## 1 Introduction  
The health monitoring and fault diagnosis of rolling bearings are critical for ensuring the normal operation of mechanical equipment [1]. The stable and safe operation of rolling bearings directly impacts the overall stability and efficiency of the entire system. Traditional fault diagnosis methods based on single-modal signals have certain limitations as they cannot comprehensively and accurately reflect the operating conditions and health status of bearing gearboxes, thus restricting their performance in terms of accuracy and efficiency [2]. Considering the high-pressure and high-temperature characteristics of the bearing's working environment, the importance of these monitoring and diagnosis processes is further heightened. On the one hand, physics-based methods perform fault diagnosis by simulating the dynamic behavior of the equipment [3, 4, 5]. While these methods have a practical physical background, their accuracy in establishment and application may be challenged as the complexity of the equipment increases. On the other hand, data-driven models construct predictive models by analyzing and processing equipment data [6, 7, 8]. Despite facing challenges regarding data quality and quantity, they exhibit excellent predictive accuracy and have become the current mainstream technology. Multimodal refers specifically to the features of different sensors or signal sources, which may differ in physical properties or measurement modalities. Existing multimodal signal fusion methods attempt to integrate features from different signals [9; 10]; however, due to a lack of effective modal representation mechanisms, the fusion of features between different signals may not be ideal, limiting the full utilization of key information in multimodal signals. Therefore, the health monitoring and fault diagnosis of rolling bearings need to overcome the limitations of single-modal and multimodal signal fusion to achieve a more comprehensive and accurate assessment of bearing health status and fault prediction. In recent years, with significant advancements in computer hardware and the rapid iteration of algorithmic models, the application of deep learning techniques in the field of rotating machinery fault detection has been rapidly increasing [11; 12; 13; 14]. These models extract deep features from raw data by cascading multiple layers of nonlinear modules within the deep learning framework. Since deep learning models are typically end-to-end, they can obtain features without manual intervention, enhancing their application scenarios. Currently, various deep learning models, such as multilayer perceptron (MLP) [15], convolutional neural networks (CNNs) [16; 17], one-dimensional convolutional neural networks, and graph convolutional networks (GCNs) [18], have been widely used in the fault diagnosis of rotating machinery, and the results obtained have been significant. However, CNNs also have drawbacks, especially due to vanishing or exploding gradients, which make it difficult to achieve fault classification with a high number of convolutional layers. Therefore, a one-dimensional convolutional neural network (1 DCNN) was proposed to simplify the structure of the CNN and maximize the classification accuracy [19; 20; 21]. In addition, the recursive gated \(\mathrm{g}^{\mathrm{n}}\mathrm{Conv}\) method proposed in the literature [22] provides an effective solution through a higher-order attention mechanism and the learning of distant features. \(\mathrm{g}^{\mathrm{n}}\mathrm{Conv}\) (n denotes the order of the higher-order interactions) combines the gated convolution and the recursive design, which is able to realize the higher-order spatial interactions and thus extract effective higher-order features. Therefore, in this study, we combine the 1 DCNN, MLP, and \(\mathrm{g}^{\mathrm{n}}\mathrm{Conv}\) methods for better fault classification and feature extraction to improve the accuracy and robustness of the model. However, most existing studies rely on fault features derived from a single modality [23; 24].