# A Fault Detection Framework for Rotating Machinery with a Spectrogram and Convolutional Autoencoder
## 4 Experimental Study
The IsoForest algorithm also yielded lower AUROC scores, likely due to its sensitivity to the noisy patterns. When dealing with a noisy target class, the individual isolation trees tend to generate too many unnecessary splits. These undesirable splits within the individual isolation trees result in poor anomaly score computation by the IsoForest algorithm. Hence, the IsoForest algorithm fails to achieve superior fault detection performance. In this experiment, we also compared the proposed fault detection framework with other deep neural network-based fault detection methods, including reconstruction error of the SAE (ReSAE) and the 2D-CAE (ReCAE), deep support vector data description (Deep SVDD), and anomaly detection with generative adversarial network (AnoGAN). For all these fault detection methods, the spectrogram was used as input. In addition, for a fairer comparison, the Deep SVDD and the AnoGAN algorithms are implemented with the CNN as a base network structure, and the CNN structures of these two algorithms have the same number of convolutional blocks as the proposed fault detection framework. The AUROC values of these fault detection methods are presented in Table 7.  
As presented in Table 7, the 2D-CAE with the MoG and LOF outperforms other deep neural network-based methods considered in the current study. On the other hand, when compared to the ReSAE, the ReCAE performs better because the convolutional block in the CAE helps to successfully handle the image-formatted spectrogram. However, those anomaly scoring methods, ReSAE and ReCAE, show undesirable performance because the reconstruction error between the input spectrogram and its reconstructed outcomes cannot properly quantify the level of fault in the signals. The Deep SVDD algorithm also fails to achieve superior performance even though the decision boundary is created in an end-to-end manner. The training procedure of Deep SVDD was designed to minimize the distance between the center of the hypersphere and normal signals in the latent feature space. However, this approach is basically related to support vector-based OCC algorithms, and hence, it is also sensitive to the noisy signals. That is to say, the Deep SVDD algorithm only focuses on reducing the volume of the hypersphere enclosing all training target classes, and the hypersphere is distorted due to a couple of noise latent feature vectors corresponding to the noisy training signals. On the other hand, because the AnoGAN is based on the generative model, this method also suffers from the mode collapse problem, which is a critical limitation of the generative model. That is to say, artificial spectrograms created by \begin{table}
\begin{tabular}{l c} \hline \hline
**Deep Neural Network-Based Fault Detection Methods** & **AUROC** \\ \hline ReSAE & 0.625 \\ ReCAE & 0.923 \\ Deep SVDD & 0.926 \\ AnoGAN & 0.645 \\
2D-CAE + MoG (Proposed) & **1.000** \\
2D-CAE + LOF (Proposed) & **1.000** \\ \hline \hline \end{tabular} The largest AUROC values are represented in bold and underline.  
\end{table} 
Table 7: AUROC values of six deep neural network-based fault detection methods. a generator only resemble the prototype spectrogram obtained from the normal states, and they cannot fully depict the elaborate patterns to discriminate between normal and fault states. Consequently, the AnoGAN method achieved poor fault detection performance.