Assessing the seismic capacity of pier columns is a crucial element in the performance-based seismic design of bridges. Such assessment necessitates a probabilistic approach to accurately determine the marginal probability distributions of seismic capacities and to characterize the dependencies among these variables. In response to this need, this paper employs Multi-Output Gaussian Process Regression (MO-GPR), a probabilistic machine learning method, to jointly model the multiple seismic capacities of pier columns. We initially introduce a probabilistic seismic capacity model that utilizes MO-GPR for pier columns and validate its predictive accuracy in comparison to Bayesian linear regression and existing empirical methods. Subsequently, the methodology is augmented by the integration of hierarchical modeling within the MO-GPR framework, resulting in a Multi-Output Hierarchical Gaussian Process Regression (MO-HGPR) model that effectively estimates intraclass correlation coefficients for specific types of datasets. It is postulated that these correlation coefficients also reflect correlations associated with multiple components of the real structure. This study employs MO-HGPR and MO-GPR separately to investigate the potential correlations of seismic capacities among pier columns and distinct limit states. The results demonstrate that the MO-GPR model exhibits superior prediction accuracy and more effectively portrays uncertainty compared to existing empirical models. Moreover, the correlations of seismic capacities among piers and limit states are both robust and significantly impact the seismic fragility of bridges. This finding highlights the essential nature of considering capacities correlations in seismic fragility or risk assessment processes.

中文翻译：

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桥墩柱抗震能力的预测和相关性估计：扩展高斯过程回归模型

评估桥墩柱的抗震能力是基于性能的桥梁抗震设计的关键要素。这种评估需要采用概率方法来准确确定地震能力的边际概率分布并表征这些变量之间的依赖性。针对这一需求，本文采用概率机器学习方法多输出高斯过程回归（MO-GPR）对桥墩柱的多重抗震能力进行联合建模。我们首先介绍了一种利用 MO-GPR 进行桥墩柱的概率抗震能力模型，并与贝叶斯线性回归和现有经验方法相比验证了其预测准确性。随后，通过在 MO-GPR 框架内集成分层建模来增强该方法，形成多输出分层高斯过程回归 (MO-HGPR) 模型，该模型可有效估计特定类型数据集的类内相关系数。假设这些相关系数也反映了与真实结构的多个组件相关的相关性。本研究分别采用 MO-HGPR 和 MO-GPR 来研究墩柱和不同极限状态之间抗震能力的潜在相关性。结果表明，与现有的经验模型相比，MO-GPR 模型表现出优越的预测精度，并且更有效地描绘了不确定性。此外，桥墩和极限状态之间抗震能力的相关性很强，并且显着影响桥梁的地震脆弱性。这一发现凸显了在地震脆弱性或风险评估过程中考虑容量相关性的本质。