Spindle stiffness is one of the most critical indicators for evaluating and measuring the service performance of spindles. The traditional static stiffness indexes only involve static analysis and rarely focus on the study of spindle-carrying capacity under operating conditions. In this paper, the explicit solution approach is used to develop a mechanical model of the spindle’s axial operating stiffness. This model was then used to explore the influence of rotational speed on the softening and hardening features of the spindle axial operating stiffness, and experimental verification was carried out. According to studies, the speed of a fixed-position preload spindle can lead its operating stiffness to exhibit a “stiffness-hardening” feature. However, when the axial displacement of the spindle is small, the operating stiffness curve of the spindle displays a noticeable “fluctuation” phenomenon for low-speed spindles. Furthermore, the speed-induced preload has a significant impact on the test results when testing spindle axial operating stiffness.

Studies using source localization results have shown that cortical involvement increased in treadmill walking with brain–computer interface (BCI) control. However, the reorganization of cortical functional connectivity in treadmill walking with BCI control is largely unknown. To investigate this, a public dataset, a mobile brain–body imaging dataset recorded during treadmill walking with a brain–computer interface, was used. The electroencephalography (EEG)-coupling strength of the between-region and within-region during the continuous self-determinant movements of lower limbs were analyzed. The time–frequency cross-mutual information (TFCMI) method was used to calculate the coupling strength. The results showed the frontal–occipital connection increased in the gamma and delta bands (the threshold of the edge was >0.05) during walking with BCI, which may be related to the effective communication when subjects adjust their gaits to control the avatar. In walking with BCI control, the results showed theta oscillation within the left-frontal, which may be related to error processing and decision making. We also found that between-region connectivity was suppressed in walking with and without BCI control compared with in standing states. These findings suggest that walking with BCI may accelerate the rehabilitation process for lower limb stroke.

The nonlinear operational stiffness characteristics of machine tool spindles directly influence machining precision and bearing service life. Traditional static stiffness tests rely on direct differential operations on raw experimental load–displacement data, which are highly susceptible to measurement noise and fundamentally fail to capture accurate nonlinear features. To address this limitation, this study proposes a physics-driven parameter identification methodology to accurately extract the static nonlinear axial stiffness characteristics of spindles under static non-rotating conditions. Specifically, the smoothness priors approach (SPA) is introduced as a robust preprocessing technique to mitigate high-frequency noise while preserving the underlying low-frequency displacement trends, thereby ensuring high-fidelity feature extraction. Subsequently, a physics-dependent spindle mechanics model is directly integrated with a two-stage hybrid optimization algorithm—combining Global Search and Pattern Search—to inversely reconstruct the actual nonlinear load–displacement relationships. Numerical simulation results demonstrate that the hybrid optimization algorithm exhibits high computational accuracy, with an identification error of only 0.67% under ideal conditions and bounded parameter identification errors within 4.68% under synthetic noise levels up to 5%. Furthermore, experimental validation conducted on a position-preloaded spindle setup under initial preloads of 507 N and 862 N yields corresponding verification errors of 12.3% and 11.6%, respectively, confirming that the proposed method can effectively extract the static nonlinear stiffness features of the spindle from noisy measurements. The results demonstrate that this approach successfully overcomes the bottlenecks of conventional techniques, providing a robust and practical tool for the precise characterization of the spindle’s static nonlinear baseline stiffness. While currently validated under static non-rotating conditions, the established framework provides a fundamental baseline for extending parameter identification to dynamic operational environments in future studies.

Hydraulic systems are critical power hubs in modern industry, yet their fault diagnosis remains inherently challenging. Although Graph Neural Networks (GNNs) excel in diagnosing rotating machinery, their direct application to hydraulic systems is hindered by strong fluid damping and non-stationary signal pulsations. These phenomena inevitably cause static graph distortion and over-smoothing in deep network architectures. To overcome these bottlenecks, we propose a Multi-scale Adaptive Graph Enhanced Graph Attention Network (MSA-EGAT). Specifically, an adaptive graph construction algorithm is formulated to dynamically optimize the nearest neighbor count K and fuzzy weight α, ensuring the topological mapping strictly aligns with fluid physical dynamics. Furthermore, the architecture integrates residual connections, multi-head attention, and multi-scale pooling to effectively suppress feature degradation. Experimental validation on a custom-built hydraulic test rig demonstrates that MSA-EGAT achieves a fault recognition accuracy exceeding 99%, successfully transferring the GNN diagnostic paradigm to fluid power systems. Comprehensive ablation studies confirm its efficacy in mitigating graph distortion and over-smoothing, while visual analysis of the constructed graphs explicitly reveals the topological manifolds of fluid state evolution, significantly improving model interpretability.