城市基础设施作为城市运行的核心载体，分析其防洪系统内部相互作用与关联特征对于城市韧性的风险识别与韧性建设具有重要意义。Copula联合概率方法在复杂系统多维度的非线性关系探索与因素间相互作用的综合概率评估方面具有明显优势。该文基于“抵抗力R-适应力A-恢复力C”构建城市基础设施防洪韧性（urban infrastructure flood resilience，UIFR）评价指标体系，并采用以Copula理论为基础的联合概率估计方法描述UIFR各维度间的关联特征与多因素共同作用的综合概率。最后，将Copula函数模型应用于京津冀地区的UIFR联合分布概率研究，并结合XGBoost-SHAP模型探究UIFR的驱动效应。结果表明：2000—2022年，京津冀地区的UIFR呈波动变化，整体表现为增大态势；北京市的UIFR最大，天津市次之，河北省最小。二维联合分布概率中，北京市A-C、天津市和河北省R-A达到较高韧性的概率分别为0.761 9、0.116 9、0.149 7；三维联合分布概率中，北京市、天津市和河北省R-A-C达到较高韧性的概率分别为0.717 2、0和0.066 2，UIFR各维度间的不均衡发展会影响UIFR的整体水平。生活垃圾无害化处理率C₅、城市人均耗电量R₄等对京津冀地区UIFR的影响较为显著，因子间复杂的交互作用共同影响京津冀地区的UIFR。该研究成果可为基础设施防洪韧性系统内部的联合风险评估与城市韧性协同发展提供数据支撑与理论指导。

Objective: As urbanization accelerates and climate change intensifies, the risks of various urban disasters have increased considerably, hindering the transition toward urban resilience. As the core carrier of urban operation, urban infrastructure plays a pivotal role in enhancing urban resilience. Analyzing the interactions and correlation characteristics within its flood control system is of great importance for risk identification and resilience building in urban systems. Previous research on urban resilience has primarily focused on statistical methods, with limited research analyzing the characteristics of urban resilience from a probabilistic perspective. The Copula joint probability method offers distinct advantages in exploring multidimensional nonlinear relationships in complex systems and conducting comprehensive probability assessments of interfactor interactions. Methods: This study developed an evaluation index system for urban infrastructure flood resilience (UIFR) based on the resistance R–adaptability A–recovery C framework. The study used survey data from 2000 to 2022 and employed a Copula-theory-based joint probability estimation approach to characterize the correlation patterns among UIFR dimensions and the comprehensive probability of multifactor joint effects. In addition, the Copula function model was applied to investigate the joint distribution probability of UIFR in the Beijing–Tianjin–Hebei region of China, which is frequently affected by floods. The eXtreme gradient boosting-SHapley additive explanations (XGBoost–SHAP) model was integrated to explore the driving effects on UIFR. Results: The results showed that: 1) from 2000 to 2022, the UIFR in the Beijing–Tianjin–Hebei region exhibited fluctuating changes with an overall upward trend. Beijing recorded the highest UIFR, followed by Tianjin, while Hebei Province ranked the lowest. 2) For the two-dimensional joint distribution probability, the probability of achieving high resilience for the A–C pair in Beijing was 0.761 9, whereas the highest probabilities of high resilience for the R–A pair in Tianjin and Hebei were 0.116 9 and 0.149 7, respectively; the lowest probability of high resilience for the A–C pair in Hebei was 0.063 4. 3) For the three-dimensional joint distribution probability, the probabilities of achieving high resilience for the R–A–C combination in Beijing, Tianjin, and Hebei were 0.717 2, 0, and 0.066 2, respectively. The unbalanced development among UIFR dimensions impaired the overall level of the UIFR. 4) The harmless domestic waste treatment rate C₅, per capita urban electricity consumption R₄, and the share of the labor force A4 had remarkable impacts on the UIFR in the Beijing–Tianjin–Hebei region, with strong interaction between C₅ and other factors. The complex interactions among factors jointly influenced the UIFR in the Beijing–Tianjin–Hebei region. Conclusions: The UIFR joint probability method based on Copula functions demonstrates strong linear correlations between theoretical and empirical probability values of each Copula function, enabling effective two-dimensional and three-dimensional joint probability assessments of urban resilience. This method offers a new perspective on the relationships between internal connectivity and different aspects of resilience in UIFR. In addition, this study identifies key risk factors affecting the UIFR improvement in the Beijing–Tianjin–Hebei region, proposing additional targeted policy recommendations for future urban resilience initiatives. This study provides data support and theoretical guidance for joint risk assessment within infrastructure flood resilience systems and the coordinated development of urban resilience.