City Research Online

Abstract

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. This paper uses Adam followed by LBFGS 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.

Publication Type:	Article
Additional Information:	© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the termsand conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).
Publisher Keywords:	structural dynamics; single-degree-of-freedom (SDOF); Extended Kalman Filter (EKF); Physics-Informed Neural Networks (PINNs); Eurocode 8; optimization algorithms; dynamic response prediction
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General) T Technology > TH Building construction
Departments:	School of Science & Technology School of Science & Technology > Department of Engineering
SWORD Depositor:	Symplectic Administrator

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