Physics-inspired deep learning network using dilated kronecker convolution for rotary machines under variable operating conditions

Asim Shahzad, Fuzheng Liu, Mingshun Jiang, Faye Zhang, Liying Ren,
Physics-inspired deep learning network using dilated kronecker convolution for rotary machines under variable operating conditions,
Journal of the Franklin Institute,
Volume 362, Issue 18,
2025,
108219,
ISSN 0016-0032,
https://doi.org/10.1016/j.jfranklin.2025.108219.
(https://www.sciencedirect.com/science/article/pii/S0016003225007112)
Abstract: The dynamics of vibration signals from rotating machinery are complicated and speed-dependent, with high-amplitude gearbox-induced spikes frequently masking bearing-related low-frequency modulations. Bearings and gearboxes are often treated as separate subsystems in traditional fault detection techniques, which ignore their intrinsic coupling and nonlinear interactions. To address this gap, we proposed a deep learning framework grounded in physics that utilizes an adaptive median filter to selectively suppress gearbox spikes. The scale-dependent bearing and gearbox features are then separated using wavelet multi-resolution analysis. The higher-order Volterra series expansion enables modeling of nonlinear coupling between gearbox transients and bearing resonances, capturing the nonlinear interplay. The primary extracted features are fused and further processed through a multi-scale dilated convolutional feature pyramid (KCFP) that adaptively captures localized fault transients and long-range amplitude modulations across bearing and gearbox signals. Finally, temporal dependencies in the vibration signals are modeled using Long Short-Term Memory (BiLSTM) networks. Integrating physics-inspired signal processing with deep learning ensures enhanced feature stability, interpretability, and diagnostic performance. Experimental validation on the HFZZ (Shandong University Intelligent Sensors Center) and CWRU dataset demonstrates superior performance, achieving 99.96 % classification accuracy. Comprehensive ablation studies confirm the individual contributions of the wavelet-Volterra expansion and self-attention mechanisms, establishing the necessity for maintaining diagnostic consistency during operational variations.
Keywords: Discrete wavelet transform (DWT); Kronecker convolution feature-pyramid (KCFP); Long-short term memory (BiLSTM); Volterra series