4.3.1. Initial Model

The initial numerical model was constructed to determine the deviation of the real state of the structure from the ideal boundary conditions (clamp and hinge) and to evaluate which of those boundary conditions better described the real state. The finite element (FE) distribution of the numerical model corresponded to the arrangemen<sup>t</sup> of the measuring points shown in Figure 8. For each initial model, the first two natural frequencies and mode shapes were determined (Figure 11).

**Figure 11.** Comparison of the experimental mode shapes of the reference tie rod 6B-C and the mode shapes associated initial numerical models for the (**a**) first and (**b**) second mode shapes.

To avoid subjective assessment of the boundary conditions, mode shapes from numerical simulation and experiments were compared using normalized RMSE (Equation (9)). For each initial numerical model and its corresponding mode shapes, the RMSE values were determined. Based on the RMSE values (Table 3), we observed that the initial model with hinged boundary conditions better correlated (values approaching 0) with the on-site measurements. Based on the results, hinged boundary conditions were identified as a good selection for the initial model and were further updated by adapting the spring sti ffness on the boundary.

**Table 3.** Root-mean-square error (RMSE) values for initial numerical models for two mode shapes.

