## 4 Validation of the Proposed Method
### Case 1: Experiment Results on the CWRU Bearing Dataset and Performance Analysis
#### 4.2.2 1 DCNN Feature Learning Verification and Analysis  
In order to demonstrate the superiority of the proposed 1 DCNN feature learning method, three other mainstream feature extraction methods, including wavelet packet transform (WPT), convolutional auto-encoder (CAE) and long short-term memory (LSTM), were applied to extract feature vectors for comparison using the same fault dataset. Firstly, the feature extractions of the raw vibration signals were conducted using the above four feature extraction methods. Then the SVM was adopted as the classifier to accomplish the fault classification task. To avoid randomicity, the grid search method and 3-fold cross validation were adopted for the parameter optimization of SVM, and the parameters c and g were set in the ranges of [0.001, 0.1] and [1, 100], respectively. The main parameters of the other methods are briefly described as follows: (1) WPT: the energy spectra were calculated after the vibration signals were decomposed by three-layer wavelet packet decomposition. (2) CAE: using two layers of the convolutional layer, two layers of the pooling layer and two layers of the full-connected layer. The convolutional kernels were \(64\times 1\) and \(8\times 1\), the length of each pooling layer was 2, the Adam optimization algorithm was used and the activation function was ReLu. (3) LSTM: the model consisted of two LSTM layers, two fully connected layers, and one softmax layer. The dropout rate was 0.2, the batch size was 128, and the iteration epoch was 30. As the dataset and the classifier used in the contrast experiments were the same, the differences in fault diagnosis performance were totally caused by the fault extraction processes. The precision rates and the recall rates of the four methods (i.e., 1 DCNN-SVM, WPT-SVM, CAE-SVM and LSTM-SVM)  
Figure 5: The rolling bearing fault data acquisition experimental bench. are summarized in Table 4. To illustrate the differences more directly, F1-measure values (percentage form) of the four methods are presented in Figure 6.  
From Table 4 and Figure 6, it can be observed that the average precision rate of SVM with manual feature extraction (WPT) was only 80.8%, while the deep learning models (LSTM-SVM, CAE-SVM) had better performances (about 10% improvement in precision rate) compared with traditional WPT feature extraction method. The 1 DCNN-SVM model achieved the best average precision rate (95%) using a four-layer convolutional neural network. The accuracy of the proposed 1 DCNN-SVM algorithm was obviously better than other competitors, which meant that the 1 DCNN had advantages in feature learning of vibration signals compared with other intelligent feature extraction methods, e.g., CAE, LSTM. All four algorithms had high diagnosis accuracies for the normal state (condition 0), however the performance of 1 DCNN-SVM algorithm was significantly better than those of the other three algorithms for the micro-fault identifications (condition 1 and condition 3). In summary, compared with WPT-SVM, CAE-SVM, and LSTM-SVM, the 1 DCNN-SVM algorithm had a more superior overall performance both in diagnosis accuracy and stability, which indicated that 1 DCNN was a more promising feature extraction tool for rolling bearings fault diagnosis. In addition, 1 DCNN could extract  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Bearing** \\ **Condition** \\ \end{tabular}