Five-Dimensional Systems Theory-Driven Cross-Domain Unified Health Assessment of Rolling Bearings: Validation via Global Ideal Body on XJTU-SY/NASA/FEMTO Heterogeneous Datasets

Rolling bearing health assessment is critical to the predictive maintenance of rotating machinery. Conventional methods rely on single features and struggle to characterize the synergistic patterns of system-wide degradation. Based on Five-Dimensional Systems Theory (5D-ST), this paper constructs a holographic mapping of bearing systems across five dimensions---Boundary (B), Structure (S), Reserve (R), Direction (D), and Intensity (I)---and defines the synergy coefficient kappa in product form as a unified health metric. Using 48 bearings from three heterogeneous datasets (XJTU-SY China, NASA USA, FEMTO France), an iterative ideal-body normalization framework is established to enable quantitative cross-dataset comparison. Statistical analysis and case-study time-series inspection show that: in early-stage degradation the D-Direction dimension achieves Pearson correlation coefficients as high as 0.87 to 0.95 with kappa, acting as the "precursor dimension" of system degradation; in late-stage degradation the S-Structure dimension takes over dominance with r=0.88, exhibiting a clear dimensional dominance transfer (D to S) paradigm. Dual-sensor configurations significantly enhance the stability of kappa curves. Five degradation modes and eight representative cases are distilled, proving that the health threshold 0.8 and the collapse threshold 0.1 possess cross-domain universality. Global unified ideal-body validation further confirms cross-domain effectiveness, providing a unified assessment framework for bearing health management and cross-domain applications such as vehicle-road synergy and air-ground integration. This paper marks the first engineering application of Five-Dimensional Systems Theory---a new systems-science framework---to rotating machinery health assessment, opening a novel path for the deep integration of systems-science theory and engineering practice.