modeling that can be extended to performance-based seismic design and to future calibration of Eurocode 8. The harmonic framework isolates the fundamental mechanisms of amplitude modulation and damping adaptation, providing a controlled environment for validating the proposed PINN–EKF approach before its application to transient seismic inputs. Controlled-variable analyses further demonstrate that key dynamic parameters can be estimated with relative errors below 1%—specifically 0.985% for damping, 0.391% for excitation amplitude, and 0.692% for excitation frequency—highlighting suitability for real-time diagnostics, vibration-sensitive infrastructure, and data-driven design optimization. This research deepens our understanding of vibratory behavior and supports future developments in smart monitoring, adaptive control, resilient design, and structural code modernization.