Diagnosing morphology-vitality relationships through multifractal urban form metrics and explainable machine learning

Understanding how urban morphology is associated with urban vitality is important for sustainable urban regeneration, yet conventional density-based indicators often fail to capture cross-scale heterogeneity in three-dimensional urban form. This study proposes a morphology-vitality diagnostic framework that integrates elevation-weighted multifractal analysis with explainable machine learning. Taking the main urban area of Jinan, China, as a case study, we derived multifractal metrics from building footprint and height data and constructed a composite vitality index using population, point-of-interest, and road-network indicators. XGBoost models and SHAP interpretation were used to examine the nonlinear association between morphological descriptors and urban vitality, while additional robustness analyses were conducted for the vitality index, feature sets, multifractal parameters, and threshold detection. The results show that the morphological heterogeneity index Δα is a key explanatory variable for vitality variation and remains highly ranked across alternative model settings. Baseline comparisons indicate that multifractal descriptors provide additional predictive information beyond conventional morphological indicators. A partial-dependence-based segmented regression further identifies a stable sensitive interval around Δα ≈ 1.82, with bootstrap and spatial-block robustness tests supporting the consistency of this threshold. Rather than implying direct causality, the proposed mismatch indicator is interpreted as a diagnostic measure of deviation between morphology-based predicted vitality and observed vitality. The framework contributes to SDG-oriented urban regeneration by providing a quantitative tool for identifying areas where morphological structure and functional performance are unevenly aligned.