Multi-scale adaptive quadratic convolutional network: reliable gearbox fault identification under severe noise

Abstract Deep learning-based gearbox fault diagnosis has advanced considerably in recent years, yet real-world operating conditions are typically complex: vibration signals are strongly contaminated by noise and affected by operating fluctuations. As a result, existing deep models remain constrained in accurate feature extraction and generalization. In this study, we design a multi-scale adaptive quadratic convolutional network (MSAQCN). We first design an adaptive-weighted quadratic neuron that dynamically adjusts the combination of linear and quadratic terms in quadratic convolutions according to the input, enabling explicit modeling of nonlinear couplings and energy interactions in vibration sequences. Building on this, we construct multi-scale branches that, via heterogeneous receptive fields, capture cross-band features ranging from sharp transients to slowly varying envelopes, while residual connections stabilize the feature distribution and mitigate gradient attenuation, thereby reducing deep-layer degradation and numerical drift. To further suppress noise and emphasize salient patterns, we introduce an attention unit in the feature fusion stage that combines time-domain modeling with channel recalibration to adaptively weight multi-scale features. By analyzing the attention distribution induced by the quadratic neurons, we further demonstrate the intrinsic interpretability of MSAQCN for gearbox fault diagnosis under noise disturbance. Results obtained from two publicly available datasets and one in-house laboratory dataset indicate that the proposed approach provides efficient and reliable diagnosis under multi-condition, strong-noise scenarios.