# Genetic Algorithm-Based Model Updating in a Real-Time Digital Twin for Steel Bridge Monitoring
## 4 FE Modeling  
The numerical model of the bridge was developed using the STKO [29] interface for OpenSees v 3.5 [27]. The model accurately represents a steel truss railway bridge with riveted connections, featuring three spans, as illustrated in Figure 6. Table 1 summarizes various sectional details of the bridge. The elastic modulus (\(E_{s}\)) of all steel members is 200 GPa. Below is a detailed description of the model's components and their respective modeling approaches:  
1. [label=(0)]
2. Braces: Modeled using T-profile truss elements to capture their axial load-bearing behavior. 3. Piers: Represented using 4-node shell elements (ASDShellQ4) to simulate their bending and shear resistance. 4. Ballast: Modeled as a series of springs to account for its elastic support and damping effects on the bridge structure. 5. Track Support Beams: Simulated using IPE beam elements to replicate their flexural and torsional stiffness. 6. Top and Bottom Chords: Modeled with double-T beam elements to accurately reflect their combined axial and bending capacities. 7. Verticals: Represented using IPE300 beam elements to capture their structural role in transferring loads between the chords and the diagonals. 8. Diagonals: Modeled using double-C beam elements to simulate their ability to withstand both tension and compression forces. 9. Boundary Conditions: The boundary conditions of the model were carefully defined to reflect real-world constraints: (1) the piers were fixed at their base to simulate their rigid connection to the foundation; (2) one abutment was constrained to block linear displacements along the x-, y-, and z-axes, as well as rotations about the x-axis, to represent a fixed support condition; (3) the other abutment was constrained to block  
Figure 5: Identified model shapes in the vertical direction via OMA. (**a**) span 1; (**b**) span 2.  
linear displacements along the y and z axes, allowing for potential thermal expansion along the x-axis; (4) the spans were connected to the piers using rigidLink elements in OpenSees, ensuring a rigid connection that transfers forces and moments effectively. The bridge is equipped with a monitoring system consisting of 12 triaxial accelerometric sensors. The sensors operate at a sampling rate of 1 kHz, providing high-resolution data for detailed analysis of the bridge's behavior. This setup enables the detection of subtle vibrations, modal properties, and potential anomalies in the structure's response. Figure 7 illustrates the deformed shapes of the dominant vibration modes identified through modal analysis for spans 1 and 2 of the bridge. Table 2 compares the corresponding natural frequencies obtained from operational modal analysis (OMA) of the real structure with those derived from the numerical model. A significant discrepancy (\(\Delta_{f}\)) is observed between the experimental and computational results, with frequency differences reaching as high as 20% for certain modes. This substantial deviation underscores the necessity of \begin{table}
\begin{tabular}{l c} \hline
**Element** & **Profile** \\ \hline Braces & T 100 \(\times\) 10 mm \\ \hline Tracks & I 200 \(\times\) 150 \(\times\) 20 mm \\ \hline Top chords & T 400 \(\times\) 10 mm \\ \hline Bottom chords & T 400 \(\times\) 32 mm \\ \hline Verticals & IPE300 \\ \hline Rail support beam & IPE500 \\ \hline \end{tabular}
\end{table} 
Table 1: Sectional details of the bridge elements. Figure 6: Finite element model developed in STKO [29] interface for Opensees. (**a**) 3D view showing extruded elements; (**b**) 3D view showing mesh details. calibrating the finite element model (FEM) to align its dynamic behavior with real-world measurements. The calibration methodology, focused on adjusting material properties via genetic algorithms, will be detailed in the subsequent section.