# Analog Circuit Fault Diagnosis Using a Novel Variant of a Convolutional Neural Network
## 4 Case Studies Using the Proposed System
### Data Collection  
The principle of the Sallen-Key bandpass filter circuit is shown in Figure 3. This circuit includes 5 resistors, 2 capacitors and an operational amplifier. In the actual environment, the circuit component values fluctuate to a certain extent under the interference of environmental factors. Therefore, the tolerances of the resistors and capacitors in the circuit are set to 5% and 10%, respectively. In the circuit component sensitivity test, capacitors C1 and C2 and resistors R2 and R3 have a greater impact on the circuit, so these components are used as test components. The input of the circuit is a single pulse with a duration of 10 \(\upmu\)s and an amplitude of 5 V, and the time domain response signal is collected at the output of the operational amplifier. The circuit has 9 modes, including No fault (NF) and 8 fault modes, namely C1 \(\downarrow\), C1 \(\uparrow\), C2 \(\downarrow\), C2 \(\uparrow\), R2 \(\downarrow\), R2 \(\uparrow\), R3 \(\downarrow\) and R3 \(\uparrow\). The symbols \(\downarrow\) and \(\uparrow\), respectively, indicate that the actual parameter value of the element is higher and lower than 50% of its nominal value. Figure 2: Schematic diagram of the MSCNN-SK structure. Figure 4 shows a set of time-domain response signals for each failure mode of the circuit under pulse input. It is easy to see from the figure that the difference in the time domain response signal is mainly in the first 75 \(\upmu\)s. After that, the difference is negligible. Therefore, the sampling range of the original time domain response signal is set to 0-75 \(\upmu\)s, the sampling interval is set to 0.5 \(\upmu\)s, and 150 sampling points can be obtained for each time domain response signal. In this case, 2000 Monte Carlo analysis was performed for each failure mode; that is, there are 2000 samples for each failure mode. Shallen-key band-pass filter circuit fault code, fault mode, component nominal value and fault value are recorded in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fault Code** & **Mode** & **Nominal Value** & **Tolerance Band** & **Fault Value** \\ \hline S0 & No fault & - & - & - \\ S1 & C1 \(\downarrow\) & 5 nF & 10\% & 2.5 nF \\ S2 & C1 \(\uparrow\) & 5 nF & 10\% & 7.5 nF \\ S3 & C2\(\downarrow\) & 5 nF & 10\% & 2.5 nF \\ S4 & C2 \(\uparrow\) & 5 nF & 10\% & 7.5 nF \\ S5 & R2\(\downarrow\) & 3 k\(\Omega\) & 5\% & 1.5 k\(\Omega\) \\ S6 & R2 \(\uparrow\) & 3 k\(\Omega\) & 5\% & 4.5 k\(\Omega\) \\ S7 & R3\(\downarrow\) & 2 k\(\Omega\) & 5\% & 1.0 k\(\Omega\) \\ S8 & R3 \(\uparrow\) & 2 k\(\Omega\) & 5\% & 3.0 k\(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Failure mode of the Shallen–Key bandpass filter circuit. Figure 4: Output signals of different fault patterns in the Salley–Key Bandpass Filter. Figure 3: Shalley–Key Bandpass Filter model. The Four-opamp double second-order high-pass filter circuit is shown in Figure 5. This circuit is composed of ten resistors, two capacitors and four operational amplifiers, which is more complex. As with the previous circuit, the tolerances of resistance and capacitance are 5% and 10%, respectively. The input of the circuit is a single pulse with a duration of 10 \(\upmu\)s and an amplitude of 5 V. The time domain response signal is collected at the output of the operational amplifier U4. In the sensitivity test, capacitors C1 and C2 and resistors R1, R2, R3, and R4 have a greater impact on the circuit, so these components are used as test ones. Thirteen modes are set in the circuit, including No fault (NF) and 12 fault modes, namely C1 \(\downarrow\), C1 \(\uparrow\), C2 \(\downarrow\), C2 \(\uparrow\), R1 \(\downarrow\), R1 \(\uparrow\), R2 \(\downarrow\), R2 \(\uparrow\), R3 \(\downarrow\), R4 \(\downarrow\) and R4 \(\uparrow\). The symbol \(\uparrow\) means that the actual parameter value of the component is higher than 50% of its nominal value; in the same way, \(\downarrow\) means lower than 50% of its nominal value.