Abstract A novel efficient stochastic incremental dynamics methodology considering first-excursion probability for nonlinear structural systems subject to stochastic seismic excitations in alignment with contemporary aseismic codes provisions is developed. To this aim, an approximate nonlinear stochastic dynamics technique for conducting first-passage probability density function (PDF) based stochastic incremental dynamic analysis is developed. Firstly, an efficient stochastic iterative linearization methodology is devised achieving convergence of the equivalent system damping ratios with the damping premises of the excitation response spectrum leading to a coherent determination of a robust scalable intensity measure (IM) which bears direct relation to its damaging potential. Subsequently, utilizing the stochastically derived time-varying forced vibrational system properties in conjunction with a combination of deterministic and stochastic averaging treatment the first-excursion PDF is efficiently determined for each and every of the considered limit-state rules (LSs). Lastly, an incremental mechanization analogous to the one used in normal incremental dynamic analysis (IDA) is proposed to ensure the necessary compatibility for applications in the fields of structural and earthquake engineering. The back-and-forth twisting pattern of IDA curves which is related with the multiple points satisfaction of the very same limit-state rule encourages the study of the problem from a first-passage perspective considering timing in addition to the intensity of the excitation variable. The selected engineering demand parameter (EDP) of the first-excursion time constitutes an excellent response related variable with twofold meaning; it performs structural behavior monitoring considering intensity and timing information whereas it is inherently coupled with limit-state requirements. The developed stochastic dynamics technique provides with reliable higher order statistics (i.e., PDF) of the chosen EDP. A structural system comprising the bilinear hysteretic model serves as a numerical example for demonstrating the reliability of the proposed first-excursion PDF-based stochastic incremental dynamics methodology. Nonlinear response time-history analysis involving a large ensemble of Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed methodology in a Monte Carlo-based context.

中文翻译：

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受地震激励的滞回结构系统的第一次偏移随机增量动力学方法

摘要 开发了一种新的有效的随机增量动力学方法，该方法考虑了受随机地震激励影响的非线性结构系统的首次偏移概率，符合当代抗震规范规定。为此，开发了一种近似非线性随机动力学技术，用于进行基于首次通道概率密度函数 (PDF) 的随机增量动力学分析。首先，设计了一种有效的随机迭代线性化方法，以实现等效系统阻尼比与激发响应谱的阻尼前提的收敛，从而导致对与其破坏潜力直接相关的稳健可扩展强度测量 (IM) 的相干确定。随后，利用随机导出的时变受迫振动系统属性，结合确定性和随机平均处理的组合，可以有效地为每个考虑的极限状态规则 (LS) 确定第一次偏移 PDF。最后，提出了一种类似于正常增量动态分析 (IDA) 中使用的增量机械化，以确保结构和地震工程领域应用的必要兼容性。IDA 曲线的来回扭曲模式与非常相同的极限状态规则的多点满足相关，鼓励从第一阶段的角度研究问题，除了考虑激励变量的强度之外，还考虑时间. 选定的首冲时间工程需求参数（EDP）构成了一个具有双重意义的极好的响应相关变量；它在考虑强度和时间信息的情况下执行结构行为监测，而它本质上与极限状态要求相结合。开发的随机动力学技术提供了所选 EDP 的可靠高阶统计数据（即 PDF）。包含双线性滞后模型的结构系统作为一个数值示例，用于证明所提出的基于首次偏移 PDF 的随机增量动力学方法的可靠性。非线性响应时间历程分析涉及大量 Eurocode 8 频谱兼容加速度图，以评估所提议方法在基于蒙特卡罗的环境中的准确性。