How to accurately quantify the uncertainty of stochastic dynamical responses affected by uncertain loads and structural parameters is an important issue in structural safety and reliability analysis. In this paper, the conditional uncertainty quantification analysis for the dynamical response of stochastic structures considering the measurement data with random error is studied in depth. A method for extracting the key measurement condition, which holds the most reference value for the uncertainty quantification of response, from the measurement data is proposed. Considering the key measurement condition and employing the principle of probability conservation and conditional probability theory, the quotient-form expressions for the conditional mean, conditional variance, and conditional probability density function of the stochastic structural dynamical response are derived and are referred to as the key conditional quotients (KCQ). A numerical method combining the non-equal weighted generalized Monte Carlo method, Dirac function smoothing technique, and online-offline coupled computational strategy is developed for calculating KCQs. Three linear/nonlinear stochastic dynamical examples are used to verify that the proposed KCQ method can efficiently and accurately quantify the uncertainty of the structural response considering measurement conditions. The examples also compare the traditional non-conditional uncertainty quantification results with the conditional uncertainty quantification results given by KCQs, indicating that considering measurement conditions can significantly reduce the uncertainty of the stochastic dynamical responses, providing a more refined statistical basis for structural safety and reliability analysis.

翻译：如何准确量化受不确定荷载和结构参数影响的随机动力响应的不确定性，是结构安全性与可靠性分析中的重要问题。本文深入研究了考虑带有随机误差的测量数据时，随机结构动力响应的条件不确定性量化分析。提出了一种从测量数据中提取关键测量条件的方法，该条件对响应的不确定性量化最具参考价值。考虑该关键测量条件，并运用概率守恒原理与条件概率理论，推导了随机结构动力响应的条件均值、条件方差及条件概率密度函数的商形式表达式，并将其称为关键条件商。发展了一种结合非等权广义蒙特卡洛方法、狄拉克函数平滑技术及在线-离线耦合计算策略的数值方法，用于计算关键条件商。通过三个线性/非线性随机动力算例验证了所提出的关键条件商方法能够高效、准确地量化考虑测量条件的结构响应不确定性。算例还将传统的无条件不确定性量化结果与关键条件商给出的条件不确定性量化结果进行了对比，表明考虑测量条件能显著降低随机动力响应的不确定性，为结构安全性与可靠性分析提供更精细的统计依据。