# Genetic Algorithm-Based Model Updating in a Real-Time Digital Twin for Steel Bridge Monitoring
## 6 Conclusions  
This study demonstrates the development and implementation of a real-time digital twin for a steel-truss railway bridge, integrating sensor-based structural health monitoring (SHM), operational modal analysis (OMA), and finite element (FE) model updating. By leveraging Stochastic Subspace Identification (SSI) for modal parameter extraction and genetic algorithm-based optimization for model calibration, the digital twin accurately captures the bridge's dynamic behavior and provides an effective tool for real-time condition assessment. The key findings of this study are as follows:  
1. Accurate modal parameter identification: the SSI method effectively extracted the bridge's natural frequencies and mode shapes from free vibration responses, demonstrating its reliability for real-world structural monitoring. 2. High-fidelity digital twin calibration: by optimizing the elastic modulus of steel components, the model updating process reduced frequency errors to below 5% and  
Figure 9: MAC Comparison between (**a**) the initial FEM and (**b**) calibrated FEM. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{**Real**} & \multicolumn{2}{c}{**Initial FE Model**} & \multicolumn{2}{c}{**Updated FE Model**} \\ \cline{3-8}  & & \(f_{real}\) (Hz) & \(f_{FE}\) (Hz) & \(\Delta_{f}\) (\%) & \(MAC\) & \(f_{FE}\) (\%) & \(\Delta_{f}\) (\%) & \(MAC\) \\ \hline \multirow{2}{*}{Span 1} & 1 & 8.85 & 10.86 & 18.51 & 0.73 & 8.85 & 0.00 & 0.97 \\ \cline{2-8}  & 2 & 16.03 & 19.50 & 17.79 & 0.88 & 16.50 & 2.85 & 0.98 \\ \hline \multirow{2}{*}{Span 2} & 1 & 6.48 & 7.48 & 13.37 & 0.19 & 6.49 & 0.15 & 0.97 \\ \cline{2-8}  & 2 & 14.38 & 17.98 & 20.02 & 0.84 & 14.88 & 3.36 & 0.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of modal data from the FEMs and the real bridge. significantly improved modal assurance criterion (MAC) values (>0.93), ensuring strong alignment between numerical predictions and experimental data. 3. Scalable and practical digital twin framework: the integration of OpenSeesPy for FE modeling and PyGAD for optimization proves to be an efficient approach for real-time SHM applications, making this methodology adaptable to other bridge structures and critical infrastructure systems. 4. Enhanced predictive maintenance and damage detection: the validated digital twin provides a reliable baseline for monitoring structural changes over time, enabling early damage detection and data-driven maintenance decisions to improve bridge safety and service life. While the proposed framework demonstrates significant advancements, certain limitations must be acknowledged, as follows: (1) Sensor noise sensitivity: modal parameters derived via SSI may be influenced by ambient noise, particularly in low-amplitude free vibration segments, potentially affecting calibration accuracy. (2) Environmental effects: temperature fluctuations and humidity, which can alter material properties and boundary conditions, were not explicitly modeled, limiting the framework's ability to distinguish between environmental and damage-induced changes. (3) Simplified material calibration: the optimization focused solely on adjusting the elastic modulus of steel, neglecting localized effects such as joint degradation or fatigue-induced micro-cracks. To address these limitations and further enhance the digital twin's robustness, future research will focus on the following: (a) The integration of multi-sensor data: incorporating strain gauges and displacement sensors to capture localized deformations and reduce reliance on accelerometer-derived modal data. (b) Environmental coupling: developing hybrid models that account for temperature, humidity, and operational load variations to isolate structural degradation from external influences. (c) Advanced optimization algorithms: implementing hybrid genetic algorithms with machine learning to refine parameter adjustments and reduce computational costs.