# A Lightweight Fault Diagnosis with Domain Adaptation for Defected Bearings
## 3 Experimental Results
### Performance Analysis  
To validate the effectiveness of the proposed method, experimental data collected from a simulation test platform are used. As shown in Figure 4, the bearing fault types include NF, BF, IF, OF, and CF, representing five common fault models. Additionally, faults of varying severity levels for IF, OF, and CF are also included to assess the method's adaptability to different fault severities. Given the limited number of data samples, the original data are divided using a 90% overlap, with each sample containing 10,240 data points. The dataset consists of 600 samples per fault type, totaling 4800 samples for all operating conditions. Figure 5 shows the time-domain waveforms of different bearing fault modes at 800 rpm. It can be observed that both healthy and rolling element faults lack clear periodic characteristics. This is due to the irregular vibration signals caused by the contact between the rolling elements and the inner and outer races, influenced by the load and contact angle. In particular, early faults produce weak signals that are easily masked by noise, making it difficult for traditional signal analysis methods to detect faults and leading to classification errors in data-driven models. Moreover, as fault severity increases, the amplitude of the waveforms in the OF, IF, and CF changes. Notably, in composite faults, the outer race fault dominates, causing the pulse features to resemble those of the outer race fault, which may lead to misclassification. To address this, the S-transform is introduced to enhance frequency-domain feature extraction and improve signal separability. As shown in Figure 6, the S-transform combines the local properties of short-time Fourier transform (STFT) with the multi-resolution features of wavelet transform, providing detailed time-frequency information to capture signal variations. As a comparison, the Continuous Wavelet Transform (CWT) and STFT are presented in Figures 7 and 8, respectively. Superior than CWT and STFT, the frequency spectrum generated by the S-transform effectively reduces noise interference, highlighting useful frequency-domain features and making different fault types easier to distinguish, thereby improving diagnostic accuracy. Additionally, compared to time-domain signals, the frequency spectrum from the S-transform is more compact, reducing data storage requirements for online deployment, which is suitable for embedded systems and edge computing devices. Table 2 presents the composition of the source domain and target domain datasets used to validate the model's effectiveness. To balance diagnostic performance and computational cost, features obtained from the S-transform are uniformly rescaled into \(64\times 64\times 3\) RGB images. These image datasets are then randomly split into training and testing sets. The pixel mean of the training set is subtracted to remove irrelevant image information, enhancing the reliability of feature extraction. Additionally, 200 of the training set images are randomly designated as a validation set for dynamic model parameter adjustment. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Datasets of the** & **Rotating** & **Health** & **Size of the Training/** \\
**Time-Frequency Images** & **Speeds** & **Conditions** & **Testing Samples** \\ \hline Source domain (S) & 800 rpm & Conditions 1–8 & 400*8/200*8 \\ Target domain (T) & 1500 rpm & Conditions 1–8 & 400*8/200*8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed information of the source and target datasets. Figure 5: Time-domain waveform of bearing fault signals from the self-designed test platform. Figure 6: Time-frequency results of bearing fault after applying the S-transform. To further evaluate the diagnostic performance of the proposed framework, a comparison is made with six MobileNet-based diagnostic methods, tested on both time-domain and time-frequency domain datasets. Each method is tested five times on eight fault types, with 200 test samples per fault type.