## 5 Models Analysis  
The identification procedure described in the previous paragraph has been employed to evaluate the capability of the GM and FDGM models to describe three completely different viscoelastic materials. Moreover, for each model, we need to understand the minimum number of parameters that can describe the dynamic characteristics of the considered viscoelastic materials. Therefore, to this purpose, the identification procedure has been performed for each model considering an increasing number of elements until the fitting of experimental data was not satisfactory. To quantitatively compare the models presented in this paper, the NRMSE is evaluated for the storage modulus and the loss tangent quantities as defined in Equation (12). The purpose of these indicators is to quantify the goodness of the models' behavior towards the experimental data reproduction. Figure 3 compares experimental data with the results obtained for the three compounds with the GM models composed by 15, 25 and 35 elements plus a spring in parallel (E\({}_{0}\) in Figure 2), while in Table 2, the relative calculated NRMSEs are reported. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Compound A**} & \multicolumn{2}{c}{**Compound B**} & \multicolumn{2}{c}{**Compound C**} \\ \hline \multirow{2}{*}{GM model} & NRMSE E\({}^{\prime}\) & NRMSE tan\(\delta\) & NRMSE E\({}^{\prime}\) & NRMSE tan\(\delta\) & NRMSE E\({}^{\prime}\) & NRMSE tan\(\delta\) \\  & (MPa) & (-) & (MPa) & (-) & (MPa) & (-) \\ \hline
15 elements & 0.0183 & 0.0876 & 0.0416 & 0.1146 & 0.0279 & 0.2358 \\
25 elements & 0.0038 & 0.0148 & 0.0306 & 0.0822 & 0.0087 & 0.2355 \\
35 elements & 0.0021 & 0.0053 & 0.0305 & 0.0789 & 0.0069 & 0.2352 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: NRMSEs for Generalized Maxwell models composed by 15, 25 and 35 elements. The identified parameters of these models are detailed in Tables A1-A3 in Appendix A. Analyzing the models' results, it is evident that the GM model composed of 15 elements appears totally insufficient to describe the compounds' frequency response because it shows unphysical local oscillations although it seems to follow the real global trend. As highlighted by the NRMSE in Table 2, by increasing the number of Maxwell elements, the fitting of experimental data is improved as well. However, it should be noted that to have significant improvements in model results, several elements must be added with a consequent increase in the parameters to be identified. The FDGM model results are reported in Figure 4. For each compound, the experimental data are compared with models composed by a spring (\(E_{0}\) in Figure 2) in parallel with 3, 4 and 5 spring-pot elements. The corresponding NRMSEs are reported in Table 3, while the parameters of these models are detailed in Tables A4-A6 in Appendix A. It should be noted that the FDGM model is able to give an acceptable representation of the curves' shapes with a three-element model which is also consistent with the NRMSE values. Also in this case, increasing the number of model elements, the fitting of experimental data improve. Figure 3: Storage modulus and loss tangent for compounds A (a), B (b) and C (c): experimental data (dashed line) vs. GM model with 15 (blue line), 25 (green line) and 35 (red line) elements. A relative comparison between the three compounds shows that, regardless of the model used, compound A returns the best fitting results than the others for the same number of elements used. By mere comparison of normalized errors, we observed (in general) a good performance of both models adopted in describing the real compounds' behavior, but GM model needs a greater number of elements than the FDGM. While FDGM was able to provide good matching with the simple configuration with only ten unknowns, for the GM, it was necessary to build up a more complicated model by adding several elements.