## 5 Experimental Case Planning, Results, and Analysis
### Experimental Case
#### 5.2.2 Case Study 2--AI Model with Limited Data  
1. Case design and dataset planning  
There are over-sampling and down-sampling methods for AI models with training data deficiencies. Over-sampling uses the classes of a few training data for data augmentation until the quantity equals the most data class. Down-sampling is the opposite of over-sampling; down-sampling performs random data selection or algorithm screening for the classes of major data. The selected quantity is the same as the classes of few data. The fundamental purpose of the two methods is to maintain the balance of AI model training data and a good classification effect can be achieved without a lot of training data based on the model characteristics. The design of the experimental cases involves a ratio of healthy data to fault data of 10:1, where the training healthy data consists of 600 samples, and all four types of fault data have 60 samples each. Both the residual VGG-based Siamese network and the transfer learning model are examples of under-sampling methods. Therefore, 60 samples are randomly drawn from the 600 healthy samples, to achieve a balanced number of healthy and faulty samples. For a ratio of 20:1, each of the four types of fault data has 30 samples, with 30 samples randomly drawn from the 600 healthy samples. DCGAN and CNN models [23] fall under over-sampling methods; when the ratio of healthy data to fault data is 10:1, the four types of fault data are each expanded from 60 samples to 600 samples. When the ratio is 20:1, 30 samples are expanded to 600 samples, providing data for training the classification model. The testing of models using both over-sampling and under-sampling methods follows an across-load fault diagnosis approach. If the training data are under 50% load, then the test data are at 100% load, and both the healthy and the four types of fault test data consist  
Figure 7: Induction motor data measurement platform. (**a**) CWT: 50% load\(\rightarrow\)100% load; (**b**) CWT: 100% load\(\rightarrow\)50% load; (**c**) two-dimensional time-domain signals transform: 50% load\(\rightarrow\)100% load; (**d**) two-dimensional time-domain signals transform: 100% load\(\rightarrow\)50% load. of 500 samples each. Conversely, if the training data are under 100% load, then the test data are at 50% load. Detailed information on experimental case data planning is shown in Table 6. The imbalance ratio is defined as follows:  
Imbalance ratio = No. of fault training data: No. of health training data. The training dataset imbalance ratio had two cases, 10:1 and 20:1. When the imbalance ratio was 20:1, the health data had 600 samples. Each failure data had 30 samples, 30 samples were selected from the health data randomly, and the AI model training was performed. 2. Residual VGG-based Siamese network training process  
The training process of the method proposed in this study is shown in Figure 8. It was observed that the model could not identify the similarity between images effectively in the initial training period. The Euclidean and Manhattan distances could not measure the distance between images accurately so the contrastive loss value was large. Therefore, the initial value of the learning rate was large, so that the optimizer algorithm could look for optimization in a wide range, and the model parameter values were corrected greatly. In the intermediate stage of training, the model began to distinguish the difference between samples, and the error loss decreased gradually. The information about the model training effect was provided for the optimizer algorithm through the loss function, and the model parameter values were adjusted slightly so that the model completed the classification tasks effectively. In the final training stage, the learning rate was reduced, allowing the optimizer to fine-tune the model parameters. As a result, the contrastive loss value changed minimally, and the training process stabilized. 3.