TLCG-VMD: A two-layer coupled graph-constrained variational mode decomposition framework for bearing fault diagnosis

Variational mode decomposition has been widely used for vibration signal analysis due to its clear variational formulation and non-recursive decomposition mechanism. However, most existing variational mode decomposition–based methods mainly improve parameter optimization, initialization, or target-mode selection within a single-layer framework. For complex bearing fault signals, a decomposed mode may still contain coupled background vibration, weak fault-induced impulses, and noise, making transient fault features difficult to expose. To address this limitation, this paper proposes a two-layer coupled graph-constrained variational mode decomposition framework for bearing fault diagnosis. The method integrates an outer robust mode decomposition layer with an inner graph-constrained baseband separation layer. The outer layer improves mode separation, while the inner layer separates each baseband mode into smooth background, sparse impulses, and residual noise. Graph regularization is used to preserve background structural consistency and facilitate weak impulse extraction. The refined inner-layer component is fed back to the outer-layer update, forming a coupled optimization process. Experiments on the Case Western Reserve University dataset show that two-layer coupled graph-constrained variational mode decomposition provides effective fault-feature enhancement and maintains robust performance under in-domain and cross-load conditions. Comparisons with EMD, EEMD, variational mode decomposition, and CEEMDAN further verify the overall effectiveness and statistical reliability of two-layer coupled graph-constrained variational mode decomposition.