Uncovering the foundation-capacity-performance logic of urban resilience: Identifying dynamic weights and nonlinear relationships through a spatial machine learning framework

Urban resilience has emerged as a critical topic in urban planning and spatial governance amidst rapid urbanization and increasing climatic uncertainty. However, the structural relationships, functional interactions, and temporal coupling among the multidimensional attributes of resilience remain insufficiently understood. To address this gap, this study introduces a Foundation-Capacity-Performance (FCP) model that links the foundational conditions, adaptive mechanisms, and spatial expressions of resilience, and develops a dynamic weighting framework integrating random forest, geographically weighted regression, and TOPSIS to capture nonlinear effects, spatial heterogeneity, and temporal consistency. Using multi-source raster data for the central urban area of Nanjing from 2005 to 2020, we quantify an overall urban resilience index and map the results onto the foundational and capacity dimensions. The results indicate that: (1) urban resilience in Nanjing increased steadily from 2005 to 2020, exhibiting a networked diffusion pattern from core districts toward near-suburban and peripheral areas; (2) early improvements were primarily driven by infrastructure robustness and system recovery, whereas later enhancement stemmed from more balanced social services, functional diversification, and ecological network optimization; (3) Key indicators (e.g., population density, built-up intensity, and connectivity) display notable nonlinear effects within threshold ranges, while ecological attributes maintain consistently positive effects; and (4) the proposed dynamic weighting model substantially outperforms static schemes in temporal consistency and interannual prediction. Overall, this study provides a coherent theoretical framework and methodological pathway for multi-period, multi-scale resilience assessment, offering quantitative evidence to support resilience-oriented urban planning and governance.