Interpretable bearing fault diagnosis using physically compiled Kolmogorov–Arnold networks

Abstract

Rolling bearing fault diagnosis under noise and varying operating conditions requires diagnostic evidence that is not only accurate but also physically verifiable. Existing deep diagnostic models often rely on post-hoc saliency or attention visualization, which may not provide stable correspondence with measurable dynamic quantities. This study proposes a physically compiled Kolmogorov–Arnold network(PC-KAN), in which underdamped impulse-response priors are embedded into front-end filtering, spline-based functional representation, and physics-constrained training, so as to generate mechanism-aligned and verifiable diagnostic evidence. Specifically, the model consists of a physically compiled filter layer (PCFL-CBAM), statistical feature aggregation, feature standardization and input normalization, a MultKAN representation module, and a linear classifier head. The PCFL is physically parameterized using the product of an exponentially decaying envelope and a narrowband oscillation, and its B-spline coefficients are initialized via dynamic-topological mapping using training-domain spectral evidence. Kernel energy constraints and bandwidth constraints are adopted to mitigate the degradation of convolutional kernel morphology and frequency band drift. The convolutional block attention module (CBAM) is employed to enhance the responses at critical channels and informative temporal locations. A three-stage freeze-thaw training strategy is applied to sequentially achieve the construction of discriminative mappings and the refinement of physical semantics. Experiments on bearing fault datasets show that the proposed method achieves competitive diagnostic performance while providing interpretable evidence including kernel frequency responses, damping-related parameters, bandwidth concentration, and sparse decision paths. The results indicate that PC-KAN is most valuable as a mechanism-aligned diagnostic framework rather than merely as a highest-accuracy classifier.