Explainable Machine Learning for Evaluating Coupling and Coordination of the Sustainability Trilemma: A Case Study of Hebei Province

Achieving coordinated development among social equity (SE), economic development (ED), and ecosystem health (EH) is central to resolving the sustainability trilemma. This study investigated the spatiotemporal evolution and driving forces of SE–ED–EH coordinated development in Hebei Province, China, from 2005 to 2020 using a 1 km grid dataset. A comprehensive analytical framework integrating the Coupling Coordination Degree (CCD) model, fuzzy C-means clustering, and interpretable machine learning (XGBoost–SHAP) was developed to quantify changes in coupling and coordination (CC) levels and reveal nonlinear threshold effects. Results show pronounced spatial heterogeneity: urban cores exhibit “high coupling degree (C)–high coordination degree (T)–high CC level,” southeastern plains show “high C–low T–medium CC level,” and northwestern mountainous areas present “low C–medium/high T–low CC level.” Six dominant temporal evolution types were identified. XGBoost–SHAP reveals that nighttime lights (NL), population density (POP), and elevation (DEM) are the dominant drivers, with clear threshold ranges (NL 500–1500 nits; POP threshold near 40 persons km−2 with diminishing returns beyond 100 persons km−2; DEM constraint at 1000–1250 m) and strong interaction effects. The results suggest that Hebei is entering a quality- and structure-oriented rebalancing stage, where threshold-based management is critical for avoiding marginal loss of coordinated development. This study demonstrates that interpretable machine learning provides a transferable paradigm for threshold calibration, spatial zoning, and policy optimization aligned with SDGs, particularly applicable for resource-constrained regions undergoing late industrial transition.