When faults occur in rolling bearings, vibration signals exhibit sensitivity to periodic impact components, susceptibility to complex background noise, and non-stationary and nonlinear characteristics. Consequently, using traditional signal processing methods to effectively identify bearing faults presents significant challenges. To facilitate the accurate fault diagnosis of bearings in noisy conditions, we propose an intelligent fault diagnosis method using the Archimedes optimization algorithm (AOA), coupled with a one-dimensional multi-scale residual convolutional neural network (1D-MRCNN), to optimize the variational mode extraction (VME) parameters. First, we introduce a weighted correlated kurtosis (WCK) indicator, formulated using the correlation coefficient and correlated kurtosis as the objective function, to optimize the VME’s center frequency ω and penalty factor α, enabling targeted signal extraction. Second, deep learning techniques are employed to construct the 1D-MRCNN. The neural network then processes the extracted signal for feature extraction and automated fault-type identification. Our simulation results show that the WCK objective function effectively isolates impact components under fault conditions, and our experimental validation confirms that the proposed method accurately identifies diverse fault types across multiple noise levels.