## 4 Experimental Validation
### CASE 2: Fault Diagnosis of a Roller Bearing Unit
#### 4.2.2 Comparative Analysis of Experimental Results  
For this experiment, the dataset used is the 12 \(k\) drive-end bearing fault data collected at a 12 kHz sampling rate. Under conditions of a 2-horsepower motor load and a motor speed of 1750 rpm, a dataset comprising 10 classes was prepared, including 9 fault types (involving inner and outer race faults at different locations and rotor faults), as well as normal operational data. From the initial data, subsequences of a length of 1024 were extracted as samples, with a step size of 512 used to select subsequent samples. A total of 2330 of the first samples were used for the experiment. Table 4 presents the ten working conditions of a rolling bearing. Among them, Class 1 represents data collected under normal operating conditions, while Classes 2 to 10 correspond to data recorded during motor faults. The faults are primarily located in three areas: the inner ring, outer ring, and rolling element. Each fault type is further divided based on defect diameter, including 0.07 inches, 0.14 inches, and 0.21 inches, yielding a total of nine fault categories. Figure 9 illustrates sample waveforms for each of the nine fault types: (a) inner ring fault with a 0.07-inch defect, (b) tolling element fault with a 0.07-inch defect, (c) outer ring fault with a 0.07-inch defect, (d) inner ring fault with a 0.14-inch defect, (e) rolling element fault with a 0.14-inch defect, (f) outer ring fault with a 0.14-inch defect, (g) inner ring fault with a 0.21-inch defect, (h) rolling element fault with a 0.21-inch defect, and (i) outer ring fault with a 0.21-inch defect. These fault categorizations allow for a comprehensive dataset to effectively assess the fault diagnosis model's performance across varying fault types. Figure 8: Visualization of clustering effects of different signal features based on EMD and IMFE. This section compares the diagnostic results of different entropy-based algorithms, including FE, MFE, FE combined with waveform factor, and the proposed method. The scale factors for MFE and IMFE are set to \(scales=[2,3,4]\), with an embedding dimension of 2 and a time delay of 1. The embedding dimension (\(m\)) and similarity tolerance \(r\) parameters were optimized through multiple experiments to achieve the best performance of the proposed method, with \(m=2\) and \(r=0.2\). The features extracted using IMFE are reduced to three dimensions by LDA. Given that the maximum dimensionality reduction achievable by LDA corresponds to the total number of fault categories minus one, which is 9 in the case of 10 categories, the dimensionality was reduced to 9 in this article. This choice ensures that as much feature information as possible is retained while maintaining the ability to effectively distinguish between different categories. All methods are classified using an SVM classifier and validated through \(K\)-fold cross-validation, where \(K\) is set to 10 (i.e., the dataset is split into 10 folds, each containing 233 samples). In all comparative experiments, the parameters of the SVM were kept consistent, with the penalty parameter (C) set to 1.0. As shown in Figure 10, the proposed method achieves a consistently high classification accuracy across all folds. Table 5 shows a comparison of diagnostic results, showing the average classification accuracy over ten runs, as well as the highest and lowest accuracy achieved across these runs. The proposed IMFE method demonstrates superior performance compared to the baseline entropy methods, with a notable improvement in diagnostic accuracy across various scales and validation folds.