Symmetry

Evaluating the human–machine interface (HMI) of service robots remains challenging due to the complex integration of perceptual aesthetics and functional rationality. To address this, we propose a hybrid multidimensional HMI evaluation method that quantifies three key dimensions—layout aesthetics, color aesthetics, and functional layout rationality—by integrating visual cognition theory and axiomatic design (AD). The framework operationalizes five layout principles (balance, proportion, unity, regularity, density) and a four-component color model (color difference, distribution, harmony, and personality), complemented by a biologically grounded metric—visual perceptual intensity (VPI)—derived from cone cell response theory. Subjective weights from expert judgments (via analytic hierarchy process, AHP) and objective weights from the entropy weighting method (EWM) are fused within an AD-based information axiom framework to enable balanced, data-driven assessment. Applied to five candidate HMIs for a medical service robot (N = 15 participants), the method identified the design scheme x₃ as optimal when the balancing coefficient α ≥ 0.5 (reflecting greater emphasis on subjective judgment), whereas design scheme x₂ was preferred when α < 0.5 (prioritizing objective data). Given the modest sample size, correlation analysis revealed moderate-to-large—though not reaching conventional significance—between evaluation indicator scores and eye-tracking behavior: unity correlated with total fixation duration (Pearson_r = 0.682), and color harmony with first fixation duration (Pearson_r = 0.788), suggesting alignment between design attributes and visual attention patterns. These preliminary findings suggest that key design attributes may influence visual attention patterns, supporting the framework’s potential to link aesthetic and visual choices to measurable perceptual outcomes.

Thin-seam shearers operating in complex coal seams work under adverse conditions with poor visibility, making sensor installation difficult and signal sensing and collection challenging. As a result, identifying the cutting state becomes difficult, which significantly impacts the intelligent control of the shearer’s cutting section. Additionally, the complex working conditions lead to low reliability and shorten the service life of the spiral drum. The spiral drum is a typical symmetrical structure, and its load exhibits both symmetry and nonlinearity. The load under different gangue-inclusion conditions is developed in MATLAB R2022a. The occurrence times and corresponding load-spectrum data of the spiral drum, both under natural wear and sudden impact conditions, are extracted. Analysis reveals that the maximum stress under natural wear conditions exceeds 300 MPa, while under sudden impact conditions it reaches over 600 MPa. Fatigue analysis is carried out with the help of the ANSYS Ncode 2022 R1 module to identify the weak positions of fatigue damage in the spiral drum structure. Reliability models for natural wear and sudden impact failures are established using the Gamma and Weibull distributions, respectively. Parameter estimation is performed, and competing failure reliability models are constructed under independent and correlated conditions of the two failure modes. This approach obtains the competing reliability curve of the spiral drum, providing data support and new ideas for its reliability design.

Excavation unloading in deep rock masses involves a transition from symmetric states of energy storage to asymmetric energy dissipation, in which variations in intermediate principal stress (${\sigma }_2$) play a critical role. To investigate these symmetry-breaking mechanisms, controlled-rate true triaxial unloading experiments were performed on sandstone using a miniature creep-coupled testing system. During unloading of ${\sigma }_3$ at 0.1–0.3 MPa/s, the evolution of elastic, dissipated, and plastic energies was quantitatively evaluated. The results reveal pronounced asymmetric energy responses governed by both ${\sigma }_2$ and the unloading rate. Dissipated energy dominates the entire unloading process, while elastic energy exhibits a non-monotonic trend with increasing ${\sigma }_2$—first rising due to enhanced confinement and then decreasing as premature failure occurs. Higher unloading rates significantly accelerate total, elastic, and dissipated energy conversion and intensify post-peak brittleness. A new metric, plastically released energy, is proposed to quantify the asymmetric energy release from peak to residual state after failure. Its dependence on ${\sigma }_2$ is strongly non-monotonic, increasing under moderate ${\sigma }_2$ but decreasing when ${\sigma }_2$ is sufficiently high to trigger failure during unloading. This behavior captures the essential symmetry-breaking transition between elastic energy accumulation and irreversible plastic dissipation. These findings demonstrate that true triaxial unloading induces energy evolution patterns far from symmetry, controlled jointly by ${\sigma }_2$ and unloading kinetics. The established correlations between ${\sigma }_2$, unloading rate, and plastically released energy enrich the theoretical framework of energy-based symmetry in rock mechanics and offer insights for evaluating excavation-induced instability in deep underground engineering.