In traditional rolling bearing dynamic models, the contact profile of rolling elements is often neglected. Based on the comprehensive analysis of a rolling ball entering and leaving a defect, an equivalent profile quantitative characterization function for localized defects is established, integrating the geometric-motion principles of rolling bearings. From this, an enhanced dynamic model for system failures in rolling bearings is constructed. Using theoretical analysis and numerical simulations based on the dynamic model, the mapping relationship between the location dimensions of outer raceway defect for rolling element bearings and the characteristics of vibration signals is explored, offering a mechanistic foundation for the construction and extraction of quantitative diagnostic indicators. To address the challenge presented by noise interference affecting the diagnostic accuracy of location formulas in real signals, a new algorithm for adaptively decomposing multi-channel time series is used in this paper. In analyses of both simulated and experimental signals, it is shown that the subtle fault quantification features hidden within the original multi-channel signals are more effectively extracted using tensor singular spectrum decomposition.