# A Fault Detection Framework for Rotating Machinery with a Spectrogram and Convolutional Autoencoder
## 4 Experimental Study
PCA-based feature extraction also tends to yield worse performance than the 2D-CAE because PCA cannot adequately accommodate the nonlinearity inherent in the input distribution of spectrograms. In addition, PCA handles the elements of the spectrogram as individual features, which hinders the successful recognition of localized characteristics within the spectrogram. While the stacked AE can deal with the nonlinear patterns through nonlinear activation functions, it still cannot capture the localized properties of the spectrogram, the same as the PCA and kernel PCA. On the other hand, the fault detection performance of the denoising 2D-CAE is comparable to that of the original 2D-CAE because it can properly deal with the noise in signals. However, this DNN-based method might not be appropriate for the fault signal detection problems because the optimal level of noise added to the spectrogram is not easy to determine. Furthermore, standard 2D-CAE can also partially eliminate some of the input noise [67]. Therefore, we suggest using 2D-CAE as the feature extraction method for fault detection with the spectrogram. In these comparative results, the PWDE and OCSVM algorithms perform better in the PCA-based feature extraction scheme. These two methods are based on the kernel function, and they can accommodate the nonlinear structures of the normal signals. This property works well in the latent features obtained from linear feature extraction methods, such as PCA. On the other hand, in latent features obtained from other DNN-based feature extraction methods, the nonlinearity of the normal signals is already accommodated, and the kernel function-based one-class classification methods might not be effective. The experimental results in Tables 4 and 6 also provide noteworthy implications regarding the OCC algorithms as a fault detector within the proposed framework. As shown in these results, the LOF and MoG generally achieved the first and second highest performance because they can consider the local patterns of extracted features. That is to say, these two OCC algorithms can construct more sophisticated decision boundaries, and this helps to accommodate the complicated patterns within the extracted features obtained from any signal representation schemes or feature extraction methods. It should be noted that \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Signal Representations** & **[PERSON]’s T\({}^{2}\) Statistic** & **MoG** & **PWDE** & **OCSVM** & **IsoForest** & **LOF** \\ \hline Manually defined features & 0.882 & 0.966 & 0.870 & 0.834 & 0.847 & 0.975 \\ Spectrogram + PCA & 0.902 & 0.994 & **0.970** & **0.910** & 0.898 & 0.997 \\ Spectrogram + Kernel PCA & 0.895 & 0.982 & **0.970** & 0.904 & 0.884 & 0.997 \\ Spectrogram + Stacked AE & 0.938 & 0.998 & 0.917 & 0.851 & 0.867 & 0.993 \\ Spectrogram + Denoising 2D-CAE & 0.962 & 0.997 & 0.912 & 0.842 & 0.876 & 0.989 \\ Spectrogram + standard 2D-CAE (Proposed) & **0.966** & **1.000** & 0.942 & 0.831 & **0.907** & **1.000** \\ \hline \hline \end{tabular}  
* The largest AUROC values are represented in bold and underline.  
\end{table} 
Table 6: AUROC values for the different feature extraction methods with the spectrogram and six OCC algorithms. the vibration signals obtained from the real-world rotating machinery might generate noisy vibration signals corrupted by sampling errors or the interference of uncontrollable physical factors [15; 16]. The extracted features obtained from these corrupted vibration signals also might be noisy, and it eventually leads to an unsatisfactory fault detection performance by the OCSVM and IsoForest algorithms. For example, in the case of OCSVM, the support vectors are often selected around the outer side of normal signal structures, which could potentially include noisy normal signals. As a result, the final decision boundary of the OCSVM is susceptible to the influence of noise or outliers, leading to a poor fault detection performance [70; 77].