As wheels are important components of train operation, diagnosing and predicting wheel faults are essential to ensure the reliability of rail transit. Currently, the existing studies always separately deal with two main types of wheel faults, namely wheel radius difference and wheel flat, even though they are both reflected by wheel radius changes. Moreover, traditional diagnostic methods, such as mechanical methods or a combination of data analysis methods, have limited abilities to efficiently extract data features. Deep learning models have become useful tools to automatically learn features from raw vibration signals. However, research on improving the feature-learning capabilities of models under noise interference to yield higher wheel diagnostic accuracies has not yet been conducted. In this paper, a unified training framework with the same model architecture and loss function is established for two homologous wheel faults. After selecting deep residual networks (ResNets) as the backbone network to build the model, we add the squeeze and excitation (SE) module based on a multichannel attention mechanism to the backbone network to learn the global relationships among feature channels. Then the influence of noise interference features is reduced while the extraction of useful information features is enhanced, leading to the improved feature-learning ability of ResNet. To further obtain effective feature representation using the model, we introduce supervised contrastive loss (SCL) on the basis of ResNet + SE to enlarge the feature distances of different fault classes through a comparison between positive and negative examples under label supervision to obtain a better class differentiation and higher diagnostic accuracy. We also complete a regression task to predict the fault degrees of wheel radius difference and wheel flat without changing the network architecture. The extensive experimental results show that the proposed model has a high accuracy in diagnosing and predicting two types of wheel faults.