Motor fault diagnosis faces challenges in industrial scenarios

including small sample sizes

distribution shifts

and edge device deployment. Traditional two-dimensional representation methods

such as the gramian angular field (GAF) and continuous wavelet transform (CWT)

suffer from phase sensitivity and scale dependency

which limits their ability to meet the requirements of deep learning for feature consistency and generalization. To address these issues

this paper proposes the Fourier regularized Gram matrix (FRGM)

a novel two-dimensional representation method designed for deep learning applications. By decoupling the time-domain signal phase through frequency-domain analysis and low-rank approximation

FRGM eliminates the influence of phase on time-series signals

achieving feature space consistency across inputs of different lengths. This provides a theoretical foundation for model lightweighting and cross-scenario adaptability. Based on FRGM

this paper develops a dynamic distillation framework (FRGM-DistillNet) that utilizes flexible teacher-student model configurations to adapt to three types of industrial diagnostic scenarios: edge devices with limited computational resources but abundant data

central servers with ample computational power but scarce data

and environments where both resources and data are scarce. Experimental results demonstrate that FRGM’s phase-invariance and high information density effectively resolve distribution shifts and feature collapse. The dynamic distillation framework exhibits significant advantages across all three scenarios. This study offers an efficient and reliable solution for motor fault diagnosis in industrial settings

combining theoretical innovation with practical engineering value.