Noise-resilient meta-learning on the Grassmann manifold for few-shot fault diagnosis of industrial robots

Fault diagnosis for industrial robots is critically challenged by the limited labeled data and noise. Conventional meta-learning methods assume Euclidean data structures and lack adaptive mechanisms to cope with noise. Thus, they are highly vulnerable to noisy perturbations, resulting in suboptimal discriminative power and unstable prototype estimation. To address these challenges, we propose a noise‑resilient meta‑learning (NRML) framework on the Grassmann manifold. Specifically, a noise‑aware damped distance (NADD) is developed to provide a robust similarity measure under varying noise levels. NADD employs a task‑adaptive damping mechanism that dynamically balances the discriminative sensitivity and noise robustness, and it is formally proven to be a valid distance. Furthermore, an energy‑thresholded subspace prototype (ETSP) is designed for adaptive and compact class representation on this manifold under extremely limited and noisy support samples. Comprehensive experiments on a public bearing dataset and a homemade industrial robot dataset demonstrate that NRML consistently outperforms multiple classical and state-of‑the‑art few‑shot diagnosis methods. The experimental results indicate that the proposed manifold‑based adaptive framework offers a practical and effective solution for robust few‑shot fault diagnosis of industrial robots.