# Model Updating of a Freight Wagon Based on Dynamic Tests under Different Loading Scenarios
## 3 Dynamic Tests
### Modal Identification  
The identification of the modal parameters for the unloaded and loaded vehicle, particularly the natural frequencies, mode shapes and damping coefficients, was performed by the application of the enhanced frequency domain decomposition (EFDD) method implemented in the ARTeMIS software [48], which is a well-established and robust technology capable of providing accurate results even in the presence of noise on the measured data [49; 50]. In this method, the natural frequencies are identified based on the peaks of the average and normalized singular values of the spectral matrices, and the modal configurations are derived from the corresponding singular vectors. Figure 8 depicts the average and normalized singular values of the spectral matrices of all test setups, derived from the application of the EFDD method, and considering the unloaded (Figure 8a) and loaded (Figure 8b) configurations. The peaks corresponding to the five globally identified operational mode shapes are identified in the figure by dashed lines. The remaining peaks are possibly related to [51; 52]: (i) local operational mode shapes not properly characterized by the sensors layout (vibrations of stanchions and elements of the wagon's platform), (ii) presence of harmonics due to equipment in operation, (iii) influence of the excitation provided by people and impulse hammers, and (iv) noise on measured data or derived from the signal-processing operations. Figure 7: Dynamic tests of Sgnss wagon: DAQ and accelerometers on the platform and bogies. Figure 9a,b illustrate, in perspective, five identified operational mode shapes for the _Sgns_ vehicle considering the unloaded and loaded configurations, respectively. The deformed modal configurations are represented by red lines, in the case of the unloaded configuration, or blue lines, in the case of the loaded configuration, and the undeformed mesh are represented by grey lines. The average values of the natural frequencies and corresponding damping coefficients are also indicated. Generally, the modal configurations have a very good definition and involve structural movements of the vehicle platform, which in some cases, to more or less extent, are coupled with rigid body movements. The modal configuration of the unloaded and loaded configurations are similar but have distinct modal ordinates, as can be observed in Figure 9a,b. Mode 1 is a rigid body mode associated with the rotation of the vehicle platform along its longitudinal axis (rolling). However, especially for the unloaded configuration, some coupling with the torsion movement of the vehicle platform is visible. Mode 2 is a flexural movement of the platform associated with its second torsion mode. Mode 3 involves the bending of the vehicle platform coupled with the rigid body bouncing movement. Mode 4 is associated with a higher-order torsion mode of the vehicle platform. Mode 5 is a local bending mode combined with rigid body pitching movement of the platform. In all the identified modal configurations, the movements of the bogies are negligible in comparison to the movements of the vehicle platform, with the exception of Mode 5, where a coupling effect was detected. Figure 8: EFDD method—average normalized singular values of the spectral matrices: (**a**) unloaded configuration, (**b**) loaded configuration. Additionally, as expected, due to the high ratio between towed load and tare weight, as is typical in this type of freight wagons, the natural frequencies for the loaded vehicle are significantly lower in comparison to the unloaded wagon. The range of frequency values is between 3.65 Hz and 16.63 Hz for the unloaded configuration, and between 1.54 Hz and 6.66 Hz for the loaded configuration. The damping coefficients obtained for the loaded configuration (0.79% to 2.63%) are of the same order of magnitude but consistently higher, mode-by-mode, in comparison to the  
Figure 9: Experimental modal parameters: (**a**) unloaded configuration, (**b**) loaded configuration. unloaded configuration (0.60% to 2.00%).