Symmetry

Symmetry and asymmetry jointly govern the dynamics and surface integrity of thin-wall AA7075 end milling. In this work, a symmetry-aware simulation and experimental framework is developed to connect process parameters with milling forces, dynamic response, surface quality, and through-thickness residual stress. A mechanistic milling-force model is first established for multi-tooth end milling, where the periodically repeated tooth-order excitation provides a nominally symmetric load pattern along the tool path. The predicted forces are then used as input for finite-element modal and harmonic-response analysis of a thin-walled component, revealing how symmetric and anti-symmetric mode shapes interact with the tooth-order excitation to generate locally amplified, asymmetric vibration of the compliant wall. Orthogonal and single-factor milling experiments on AA7075 thin-wall specimens are performed to calibrate and validate the force model, and to quantify the influence of feed per tooth, axial depth of cut, spindle speed, and radial width of cut on deformation, surface roughness, and geometric accuracy. Finally, a thermo-mechanically coupled finite-element model is employed to evaluate the residual-stress field, showing a characteristic pattern in which an initially symmetric thermal–mechanical loading produces depth-wise symmetry breaking between tensile surface layers and compressive subsurface zones. The proposed symmetry-aware framework, which combines milling-force theory, finite-element simulation, and systematic experiments, provides practical guidance for selecting parameter windows that suppress vibration, control residual stress, and improve the machining quality of thin-wall AA7075 components.

Ionospheric delay errors significantly reduce the positioning accuracy of global navigation satellite systems (GNSSs), whereas precise ionospheric modeling can effectively mitigate this issue. The ionosphere exhibits large-scale symmetry, and spherical harmonics (SHs) can effectively describe this property due to their rotational symmetry on the sphere. However, mathematical fitting models such as spherical harmonic functions and polynomial models encounter boundary inaccuracies caused by edge effects. To address this problem, we developed a spherical harmonic–radial basis function (SH-RBF) hybrid method based on the integration of spherical harmonics and radial basis function interpolation techniques. This method leverages the global symmetry of spherical harmonics and utilizes the local adaptability of radial basis functions to correct regional distortions. Validation using European GNSS data during both geomagnetically quiet and active periods, in comparison with the CODE global ionospheric map (GIM), demonstrates that the modeling accuracy of spherical harmonics surpasses that of POLY during geomagnetically quiet periods. Compared to spherical harmonics, SH-RBF improves overall modeling accuracy by 8.87–27.27% and enhances accuracy in edge regions by 34.16–83.91%. During geomagnetically active periods, the SH-RBF method also achieves notable improvements. This study confirms that SH-RBF is a reliable technique for significantly reducing edge effects in regional ionospheric modeling.

Renewable energy’s growing penetration erodes traditional power systems’ inherent dynamic symmetry—balanced inertia, damping, and frequency response. This paper proposes a self-adaptive virtual synchronous generator (VSG) control strategy for a photovoltaic hybrid energy storage system (PV-HESS) based on a radial basis function (RBF) neural network. The strategy establishes a dynamic adjustment framework for inertia and damping parameters via online learning, demonstrating enhanced system stability and robustness compared to conventional VSG methods. In the structural design, the DC-side energy storage system integrates a passive filter to decouple high- and low-frequency power components, with the supercapacitor attenuating high-frequency power fluctuations and the battery stabilizing low-frequency power variations. A small-signal model of the VSG active power loop is developed, through which the parameter ranges for rotational inertia (J) and damping coefficient (D) are determined by comprehensively considering the active loop cutoff frequency, grid connection standards, stability margin, and frequency regulation time. Building on this analysis, an adaptive parameter control strategy based on an RBF neural network is proposed. Case studies show that under various conditions, the proposed RBF strategy significantly outperforms conventional methods, enhancing key performance metrics in stability and dynamic response by 16.98% to 70.37%.