## 5 Results
### Non-Linear Wear-State Classification Approach  
The results achieved using non-linear wear-state classes and STFT features are presented in Table 6. For the SVM experiments, the lowest performance recorded was 53.9% for the linear band features using a cubic kernel function SVM model. The highest performance of 73.6% was achieved by the one-third octave band features using a medium Gaussian kernel function.  
In the case of the \(k\)-NN experiments, the lowest performance recorded was 60.1% from the linear frequency band features with the Fine \(k\)-NN. The highest performance accuracy of 73.2% was achieved using the one-third octave band features with Coarse \(k\)-NN. This was also the highest classification performance achieved overall for the STFT analysis feature study.  
The normalised MAE results for the STFT spectral features using SVM classification models indicate that the Medium and Coarse Gaussian kernel function using the one-third octave band features was also the best-performing model with the lowest normalised MAE score. Similarly for the \(k\)-NN experiments, the one-third octave using Coarse \(k\)-NN achieved the lowest error score.  
The non-linear wear-state results for the Signal-Envelope-derived features using are presented in Table 7. For the SVM models, the lowest performance recorded was 9.5% for the squared one-third octave band features using a cubic kernel function, whereas the highest performance of 73.1% was achieved for the summed one-third octave band envelope features using a linear SVM kernel function. In the case of the \(k\)-NN classification results, the lowest performance recorded was 62.0% for the squared one-third octave band features using a Fine \(k\)-NN classifier.  
The highest performance accuracy was 74.3% for the one-third octave band FFT features using a cosine \(k\)-NN classifier. This was also the highest classification performance achieved overall for the Envelope Analysis \(k\)-NN study and importantly for all of the experimental studies reported in this work. The normalised MAE results using the signal envelope derived spectral features applying SVM classification models indicate that the Linear kernel function using the one-third octave band features were the best-performing model with the lowest MAE score of 0.09.  
The Cosine \(k\)-NN model proved to be the best options for the non-linear temporal classes, with an error score of 0.08, which was also the lowest overall error score across all four experimental studies presented. Accordingly, these best MAE values also correspond with the best classification accuracy achieved, which is not unexpected.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**SVM**} \\ \hline
**Features** & **Linear** & **Quadratic** & **Cubic** & **Fine G** & **Medium G** & **Coarse G** \\ \hline \(\mathcal{F}\Big{\{}x[n]\Big{\}}\) & 66.8 \(|\) 0.12 & 61.6 \(|\) 0.18 & 59.1 \(|\) 0.19 & 63.2 \(|\) 0.14 & 65.6 \(|\) 0.13 & 65.4 \(|\) 0.11 \\ \(L[m,k]\) & 59.1 \(|\) 0.15 & 59.7 \(|\) 0.19 & 53.9 \(|\) 0.23 & 63.2 \(|\) 0.15 & 60.4 \(|\) 0.15 & 65.1 \(|\) 0.11 \\ \(O[m,k]\) & 71.2 \(|\) 0.11 & 68.8 \(|\) 0.15 & 62.8 \(|\) 0.17 & 62.4 \(|\) 0.15 & **73.6 \(|\) 0.10** & 68.4 \(|\) 0.10 \\ \hline \hline  & \multicolumn{6}{c}{**k-NN**} \\ \hline
**Features** & **Fine** & **Medium** & **Coarse** & **Cosine** & **Cubic** & **Weighted** \\ \hline \(\mathcal{F}\Big{\{}x[n]\Big{\}}\) & 64.0 \(|\) 0.16 & 65.0 \(|\) 0.15 & 66.7 \(|\) 0.11 & 66.9 \(|\) 0.15 & 64.8 \(|\) 0.15 & 64.5 \(|\) 0.15 \\ \(L[m,k]\) & 60.1 \(|\) 0.18 & 62.0 \(|\) 0.17 & 64.8 \(|\) 0.11 & 63.2 \(|\) 0.15 & 63.2 \(|\) 0.17 & 61.0 \(|\) 0.17 \\ \(O[m,k]\) & 69.4 \(|\) 0.13 & 68.9 \(|\) 0.12 & **73.2 \(|\) 0.10** & 69.5 \(|\) 0.12 & 68.7 \(|\) 0.11 & 69.7 \(|\) 0.12 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Non-linear wear-state classification results (%) and normalised MAE for STFT data, where G denotes Gaussian.