Nonlinear effects of built environment perception and objective features on street vitality in historic districts

Historical districts face dual pressures of preserving cultural heritage and sustaining socioeconomic vitality, yet many suffer declining street vitality due to homogenized commercialization or limited functional mix. Using Harbin's Daowai Historic District as a case study, this research examines the nonlinear and interactive effects of both built environment objective features and subjective perceptions on street vitality, integrating multi-source data with XGBoost and SHAP. Key findings include: (1) Boring and depressing are negatively associated with vitality, while lively and wealthy show positive correlations. Contrary to Jacobs' emphasis on visual diversity and eyes on the street, we find that excessive aesthetic and safety scores suppress vitality; (2) Built environment exhibit significant threshold effects, but the thresholds and nonlinear trends in the historic district differ from those at the urban contexts; (3) Interaction effects are observed among various variables, such as between functional density and distance to transit; (4) Based on cluster analysis, we propose classification and renewal strategies for streets. The study reveals the subjective-objective multidimensional nonlinear mechanism shaping historical district street vitality, providing a scientific foundation for fine-grained, vitality-oriented renovation. The identified threshold effects offer practical references for revitalization strategies in densely built historic districts across Asia.