Rolling bearings serve as the most widely utilized general components in drive systems for rotating machinery, and they are susceptible to regular malfunctions. To address the performance degradation encountered by current convolutional neural network-based rolling-bearing-fault diagnosis methods due to significant noise interference and variable working conditions in industrial settings, we propose a rolling-bearing-fault diagnosis method based on dual multi-scale mechanism applicable to noisy-variable operating conditions. The suggested approach begins with the implementation of Variational Mode Decomposition (VMD) on the initial vibration signal. This is succeeded by a denoising process that utilizes the goodness-of-fit test based on the Anderson–Darling (AD) distance for enhanced accuracy. This approach targets the intrinsic mode functions (IMFs), which capture information across multiple scales, to obtain the most precise denoised signal possible. Subsequently, we introduce the Dynamic Weighted Multi-Scale Feature Convolutional Neural Network (DWMFCNN) model, which integrates two structures: multi-scale feature extraction and dynamic weighting of these features. Ultimately, the signal that has been denoised is utilized as input for the DWMFCNN model to recognize different kinds of rolling-bearing faults. Results from the experiments show that the suggested approach shows an improved denoising performance and a greater adaptability to changing working conditions.

Freeform machining of impellers involves extended cycle times, leading to high energy consumption and costs necessitating efficient process optimization. This study develops a CAD/CAM-integrated hybrid Taguchi-Artificial Neural Network (ANN) model to optimize machining parameters for a freeform impeller. Four controllable factors, namely cutting feed ($C_f$), feed Z ($F_z$), retract feed ($R_f$), and cutter diameter ($C_D$), were investigated at five levels using an L25 orthogonal array, with machining time as the response. Taguchi analysis identified cutting feed as the most dominant factor, while retract feed was insignificant, and a first-order regression model yielded an R² of 95.88%. A two-layer feedforward neural network with six hidden neurons achieved an R² of 0.9999 and a mean absolute error of 0.0976 min. To rigorously validate generalization, leave-one-out cross-validation was employed, identifying three hidden neurons as optimal with a cross-validated R² of 0.9823, RMSE of 0.5350 min, and MAE of 0.3429 min. The final model trained on all samples achieved an R² of 0.9996. Comparison with a quadratic regression model on the same test set confirmed the superior predictive capability of the ANN ($R^2=0.9992$ vs. $0.9983$). Optimal parameters ($C_f=\mathrm{12,000} \mathrm{m}\mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$, $F_z=600 \mathrm{m}\mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$, $R_f=4000 \mathrm{m}\mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$, $C_D=6 \mathrm{m}\mathrm{m}$) were validated through simulation, yielding a machining time of 11.05 min, representing a 52.6% reduction from 23.32 min. The hybrid Taguchi–ANN framework effectively optimizes freeform impeller machining, significantly enhancing productivity while maintaining process reliability.

High-speed machining of complex freeform geometries faces fundamental challenges in balancing computational efficiency, kinematic constraints, and precision, particularly in high-curvature regions where traditional interpolation methods suffer from geometric errors and jerk-induced vibrations. This study presents a Galerkin-NURBS interpolation framework that integrates Galerkin projection to optimize NURBS parameterization, minimizing geometric approximation error, and couples it with a jerk-limited S-curve trajectory planning algorithm that enforces $C^3$ continuity while respecting feedrate, acceleration, and jerk constraints. Numerical simulations and machining experiments were conducted on butterfly-shaped and horse-shaped curves using a five-axis CNC machine equipped with rotary/linear encoders and validated via profilometer-based surface roughness measurements. The proposed method achieved a 32.9% reduction in processing time (3.091 s) compared to the CQSF method (4.61 s) and a 35.1% reduction in interpolation steps relative to FSRC. Surface roughness ($R_a$) values ranged from 0.1271 μm to 0.2009 μm, with most measurements compliant with ISO 21920-1:2021; the maximum value (0.2009 μm) represents the upper bound of the standard’s high-precision threshold for aluminum alloy 6061. These findings demonstrate that the proposed framework significantly improves machining efficiency and surface quality while maintaining geometric fidelity, making it suitable for precision manufacturing applications where sensor-guided process optimization is critical.