# KACFormer: A Novel Domain Generalization Model for Cross-Individual Bearing Fault Diagnosis
## 1 Introduction  
Bearing fault diagnosis is critical for the smooth operation of rotating machinery, which plays an essential role in various industries, from power generation to manufacturing. Bearings are fundamental components that facilitate rotation and support mechanical systems. In recent years, many scholars have researched how to extract information from vibration signals for fault diagnosis [1, 2], proposing numerous advanced methods [3], among which intelligent fault diagnosis based on deep learning has garnered particular attention in recent years [4, 5]. [PERSON] et al. [6] first designed a deep Convolutional Neural Network (CNN) with wide first-layer kernels (WDCNN) for fault diagnosis under the source domain setting,where both training and testing data were collected from the same set of bearing individuals. This architecture was tailored to enhance the network's ability to capture long-range dependencies and extract detailed features from the vibration signals. Further, they proposed a convolutional neural network with training interference (TICNN) [7] to enhance performance under noisy environmental conditions and different working loads, which better meets the need of practical industrial scenarios. [PERSON] et al. [8] proposed a novel meta-learning framework called generalized MAML to analyze the acceleration and acoustic signals obtained from bearings under different working conditions. [PERSON] et al. [9] introduced a zero-shot fault semantics learning model for diagnosing compound faults. Additionally, [PERSON] et al. [10] developed a dual adversarial learning-based multi-domain adaptation network for collaborative fault diagnosis across both bearings and gearboxes, with comparative results confirming its superior performance and effectiveness over other methods. Most current intelligent fault diagnosis models are trained and tested within the same individual. However, in practical industrial scenarios, the test objects are usually new components with potential individual differences [11], including manufacturing differences, production inconsistencies, assembly issues, and variations in fault manifestation. Consequently, differences in data distribution between the test and training individuals may hinder the model's ability to accurately perform fault classification. Recently, scholars have begun to focus on more practical cross-domain issues beyond cross-condition scenarios, such as cross-machine problems [12; 13], which are more closely aligned with real-world industrial applications. Cross-individual scenarios are practical, yet they remain insufficiently explored. This presents a challenging task that requires further attention [14; 15]. To demonstrate the challenge, the widely cited Case Western Reserve University (CWRU) bearing dataset serves as an illustrative example. Vibration signals corresponding to three distinct bearing fault types, Ball, Inner Race (IR), and Outer Race (OR) from the drive end (DE), were segmented using a sliding window approach to construct the source domain dataset. Respectively, Figures 1a-c and 2a-c present the t-SNE [16] (t-Distributed Stochastic Neighbor Embedding) visualization of the training and testing data distribution for the in-domain task and cross-individual task, where the blue markers represent the dimensionally reduced training set samples and the red markers denote the test set samples in the embedded space. Figure 1: _Cont._  
The t-SNE (t-Distributed Stochastic Neighbor Embedding) visualization reveals the following: (1) compact clustering of same-individual samples (intra-domain consistency), and (2) pronounced distribution shifts between the source (training) and target (testing) individuals, empirically demonstrating the cross-individual generalization challenge in bearing fault diagnosis. Inspired by the Kolmogorov-Arnold representation theorem (KART) [17], [PERSON] et al. proposed Kolmogorov-Arnold networks (KANs) as promising alternatives to multi-layer perceptrons (MLPs).