<p>Mechanical components in complex industrial systems face evolving fault types, requiring diagnostic models with class-incremental learning capabilities. However, limited fault data and catastrophic forgetting hinder the effectiveness of deep learning approaches. This paper proposes a class-incremental fault diagnosis method based on the Convolutional Kolmogorov–Arnold Network–Kolmogorov–Arnold Network (CKAN-KAN), using bearing faults as a representative case. A convolutional kernel with trainable activation functions is designed for sliding-window convolution, enabling strong feature transferability and a stable feature space after new classes are introduced. The CKAN-KAN model is further established by integrating the multi-layer CKAN extractor with the KAN classifier. The locality principle of the B-spline curve is analyzed to explain the forgetting-resistant characteristics of the CKAN-KAN model. To address data scarcity, simulated data and CycleGAN-generated samples are used to synthesize high-fidelity fault data, supporting effective incremental learning under few-shot and zero-shot conditions. Experiments verify the B-spline locality principle and demonstrate that the proposed model achieves statistically significant improvements in diagnostic accuracy compared with state-of-the-art models. These results confirm the effectiveness of the proposed method for class-incremental fault diagnosis under data scarcity and continuous learning scenarios, while resisting catastrophic forgetting.</p>