As the return path of traction current in DC traction power supply system (DC TPSS), running rail maintains certain insulation with the ground. Due to the environment and prolonged operation, insulation weaknesses frequently occur in the running rails. The amplitude of stray current (SC) in the system can significantly increase under fault conditions, affecting the safe operation of both the system and trackside equipment. An improved multi-scale convolution intra-class adaptive model (IMCIAM) is proposed in this paper. The model addresses the issue that existing deep learning (DL) methods are not suitable for locating insulation weaknesses under variable working conditions. In terms of data augmentation, a new method is proposed based on the characteristics of urban rail transit. The Squeeze-and-Excitation module is integrated into the convolutional neural network (CNN). The multi-scale feature extractor captures more useful information. Transfer learning is achieved by reducing the marginal distribution distance between the two domains using maximum mean discrepancy (MMD). Experiments are carried out using the proposed fault localization method on datasets. Experimental results demonstrate that the model achieves high fault localization accuracy for unlabeled rail potential data under variable working conditions.