## 3 System Performance  
### Sampling Regularity and Time Synchronization  
A test was conducted to assess the quality of the presented measurement system. One of the fundamental characteristics of the measurement system to be used for dynamic measurements is the regularity of sampling. It is critical for the system to achieve a constant sampling rate, i.e., the sensors need to be sampled at uniformly distributed time instances to ensure the integrity and quality of the measurement process. The test was performed by mounting four MPU-6050 accelerometers on a calibration shaker (APS 113 ELECTRO-SEIS) as shown in Figure 6. The \(\pm\)2 g MEMS-based accelerometers were attached to the front side of the moveable piston of the shaker. The shaker is equipped with a \(\pm\)3 g highly accurate capacitive accelerometer (PCB 3701G2 FA3G) [27], used to control the piston movement. The capacitive accelerometer is mounted to the back side of the piston and therefore measures acceleration at the same moving shaker element as the four MEMS accelerometers, which were each connected to an I\({}^{2}\)C port of an individual RPi. Figure 5: Schematic of signal processing and communication between smartphone and one exemplary RPi node in the mesh network. Figure 6: Measurement setup with accelerometers mounted to the moveable piston of the long stroke vibration exciter. MEMS-based accelerometer connected to RPi A, B, C, and D are attached at the front side of the piston; capacitive accelerometer mounted on the back side. The shaker was set to vibrate harmonically with a frequency of 20 Hz and with a peak amplitude of 0.45 g. The measurements were taken for 60 min with a sampling frequency of 1 kHz. Since the goal of the test is the investigation of the regularity of sampling and the time synchronization between the RPis, only the measured time histories of the RPi measurement systems are analyzed here. A sample time history window of the sensor measurements for one cycle of oscillation is presented in Figure 7. Note that the amplitude differences visible between the four sensors subjected to the same physical motion is mostly due to the appreciable noise of the low-cost MEMS sensors and not related to the quality of the RPi systems. First, the regularity of the sampling was examined. For each RPi, the distributions of the measured time steps \(\Delta t\) were determined. Setting a sampling rate of 1 kHz, the sampling period \(\Delta t\) nominally is 1 ms. The histograms, given in Figure 8, show the distribution of the time steps as measured. The four systems show similar sampling behavior with a time step closely varying around the nominal value of 1 ms, and the difference to that nominal values not exceeding 60 us. The dashed lines indicate the 99 th percentile and lie within 4 us of the nominal value, confirming robust regularity. Further sampling quality measures are presented in Table 2. Ninety-nine percent of the time steps differ by less than 3.4 us, the maximum difference to the ideal sampling step being less than 60 us. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sensor** & \(\mathbf{\Delta t_{99\%}}-\mathbf{\Delta t_{nom}}\) & \(\mathbf{\Delta t_{max}}-\mathbf{\Delta t_{nom}}\) \\  & **[ms]** & **[ms]** \\ \hline A & 0.0032 & 0.045 \\ B & 0.0031 & 0.040 \\ C & 0.0034 & 0.058 \\ D & 0.0028 & 0.041 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of differences of measured time steps \(\Delta t\) from MPU-605 accelerometers to the nominal value \(\Delta t_{nom}\) with a sampling frequency of 1 kHz. Figure 7: Sample time history of one cycle of the measured accelerations from MPU-6050 accelerometers connected to four separate RPis with a sampling frequency of 1 kHz and a period of \(T=50\) ms. The accuracy of the time synchronization between the RPis was also verified for the measurement system. Thereby, RPi A was considered as a reference, and the time offsets of the other three signals were computed.