This study introduces the long-range Ising model from statistical mechanics to the Performance-Based Earthquake Engineering (PBEE) framework for regional seismic damage analysis. The application of the PBEE framework at a regional scale involves estimating the damage states of numerous structures, typically performed using fragility function-based stochastic simulations. However, these simulations often assume conditional independence or employ simplistic dependency models among the damage states of structures, leading to significant misrepresentation of regional risk. The Ising model addresses this issue by converting the available information on binary damage states (safe or failure) into a joint probability mass function, leveraging the principle of maximum entropy. The Ising model offers two main benefits: (1) it requires only the first- and second-order cross-moments, enabling seamless integration with the existing PBEE framework, and (2) it provides meaningful physical interpretations of the model parameters, facilitating the uncovering of insights not apparent from data. To demonstrate the proposed method, we applied the Ising model to 156 buildings in Antakya, Turkey, using post-hazard damage evaluation data, and to 182 buildings in Pacific Heights, San Francisco, using simulated data from the Regional Resilience Determination (R2D) tool. In both instances, the Ising model accurately reproduces the provided information and generates meaningful insights into regional damage. The study also investigates the change in Ising model parameters under varying earthquake magnitudes, along with the mean-field approximation, further facilitating the applicability of the proposed approach.

翻译：本研究将统计力学中的长程伊辛模型引入基于性能的地震工程（PBEE）框架，用于区域地震损伤分析。在区域尺度应用PBEE框架涉及对大量结构损伤状态的估计，通常采用基于易损性函数的随机模拟方法。然而，这些模拟通常假设结构损伤状态之间条件独立或采用过于简化的依赖模型，导致区域风险表征存在显著偏差。伊辛模型通过最大熵原理，将二值损伤状态（安全或失效）的可用信息转化为联合概率质量函数，从而解决了这一问题。该模型具有两大优势：（1）仅需一阶和二阶交叉矩即可构建，能够与现有PBEE框架无缝集成；（2）模型参数具有明确的物理解释，有助于揭示数据中不直观的隐含规律。为验证所提方法，我们分别将伊辛模型应用于土耳其安塔基亚的156栋建筑（采用震后损伤评估数据）和旧金山太平洋高地的182栋建筑（采用区域韧性评估工具R2D的模拟数据）。两个案例中，伊辛模型均准确复现了给定数据信息，并对区域损伤模式产生了有意义的洞见。研究还探讨了不同震级下伊辛模型参数的变化规律，并结合平均场近似方法，进一步提升了该方法的适用性。