# Forward Fall Detection Using Inertial Data and Machine Learning
## 2 Materials and Methods
### Generating the Fall Event Training Values Using a Digital Model
Hunt-Crossley contact forces are applied to the pelvis, specifically between the pelvis contact sphere and a platform contact surface in the simulation model. The parameters influence the behavior of the contact force during the simulation. The right thigh, left thigh, and torso contact forces are also set up between their contact spheres and pelvis. The upper right and left arms have contact forces to the torso and forearms to the upper-arms contact spheres. The angle of the platform is used to control the amount of potential energy converted to kinetic energy with each stride. Energy must be added to the system to offset losses from \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline upperStiffness & 0.7 [Nm/rad] & damping & 0.8 [Nm/(rad/s)] \\ lowerStiffness & 0.4 [Nm/rad] & transition & 5 [\({}^{\circ}\)] \\ kneeUpperLimit & 0.7 [Nm/rad] & torsoUpperLimit & 0 [rad] \\ kneeLowerLimit & \(-140\) [\({}^{\circ}\)] & torsoLowerLimit & 0 [rad] \\ hipUpperLimit & \(100\) [\({}^{\circ}\)] & HeadUpperLimit & 0 [rad] \\ hipLowerLimit & \(-100\) [\({}^{\circ}\)] & HeadLowerLimit & 0 [rad] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coordinate Limit Force Parameters. Figure 7: Topology view of the digital model. ground contact to maintain a stable motion. A planar joint, which permits three degrees of freedom between the pelvis and the platform, connects the walker's pelvis to the platform. The shanks and thighs are joined by pin joints, as are the thighs and pelvis, and arms and torso. After setting up the appropriate contact forces, the rigid platform is inclined at a 2-degree angle to control the amount of potential energy converted to kinetic energy. Because the knee upper and lower stiffness values are set up to 0.7, respectively, 0.4 Nm/rad, the knees bend upon the falling event, and will first touch the platform resulting in a damped forward fall (Figure 8). By using the forward dynamic tool, and setting the run time to 4 s, the simulation is finished, and the pelvis speed values relative to the platform according to the X and Y axis are recorded relative to time, with a step of \(\Delta t=0.02\) s resulting in 201 data samples. The values obtained are illustrated in Figure 9a, where it is shown that the velocity increases as soon as the model starts to fall. Depending on the type of fall (damped or undamped) there will be 1 or two spikes. The minus sign of the velocity on the X-axis is considered in relation to the platform, in the vertical direction. The speed values are exported and converted to acceleration data, as shown in Figure 9.  
\[a=\frac{\Delta v}{\Delta t}\,\mathrm{m}/\mathrm{s}^{2} \tag{2}\]  
To obtain the acceleration values for the undamped forward fall, the coordinate limit force parameters upperStiffness and lowerStiffness are set to 5 Nm/rad, the kneeUpperLimit is set to 5\({}^{\circ}\) and kneeLowerLimit to \(-5\). The rigid platform remains inclined at a 2-degree angle and the simulation is run for 4 s using the Open Sim forward dynamics tool, as shown in Figure 10.  
Figure 8: Damped forward fall simulation. Figure 9: Training data acquired through simulation for the forward damped fall: (**a**) Recorded speed on the X and Y axis [m/s]; (**b**) Recorded acceleration on the X and Y axis. By placing the digital model in the correct position, several types of falls can be obtained, including damped falls by applying hand contacts. The scope of the current simulation is to obtain a pure forward fall to imitate a faint event, during which the person falls on his head without any damping. After the velocity values are recorded, the acceleration data is extracted, as shown in Figure 11, and normalized for all cases.