## 6 Results
### Results from the Numerical Simulations
#### 6.2.1 Further Analysis of the Experimental Data  
Some further tests were performed to better define the advantages of the proposed TECCs feature. For brevity sake, only the results for experimental data are reported; the same findings were observed for numerical data. Firstly, the number and distribution of output channels were investigated. Four setups have been considered: setup #0, including all channels (numbered 2 to 5, see Figure 8), for which the results are already reported in Figure 13 and Table 9; setup #1 (channels 3, 4, and 5); setup #2 (channels 3 and 4); and finally, setup #3 (constituted by channels 4 and 5). Table 10 enlists the results for these last three setups. Remarkably, this test evidenced what was already observed in [21], that is to say, MFCCs and similar features produce less accurate results when all of the acquisition channels are considered. This point was confirmed here for type 1 errors in two out of the three new setups considered. The same effects were encountered here for TECCs as well, with the same conditions: MFCCs systematically fail in labelling case 5 as undamaged, due to its relatively large shift in frequency, while TECCs struggle in classifying cases 10, 15, and 16 as damaged due to their lower level of nonlinear distortion. Secondly, a comparison with a non-cepstral feature, the aforementioned AR coefficients, was also performed and reported in Table 10. The AIC approach was applied similarly to what done in [21]. An order of 12 was used for sensor setup #1 and #2; order 10 was applied instead for the sensor setup #3. It can be seen that the percentage of type 1 error is generally higher than most of the cepstral features that are proposed here. The Central Processing Unit (CPU) time that was required for the training phase was then evaluated for all types of DSFs on non-optimised (yet comparable) versions of the code. This was tested by means of the Matlab(r) stopwatch timer tic-toc; Table 11 reports the results. One can clearly see that the computational time is comparable over the several sensor setups considered. Note that the timing accounts for training operations (feature extraction and population statistics estimation) and for threshold definition; the time required for data preprocessing, differently from what done in [21], was not considered, as it is identical for all features. This returns some faster results with respect to what is reported there. Moreover, the codes were run 10 times to avoid any computational variability; the average result is reported. As expected, the difference between MFCCs, similar variants, GTCCs and TECCs are minimal. It can be observed that GTCCs takes slightly longer than MFCCs (in the order of some fractions of a second), since there it is needed to build up the more complexly shaped gammatone filterbank. The TECCs require that additional time plus a bit more to compute the TKE operator out of the provided time arrays. In the case with all acquisition channels considered, these two operations make the code run in almost 30% more time (0.43 s on average). However, this delay is basically irrelevant if compared to the one that is needed to extract other features, such as the Auto-Regressive (AR) model coefficients [21]. Lastly, the standard deviation is proposed as a metric of dispersion for the results of the several realisations that belong to the same damage case, to quantitatively express the robustness of the classification. Table 12 enlists the results for all 17 cases. Only the values for the sensor setup #0 and for MFCCs, log-scale CCs, linear CCs, BFCCs, GTCCs, and TECCs are reported here due to space constraints. The same behaviour was observed for the other setups as well. By considering ten realisations per investigated case, it can be observed that the use of TECCs as a DSF produce a much smaller scattering of the results, with the standard deviation never exceeding \(\sigma=6\), while the same measure goes well over 50 or even 70 for MFCCs in some cases.