# Small-Sample Bearings Fault Diagnosis Based on ResNet18 with Pre-Trained and Fine-Tuned Method
## 4 Experimental Verification
### Case 1: CWRU Bearing Dataset  
For the experiment, the drive end acceleration data from SKF bearings obtained from the CWRU bearing dataset were utilized, with a sampling frequency of 12 kHz. As shown in Figure 7, the faulty bearing is made by EDM. The dataset simulates four working conditions of 0 horsepower (HP), 1 HP, 2 HP and 3 HP, corresponding to four speeds of 1797 r/min, 1772 r/min, 1750 r/min and 1730 r/min, respectively. The single-point diameter damage of the bearing selected in the experiment is 0.007 mm, 0.014 mm and 0.021 mm, respectively. Rolling element faults, inner ring faults and outer ring faults are present within each fault diameter. The experimental dataset comprises nine sets of fault data and one set of normal data. The working condition is 0 HP. Each sample is sliced into segments with a fixed length of 1024 data points, and 512 adjacent samples overlap. To facilitate feature extraction by the neural network, the samples are normalized to fall within the range of [0, 1]. There are 10 fault types in the dataset, with 100 samples for each type of fault. The dataset is divided into training and testing sets in a 2:8 ratio. The training set contains 200 samples, while the testing set includes 800 samples. The detailed dataset information is shown in Table 1.  
Figure 7: CWRU test bench. The chosen modal number significantly influences the effectiveness of VMD decomposition. When a small modal number is chosen, the VMD algorithm, acting like an adaptive filter bank, filters out essential information from the original signal, thus impacting the accuracy of subsequent predictions. With a large modal selection value, the center frequencies of neighboring modal components become closer, leading to the duplication of modes or introduction of additional noise. The primary distinction between different modes is the variance in central frequency. The suitable modal value is determined by examining the distribution of central frequencies across various modal numbers. As depicted in Table 2, with a modal number of 9, modal components with similar frequencies begin to appear, so \(k\) is taken as 8. When \(k\) equals 8, the central frequency resolution is preserved, and the stability and distribution uniformity of the central frequency are also maintained. With the SDP transformation in progress \(\theta\), generally, the SDP image formed by taking 60\({}^{\circ}\) is a six-petal snowflake image. In order to make the IMF component decomposed by VMD correspond to the image transformed by SDP, we evaluated the kurtosis of eight IMF components decomposed by 10 kinds of faults. Next, we calculated the average kurtosis of these IMF components. Table 3 displays the average kurtosis of IMF components. Six IMF components are chosen based on the maximum kurtosis criterion. The six IMF components are successively generated on the same SDP image by SDP transformation, and the size of the generated image is 3 \(\times\) 224 \(\times\) 224. The discrepancies in SDP diagrams among various bearing fault types are manifested in the thickness of the symmetrical arm, the degree of curvature change, the degree of dispersion and aggregation of mapping points. Our study covers \(g\) values from 0 to 50 and \(l\) values from 1 to 5. To maximize the distinction among the 10 types of bearing faults in SDP images, it is necessary to select appropriate parameters. Therefore, we used the Pearson correlation analysis method in reference [35] to determine the most appropriate parameters.