Abstract Uncertainty quantification (UQ) and global sensitivity analysis (GSA) of dynamic characteristics of complex systems subjected to uncertainty are jointly investigated in this paper. An efficient approach based on arbitrary polynomial chaos expansion (aPCE) is presented for analytical, unified implementation of UQ and GSA in structural dynamics. For UQ of dynamic characteristics, statistical moments and probability distributions of dynamic characteristics are analytically derived. Specifically, the aPCE is used to analytically calculate the statistical moments, and then the maximum entropy principle (MEP) is adopted to derive the closed-form expressions of the probability distributions using the obtained statistical moments. As an extension of UQ, GSA, which aims to assess the quantitative contributions of different structural parameters to the resultant variations of dynamic characteristics, is also analytically achieved by simply post-processing the aPCE coefficients. The present aPCE UQ and GSA method is highly computationally efficient for large-scale, complex structures, and it is also generally applicable independent of parameter distributions. The proposed aPCE-based approach for UQ and GSA is validated through a numerical truss bridge by the brute-force Monte Carlo simulation (MCS), and then is applied to a long-span steel arch bridge.

中文翻译：

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结构动力学不确定性量化和全局灵敏度分析的任意多项式混沌展开法

摘要 本文联合研究了复杂系统在不确定性下的动态特性的不确定性量化（UQ）和全局灵敏度分析（GSA）。提出了一种基于任意多项式混沌展开 (aPCE) 的有效方法，用于在结构动力学中分析、统一实现 UQ 和 GSA。对于动态特性的UQ，解析导出动态特性的统计矩和概率分布。具体来说，利用aPCE解析计算统计矩，然后利用最大熵原理(MEP)，利用得到的统计矩推导出概率分布的闭式表达式。作为 UQ、GSA 的延伸，旨在评估不同结构参数对动态特性结果变化的定量贡献，也可以通过简单地对 aPCE 系数进行后处理来分析实现。目前的 aPCE UQ 和 GSA 方法对于大规模、复杂的结构具有很高的计算效率，并且它也可以独立于参数分布而普遍适用。提出的基于 aPCE 的 UQ 和 GSA 方法通过蛮力蒙特卡罗模拟 (MCS) 的数值桁架桥进行了验证，然后应用于大跨度钢拱桥。并且它也可以独立于参数分布而普遍适用。提出的基于 aPCE 的 UQ 和 GSA 方法通过蛮力蒙特卡罗模拟 (MCS) 的数值桁架桥进行了验证，然后应用于大跨度钢拱桥。并且它也可以独立于参数分布而普遍适用。提出的基于 aPCE 的 UQ 和 GSA 方法通过蛮力蒙特卡罗模拟 (MCS) 的数值桁架桥进行了验证，然后应用于大跨度钢拱桥。