The Probabilistic Seismic Demand Analysis (PSDA) which is frequently implemented in the first generation performance-based earthquake engineering quantifies seismic behavior of a structure by computing mean annual frequency of exceeding a specific value of a desired demand parameter given all anticipated earthquakes. This framework, based on the total probability integration formula, provides a technical basis on which aleatory uncertainties, uncertainties originated due to inherent randomness of the phenomena, are explicitly addressed. However, variability in the mean value of different model parameters, referred to as epistemic uncertainties and mainly due the finite-sample size of observations, is neglected. In this study, as an alternative to total probability integration, a reliability-based formulation tailored to effortlessly reflect both aleatory and epistemic uncertainties is put-forward to perform unified PSDA. Next, as an application of the proposed methodology, a reliability-based seismic demand curve of a 4-story example building is developed. Results demonstrate that the Second-Order Reliability Method (SORM) and important sampling method (ISM) along with multi-step Monte Carlo simulation (MSMCS) methods are appropriate candidates for computing reliability-based PSDA with differentiable and nondifferentiable performance functions, respectively.

中文翻译：

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使用可靠性方法的结构概率地震需求分析

在第一代基于性能的地震工程中经常实施的概率地震需求分析 (PSDA) 通过计算在所有预期地震情况下超过所需需求参数的特定值的年平均频率来量化结构的地震行为。这个基于全概率积分公式的框架提供了一个技术基础，在这个基础上，偶然的不确定性，由于现象的固有随机性而产生的不确定性，被明确地解决了。然而，不同模型参数的平均值的可变性，称为认知不确定性，主要是由于观察的有限样本大小，被忽略了。在本研究中，作为全概率积分的替代方案，提出了一种基于可靠性的公式，可以轻松地反映偶然和认知不确定性，以执行统一的PSDA。接下来，作为所提出方法的应用，开发了一个 4 层示例建筑的基于可靠性的地震需求曲线。结果表明，二阶可靠性方法 (SORM) 和重要抽样方法 (ISM) 以及多步蒙特卡罗模拟 (MSMCS) 方法分别是计算具有可微和不可微性能函数的基于可靠性的 PSDA 的合适候选者。