Accurate forecasts of the Remaining Useful Life (RUL) of mechanical equipment are vital for lowering maintenance costs and maintaining equipment reliability and safety.Data-driven RUL prediction methods have made significant progress, but they often assume that the training and testing data have the same distribution, which is often not the case in practical engineering applications. To address this issue, this paper proposes a residual useful life prediction model that combines deep learning and transfer learning.In this model, called TCAM-EASTCN (Transfer Convolutional Attention Mechanism for Early-life Stage Time Convolutional Network), an unsupervised domain adaptation strategy is introduced based on the characterization of subspace distances and orthogonal basis mismatch penalties in the Convolutional Attention Mechanism for Early-life Stage Time Convolutional Network (CAM-EASTCN). This approach minimizes the distribution differences between different domains, enhancing the learning of cross-domain invariant features and effectively reducing the distribution gap between the source and target domains, thereby improving the accuracy of RUL prediction under varying conditions. Experimental results demonstrate that TCAM-EASTCN outperforms other models in terms of RUL prediction accuracy and generalization.