# Analog Circuit Fault Diagnosis Using a Novel Variant of a Convolutional Neural Network
## 4 Case Studies Using the Proposed System
### Feature Visualization Analysis  
The t-SNE technology is a non-linear unsupervised dimensionality reduction method commonly used in the field of deep learning. This method can visualize high-dimensional features in a two-dimensional space to intuitively judge whether the high-dimensional features are discriminative [17; 18]. This section uses t-SNE technology to visualize the original fault data of the two benchmark test circuits and the high-dimensional features extracted from the last layer of the BPNN, RNN, LSTM, 1 DCNN and MSCNN-SK models in two dimensions. The original data of the Sallen-Key band-pass filter circuit and the features extracted from each model are visualized in two dimensions and shown in Figure 7. From Figure 7a-d, in the two-dimensional scattered point distribution of the original fault data and the features extracted by networks such as BPNN, RNN and LSTM, there are a small number of overlapping sample points in the fault modes S2 and S8, and the remaining fault mode sample points are completely separated. Figure 7e,f, respectively show the two-dimensional visualization results of the features extracted by the 1 DCNN and MSCNN-SK networks. It can be clearly seen from the figure that the sample points of each failure mode have been completely separated, and the two-dimensional scattered points have independent distribution areas. In addition, the two-dimensional scattered points of each failure mode in Figure 7f are more closely distributed. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Norm** & **BPNN** & **RNN** & **LSTM** & **1 DCNN** & **MSCNN-SK** \\ \hline Maximum & 100.00 & 99.91 & 100.00 & 100.00 & 100.00 \\ Minimum & 99.98 & 99.85 & 99.87 & 100.00 & 100.00 \\ Average & 99.99 & 99.87 & 99.93 & 100.00 & 100.00 \\ SD & 0.01 & 0.02 & 0.06 & 0.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Shallen–Key band-pass filter circuit fault diagnosis comparative experiment. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Norm** & **BPNN** & **RNN** & **LSTM** & **1 DCNN** & **MSCNN-SK** \\ \hline Maximum & 99.15 & 96.46 & 99.21 & 99.09 & 99.92 \\ Minimum & 98.91 & 88.17 & 98.95 & 98.95 & 99.80 \\ Average & 99.04 & 92.13 & 99.09 & 99.03 & 99.87 \\ SD & 0.08 & 2.03 & 0.08 & 0.04 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Four-opamp double second-order high-pass filter circuit fault diagnosis comparative experiment. The original and characteristic two-dimensional visualization effect of the Four-opamp biquad high-pass filter is shown in Figure 8. It can be seen from Figure 8a that the sample distribution of each failure mode of the original data is relatively close, and there is a large amount of overlap. Figure 8b,c are two-dimensional scatter plots of the features extracted by the BPNN network and the RNN network. There are still some overlapping sample points in some failure modes in the figure. The two-dimensional scatter diagram of features extracted from LSTM network and CNN network is shown in Figure 8d,e. Most two-dimensional scatter points of fault modes have been completely separated, and the number of overlapping sample points is relatively small, but the distribution range of most fault mode samples is relatively scattered. Figure 8f draws a scatter diagram of the features extracted by the MSCNN-SK network. It can be seen that the two-dimensional scatter points of the same failure mode are concentrated, and there are almost no overlapping sample points, which is easy to distinguish. Figure 7: Two-dimensional scatter distribution of original data and features extracted from each network model in the Shallen–Key bandpass filter circuit formed by T-SNE method. (**a**) Circuit fault data. (**b**) Features extracted by the BPNN network. (**c**) Features extracted by the RNN network. (**d**) Features extracted by the LSTM network. (**e**) Features extracted by the 1 DCNN network. (**f**) Features extracted by the MSCNN-SK network.