Multi-Scale Wavelet-integrated Kolmogorov-Arnold Network (MS-WavKAN) for robust bearing fault diagnosis under harsh industrial noise

Abstract

Rolling element bearings are critical components in rotating machinery, and their unexpected failures cause a substantial proportion of unplanned industrial downtime. A central challenge in bearing fault diagnosis is the rapid attenuation of diagnostic information under harsh industrial noise, which obscures the transient impulses generated by mechanical defects. This paper introduces an end-to-end wavelet-structured learning paradigm, MS-WavKAN, which embeds a structural wavelet prior into the network architecture by replacing the B-spline basis of standard Kolmogorov-Arnold Networks with learnable Morlet wavelet activations whose Gaussian-modulated cosine form is matched to the shape of bearing-impact transients. The model is rigorously evaluated on the Paderborn University (PU) dataset—which contains real fatigue damage bearings evaluated under a cross-speed/cross-force protocol (1500 rpm/400 N → 900 rpm/1000 N)—and on the CWRU benchmark under a cross-load protocol (0 hp → 2 hp). MS-WavKAN achieves 87.5% ± 1.4% on clean PU and 79.0% ± 2.6% at −4 dB SNR, outperforming lightweight baselines and an encoder-matched B-spline KAN variant (paired t-test, p  < 0.05). The wavelet basis delivers localised-oscillatory nonlinearities structurally matched to impulsive bearing-fault content, using ∼6× fewer head parameters than B-splines: with ≈ 71 k parameters MS-WavKAN outperforms an ≈82 k B-spline-KAN variant sharing the same encoder. It also retains strong performance under composite noise (−4 dB AWGN + 50 Hz harmonic interference), a condition representative of real factory floors. The theoretical BPFI/BPFO kinematic frequencies provide an interpretive reference for the learned activations. With only approximately 71 k parameters, MS-WavKAN is suitable for real-time edge deployment on low-power microcontrollers.