Economic Optimization of Bike-Sharing Systems via Nonlinear Threshold Effects: An Interpretable Machine Learning Approach in Xi’an, China

As bike-sharing systems become increasingly integral to sustainable urban mobility, understanding their economic viability requires moving beyond conventional linear models to capture complex operational dynamics. This study develops an interpretable analytical framework to uncover non-linear relationships governing bike-sharing economic performance in Xi’an, China, utilizing one-month operational data across 202 Transportation Analysis Zones (TAZs). Combining spatial analysis with explainable machine learning (XGBoost–SHAP), we systematically examine how operational factors and built environment characteristics interact to influence economic outcomes, achieving superior predictive performance (R2 = 0.847) compared to baseline linear regression models (R2 = 0.652). The SHAP-based interpretation reveals three key findings: (1) bike-sharing performance exhibits pronounced spatial heterogeneity that correlates strongly with urban functional patterns), with commercial districts and transit-adjacent areas demonstrating consistently higher economic returns. (2) Gradual positive relationships emerge across multiple factors—including bike supply density (maximum SHAP contribution +1.0), commercial POI distribution, and transit accessibility—with performance showing consistent but moderate improvements rather than dramatic threshold effects. (3) Significant interaction effects are quantified between key factors, with bike supply density and commercial POI density exhibiting strong synergistic relationships (interaction values 1.5–2.0), particularly in areas combining high commercial activity with good transit connectivity. The findings challenge simplistic linear assumptions in bike-sharing management while providing quantitative evidence for spatially differentiated strategies that account for moderate threshold behaviors and factor synergies. Cross-validation results (5-fold, R2 = 0.89 ± 0.018) confirm model robustness, while comprehensive performance metrics demonstrate substantial improvements over traditional approaches (35.1% RMSE reduction, 36.6% MAE improvement). The proposed framework offers urban planners a data-driven tool for evidence-based decision-making in sustainable mobility systems, with broader methodological applicability for similar urban contexts.