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.

The axial nonlinear stiffness of machine tool spindles critically governs machining stability, yet isolating its thermal-driven evolution from intertwined, antagonistic rotational dynamic interferences remains a long-standing challenge. The main contribution of this study is the “Double Decoupling” framework, which isolates the thermal-driven evolution of spindle axial stiffness from dynamic interferences and distinguishes internal preload relaxation from localized component expansion. Experimentally, a “thermal-equilibrium and rapid-shutdown” methodology is developed to physically isolate quasi-static thermal boundaries, successfully capturing pristine intrinsic stiffness profiles within a critical 5 s post-shutdown window. Analytically, a thermomechanical model coupling micro-geometric thermal distortions with dynamic preload evolution is established. Our findings quantitatively elucidate that temperature escalation (26 °C to 43 °C) prompts a monotonic global stiffness degradation exceeding 12% in the central stiffness plateau. Thermomechanical inversions reveal that localized bearing thermal expansion plays merely a secondary role; instead, the non-uniform internal temperature field drives a macroscopic axial thermal mismatch between the spacers, triggering “thermal preload relaxation” as the primary contributor to global thermal stiffness loss. Consequently, practical thermal stiffness regulation should preferentially target macro-preload and spacer management rather than complex component dimensional compensation.