# A Statistical Approach for Modeling Individual Vertical Walking Forces
## 2 Experimental Setup and Measurements  
Properties of pedestrian walking have been investigated through an experimental campaign at the University of Modena and Reggio Emilia, Department of Engineering \"[PERSON]\" (Italy), which allowed measuring force, time and position of the vertical forces induced by single pedestrians on an instrumented floor. It is worth pointing out that this approach allows us to directly acquire the quantity of interest for the study of the footbridge. On the contrary, the measurement of the acceleration through an accelerometer, for instance, constrained to a foot, requires a suitable procedure to evaluate the step forces that may introduce large uncertainties. In fact, the human body is not a rigid system and the force applied to the floor cannot be simply inferred from the acceleration and the static mass of the person. Ground reaction forces are measured adopting the force plate system developed by [PERSON] et al. [31] and shown in Figure 1. Each unit of the force plate system is a stand-alone uniaxial force platform composed of two aluminum plates. The lower plate is constrained to the ground, hosts the force measurement devices and measures 1000 \(\times\) 1000 \(\times\) 12 (mm). The upper plate is 1000 \(\times\) 1000 \(\times\) 15 (mm) and allows the TS to walk on it. Load cells are installed between the plates, along the diagonals of the surface and at the farthest end from the plate center. A control unit acquires the signal from the four load cells in each force plate and transfers it to the management software that enables selecting the sampling frequency and viewing measurements. In the presented experiments, the sampling frequency was set to 100 Hz. Thanks to a specifically designed interface, data acquired from the four load cells are combined, and ground reaction forces as well as foot positions are evaluated for each force plate. The force plate system is characterized by a high flexibility and modularity, allowing us to set up the measuring surface on the basis of the test to perform. To characterize the intra-subject variability of the walking force induced by single pedestrians, an instrumented walkway is built with two rows of force plates placed side by side. Tests involved three test subjects. The characteristics of the three TSs are summarized in Table 1.  
Each walking test involved one person and was carried out as follows. First, the TS took a few steps before getting on the walkway, and then she walked through it with her self-selected comfortable walking speed. Once the TS left the walkway, she took a few more steps, turned around and crossed the walkway in the opposite direction. The TS kept walking back and forth for the whole duration of the test, namely 10 min. The steps taken before getting on the walkway allowed the TS to get used to her comfortable walking speed and achieve a natural rhythm when she made contact with the force plate. The TS walked astride the center of the walkway so that the right food was placed on the right row of force plates and vice versa. Note that the pacing was not prompted by any device \begin{table}
\begin{tabular}{c c c c} \hline \hline
**TS** & **Mass [kg]** & **Age [Years]** & **Gender** \\ \hline
1 & 45 & 25 & female \\
2 & 54 & 25 & female \\
3 & 55 & 22 & female \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test subject characteristics. Figure 1: Force sensors installed under the vertices of the plates. (e.g., a metronome) and the pacing rate was determined only from the post-processing of the measured signal. Since the time histories of the right and left foot are separately recorded by the two rows of force plates, the vertical force induced by a single step can be clearly recognized from the measurements. Figure 2 shows an example of the time histories of the right and left foot along with the continuous walking force obtained by adding the contribution of both feet. A total of about 700 single step forces were collected for each TS.