## 2 Method
### Modal Parameters  
Modal identification was performed using OROS Modal software (Version 5, OROS, Grenoble, France). We chose the Least Squares Complex Frequency domain (p-LSCF) method [20] owing to its  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Ranges** & **Mean** & **STD** \\ \hline Age (years) & 22–34 & 25.90 & 2.81 \\ Height (m) & 1.68–1.84 & 1.78 & 0.04 \\ Weight (kg) & 65.30–84.70 & 73.52 & 4.93 \\ Body Mass Index (BMI) & 20.73–27.04 & 23.34 & 2.09 \\ Hip-knee (cm) & 50.00–60.00 & 53.73 & 3.88 \\ Knee-tibia (cm) & 15.00–21.07 & 17.29 & 1.09 \\ Tibia-ankle (cm) & 20.00–27.93 & 22.89 & 1.52 \\ Total length (cm) & 80.00–107.00 & 93.91 & 5.72 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Subjects’ anthropometric parameters.  
Figure 1: (Left) Accelerometers locations and orientations; (right) geometry of the lower limb model in the Modal Analysis software. Points 1, 2, 3, 4 are the location of the accelerometers and the number of node for the numerical model.  
capability of separating strongly-coupled modes and avoiding the decomposition of model-related residues into singular values. Singular Value Decomposition (SVD) drastically decreases the quality of the regression [21]. The method is based on the analysis of the outputs, described in Equation (1):  
\[S_{outputs}(\omega)=H(\omega)\cdot S_{inputs}\cdot H(\omega)^{H}, \tag{1}\]  
\(\omega\) being the frequencies, \(H(\omega)\) the matrix composed of the frequency response function, exponent \({}^{H}\) the complex conjugate transpose of a matrix (Hermitian) and \(S_{inputs}\) and \(S_{outputs}\) the inputs' and outputs' spectral matrix. The outputs' estimation \(S_{outputs}^{+}(\omega)\) is obtained by integrating two residual terms to approximate the effects outside the selected range [22], using Equation (2):  
\[S_{outputs}^{+}(\omega)=\sum_{i=1}^{n_{r}}\left(\frac{\Phi_{i}g_{i}^{T}}{j\omega \lambda_{i}}+\frac{\Phi_{i}^{*}g_{i}^{H}}{j\omega\lambda_{i}^{*}}+\frac{\text{ LR}}{j\omega}+j\omega\text{ UR}\right), \tag{2}\]  
where \({}^{T}\) is the transpose of a matrix, \({}^{*}\) is the complex conjugate of a matrix, \(\Phi_{k}\) is a column vector containing mode shape \(k\), \(g_{k}^{T}\) is a line vector with the modal participation factor of mode \(k\) and \(\lambda_{k}\) are the structure poles. LR and UR stand for the lower and upper residues, which illustrate the influence of modes outside the frequency range.  
For both protocols, the range of interest was 0-200 Hz. Preliminary measurements showed that for frequencies over 200 Hz, the spectral signal was similar to noise. Moreover Standard ISO 2631-1 [23] provides a guideline for measurement and assessment in the case of exposure to whole body vibration, and defines a frequency weighting filter. More precisely, frequencies above 200 Hz are significantly filtered.  
Identification of the modal parameters, and particularly mode shapes, requires a simplified model. Thus, a model of a segmented straight line was made from four nodes with three degrees of freedom (DOFs), positioned in a way similar to the measurement points in OROS Modal software (see Figure 1). For Protocol 1, the modal characteristics of the leg were calculated: modal frequencies, damping and shapes. The results of frequencies and damping are presented as the mean and standard deviation (coefficient of variation). The coefficient of variation was calculated as the ratio between the standard deviation and the mean. The repeatability of the shapes was visually estimated. For Protocol 2, the modal characteristics of the lower limb were determined for all of the subjects: modal frequencies, damping and shapes, as indicated above. The modal frequencies were then used to validate and update the mechanical properties (Young's moduli and mass densities) used in the numerical model.