## 4 Experiments
### Fault Diagnosis of Rolling Bearings
#### 4.1.2 Results  
The rolling bearing signals were processed in accordance with the structure of the SDAE fault diagnosis method shown in Figure 4. For each dataset, 200 samples were randomly selected and inputted into the system for training the model with output of four target values. After optimization of the parameters in the model, another 200 randomly selected samples were tested for the fault pattern recognition. Figure 6 shows the example signal waveforms and their spectra for the validated four health conditions. Each signal contains 1024 data points, and each sample has its frequency spectrum with 513 Fourier coefficients. To determine the structure of a SDAE network, several parameters need to be selected, such as the length of the first visible layer, number of units in each hidden layer, and number of hidden layers. 1024 data unit to are used to form a sample not only to attempt to minimize the computing complexity but also to cover all the information representing vibration signals; thus, the size of the frequency input is 513. The complexity of the model structure is highly related to the recognition task, and it has a great influence on the recognition result. Too complex structure will lead to over-fitting, while too simple structure can result in under-fitting. The hidden layers are selected from 1 to 3 according to the number of samples, length of a sample, and the complexity of the task. The number of units in each layer is selected in the range of (300, 400, 500, 600). To obtain the best architecture for this task, a grid researching is performed. Accordingly, the selected architecture is (500, 500, 500) with three hidden layers. The learning rates for pre-training and fine-tuning are 0.8 and 0.001, respectively. The corruption level for this dataset is designed to be 0.6, which is the optimal value from 0 to 1. Figure 5: Description of the experimental platform. Figure 6: Example of the original signals and their spectra for each health condition (**a**) normal-bearing signal; (**b**) inner race fault-bearing signal; (**c**) ball fault-bearing signal; and (**d**) outer race fault-bearing signal. A DBN model was used for comparison to extrude the superiority of SDAE as a dependent component and its simplicity in the recognition system. DBN is a deep neural network comprising multiple restricted Boltzmann machine (RBM) layers, and has been applied to fault diagnosis since 2014. Each RBM comprises visible and hidden layers, where the units in the same layer are completely unconnected. DBN has been extensively used and obtained satisfactory performance in fault diagnosis since the breakthrough in deep learning. The comparison is conducted based on the same two datasets of rolling bearing fault. The structure and parameters of the training process are similar with SDAE. The training and testing set recognition accuracy is 100%. However, the label value for the testing set is floating around the actual label compared with the proposed method. One sample is misjudged in both training and testing sets with an overall accuracy of 99.50%, and the output label value has a considerably evident floating. Table 2 generalizes the recognition accuracy of the SDAE method and DBN comparison method. The proposed method achieves satisfactory performance regarding the classification accuracy and the label value clustering performance. With the same CWRU data set in rolling bearing test, some other classical methods such as SVRM, DWF and LDA, proposed in classical literature [43; 44], also have good performance. To further highlight the superiority of the proposed method, comparisons with these methods are shown in Table 3. In [43], WPT was used to transform the signals at different decomposition depths and DET was employed to reduce the dimension of features. Then SVRM was proposed to classify the fault patterns. In [25], sparse coding was introduced to select feature from the vibration signals and linear discriminate analysis (LDA) was used for fault classification.