# A New Fault Diagnosis Method for Unbalanced Data Based on 1 DCNN and L2-SVM
## 4 Experimental Verification
### Case Study 2: Application to the Lab-Measured Bearing Datasets  
#### 4.2.1 Experimental Setup  
As in Section 4.1, the presented 1 DCNN-L2 SVM has achieved high identification accuracy for the minority class samples on the CWRU-bearing datasets, but the validity of the model in reality still needs to be further studied. Therefore, in this section, we use a comprehensive experimental bench from Wuxi Houde Automation Meter Co., Ltd. (Wuxi, China) to collect unbalanced datasets at four different rotational speeds for experiments. As shown in Figure 9, the experimental bench is composed of a motor, coupling, a mass block, a shaft, an acceleration sensor, an experiment bearing (NSK6308), an eddy current sensor, and other devices. Among them, the shaft is a cylindrical object passing through the middle of a bearing. It supports rotating parts and rotates with them to transmit motion, torque, or bending moment. The acceleration sensor is usually composed of a mass block,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline Average frequency & \(\frac{\sum\limits_{i=1}^{n}{{\rm{w}}_{i}{\rm{x}}_{i}}}{\sum\limits_{i=1}^{n}{{ \rm{x}}_{i}}}\) & Mean energy & \(\frac{1}{n}{\sum\limits_{i=1}^{n}{{\rm{x}}_{i}}}\) \\ \hline \multirow{2}{*}{Crest} & \multirow{2}{*}{\(\max(|{\rm{X}}_{i}|)\)} & \multirow{2}{*}{Variance} & \(\frac{1}{n}{\sum\limits_{i=1}^{n}{{\rm{(x}}_{i}-\overline{{\rm{x}})}^{2}}}\) \\ \hline \multirow{2}{*}{Kurtosis} & \(\frac{1}{n}{\sum\limits_{i=1}^{n}{{\rm{x}}_{i}^{4}}}\) & \\ \hline \hline \end{tabular} Note: n symbols, the volume of sampling points; w, the frequency; x, the amplitude at that frequency.  
\end{table}
Table 4: Features selected in the frequency domain.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fault Location** & **Ball** & **FIX** & **Inner Race** & **NONE** & **Outer Race** \\ \hline \multirow{2}{*}{Class label} & 0 & 1 & 2 & 3 & 4 \\ \hline \multirow{2}{*}{Dataset A} & Training & 1000 & 1000 & 1000 & 1000 & 1000 \\  & validation & 900 & 900 & 900 & 900 & 900 \\  & Testing & 100 & 100 & 100 & 100 & 100 \\ \hline \multirow{2}{*}{Dataset B} & Training & 70 & 80 & 200 & 1000 & 200 \\  & validation & 30 & 20 & 100 & 900 & 200 \\  & Testing & 100 & 100 & 100 & 100 & 100 \\ \hline \multirow{2}{*}{Dataset C} & Training & 60 & 30 & 100 & 7000 & 150 \\  & validation & 40 & 70 & 200 & 900 & 250 \\ \multirow{2}{*}{(3000 r/m)} & Testing & 100 & 100 & 100 & 100 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Bearing dataset descriptions.  
a damper, an elastic element, a sensing element, and an adaptive circuit. It is mainly used to measure the vibration signal of bearings. In the experiment, the normal bearing and four kinds of fault bearings were installed on the experiment bench successively, and the acceleration sensor (HD-YD232) was the collection component of the bearing vibration signals in different states. Its sampling frequency is 8 kHz.  
The vibration signals of the bearings are collected at three different speeds of 2600, 2800, and 3000 r/min and represented by A, B, and C, as listed in Table 5. At one speed, five different data samples are collected, which include: (1) a rolling element fault signal, (2) a cage fault signal, (3) an inner ring raceway fault signal, (4) a normal signal, and (5) an outer ring raceway fault signal. Figure 10 describes the time and frequency domain diagrams of those signals.  
In Table 5, compared with the balanced Dataset A, the number of minority class samples is reduced in the unbalanced Dataset B. Moreover, the proportions of the training, validation, and testing sets are different among each sample. In Dataset C, the number of normal samples increases substantially to 8000, so Dataset C is a highly unbalanced dataset.