## 4 Applications
### Identification of Modal Information of a Steel Beam  
This application considers a simply supported steel beam as shown in Figure 12. The beam has a hollow profile of dimensions 100 \(\times\) 60 \(\times\) 3 mm and spans 5.80 m. The goal was to determine the frequency, the shape, and the damping of the first five vertical bending modes as in typical SHM tasks. The beam structure was excited by regular hammering at distinct locations (\(\sim 0.3\cdot L\)) to excite multiple modes of the beam. Two different measurement systems are available for the measurement campaign: first, a high-quality reference system including highly sensitive piezoelectric sensors (PCB 393A03) connected to a data acquisition unit featuring a synchronous input channel and 24 bit signal conversion; second, the alternative RPi-based measurement system using external MPU-6050 sensors [31]. In total, three piezoelectric sensors and seven sensor nodes were employed in the vibration test. The sensor setup is shown in Figure 12 and 13. The reference sensors are placed at midspan, at 1/4 and 1/6 of the span, where maximum displacement of the first, second and third mode is expected. The seven wireless sensor nodes are placed equally throughout the length of the beam with a center-to-center distance of 0.725 m. The sensing characteristics and the costs of the two applied measurement systems are summarized in Table 5. The superiority of the reference system can be seen from the much higher resolution. In addition to the synchronous data acquisition, it features an  
Figure 12: Experimental setup with sensors attached at the bottom of the beam. (Wooden pieces are used as support for the sensor nodes.) integrated anti-aliasing filter and allows for sampling rates up 40 kHz. However, the sampling rate was set to 1024 Hz for this experiment. Both piezoelectric and MEMS accelerometers were mounted to steel plates that were attached to the beam by means of two magnets, as shown in Figure 14. The RPi sensor nodes were located next to the beam on wooden supports. After powering the RPi, the wireless network and the meshing was set up automatically. Prior to the measurements, the time synchronization of the sensor nodes was conducted via the previously presented frontend software, which was further used to control the measurements. Figure 14: View of the sensor mounting plate equipped with a high-quality piezoelectric sensor and an external accelerometer attached to the RPi. Figure 13: Schematic of the sensor setup at the steel beam. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**System**} & **Sampling Rate** & **Resolution** & **Noise Density** & **Cost** \\  & **[Hz]** & **[bit]** & **[\(\mathrm{\SIUnitSymbolMicro g}/\sqrt{Hz}\)]** & **[e]** \\ \hline Reference system & 1024 & 23 & 1 & 12,000 \\ RPi and MPU-6050 & 1000 & 15 & 400 & \textless{}500 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Properties of the utilized measurement systems for the steel beam experiment [31]. The accelerations were recorded for more than 100 s in order to achieve a frequency resolution higher than 0.01 Hz. The time histories were measured simultaneously by all sensors of both systems. For further processing, the acceleration time histories of the MEMS accelerometer were resampled to a frequency of 2000 Hz. System identification was performed using the Matlab toolbox MACEC [32], which employs the covariance-driven approach of stochastic subspace identification and thus determines the modal information of the beam from the recorded sensor data. Suitable modes were then chosen from the stabilization diagram. The natural frequencies and damping ratios obtained from the two applied systems are compared in Table 6. The natural bending frequencies have been identified and show good agreement between the two systems with a maximum difference of 0.03 Hz in the second mode. Regarding the determined damping, a greater deviation that is more dominant for the lowest modes can be seen.