## 1 Introduction  
The fault diagnosis of rotating equipment plays a vital role in ensuring the normal operation of such equipment. Its effectiveness is directly related to the safety and economic benefits associated with the equipment in complex industrial environments [1]. With the advancement of deep learning technology, especially the breakthroughs in the study of neural networks in complex pattern recognition, research has demonstrated that deep learning neural networks offer significant advantages in data feature mining and can accurately capture valuable data related to faults. This capability provides strong support for high-precision, high-reliability fault diagnosis. However, under variable working conditions, the distribution of fault data shifts, and the internal complexity and interrelationships within the data increase. This amplifies the difficulty of accurately capturing underlying correlations in the fault data, posing significant challenges for deep learning-based fault diagnosis methods [2]. Additionally, the commonly used linear or geometric representations of Euclidean space are inadequate for capturing the complex relationships between the fault data in such dynamic environments [3]. In recent years, GNNs have gained significant attention in the field of equipment fault diagnosis due to their superior ability to capture complex data dependencies, particularly in diagnosing faults within rotating equipment under variable working conditions. A GNN is a deep learning model specially designed to process graph-structured data. These graphs are composed of nodes (data points) and edges (relationships among data points). A GNN learns the embedded representation of each node through the interaction between nodes to enhance the understanding of complex relationships among data points [4; 5; 6]. For example, [PERSON] et al. (2022) [7] proposed a rotating equipment fault diagnosis method (MHGAT) based on dynamic time warping and the GAT to achieve the automatic learning of node weights, extraction, and the aggregation of multi-scale features, addressing the limitations of Euclidean spatial data relationship mining. However, a GAT may overly focus on significant nodes under specific working conditions and may overlook key information as conditions change, resulting in a decline in diagnostic performance. [PERSON] et al. (2022) [8] proposed an improved graph attention network (GATv2) for variable operating conditions using gearbox fault diagnosis, assigning higher weights to nodes with rich information. However, the receptive field of a GAT is confined to direct neighbor nodes, which hinders the capture of a broader range of a graph's structural information. When the operating conditions change, the structure and features of the graph data will also evolve correspondingly. A GAT may struggle to extract sufficiently comprehensive feature information from these changes, thereby limiting the model's generalization ability. More recently, [PERSON] et al. (2023) [9] proposed a graph structure search network (GASN) for cross-domain fault diagnosis to address the problem that existing models have difficulty in clearly representing the correlation between data. The goal is to enhance the adaptability to unknown working conditions through a domain adversarial training strategy driven by triple losses. However, it fails to fully consider the global key fault characteristics in the timing dimension, which may lead to misjudgment. To address the issue of discrepancies in the data distribution between the source domain and the target domain caused by different operating environments, [PERSON] et al. (2024) [10] proposed using a dual-path convolutional neural network (CNN) and multi-parallel graph convolutional networks (GCN) to gradually extract features from fault data, thereby tackling the challenge of modeling fault diagnosis for rotating equipment under variable operating conditions. [PERSON] et al. (2021) [11] proposed a fault diagnosis method based on a domain adversarial graph convolutional network (DAGCN).