Deep learning-based fault diagnosis methods rely on consistent data distributions, but shifts in operational conditions often lead to distributional discrepancies between training and real-world data. Limited labeled samples for fine-tuning further hinder model performance. To address these challenges, we propose the Domain Adaptation Hypergraph Residual Adversarial Network (Res-DAHGAN), which integrates a hypergraph residual feature extractor, domain discriminator, and label classifier with a domain alignment mechanism. Res-DAHGAN enables cross-domain fault diagnosis without requiring labeled target domain data. Raw vibration signals are converted to frequency-domain spectra using the Fast Fourier Transform (FFT), and sample hypergraphs are constructed via the K-nearest Neighbor (KNN) algorithm. Both source and target domain samples are processed by Res-DAHGAN to extract domain-invariant features for fault identification. Results on two datasets show that Res-DAHGAN outperforms current state-of-the-art methods in accuracy, robustness, and generalization.