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A unified analysis framework of static and dynamic structural reliabilities based on direct probability integral method

机译：基于直接概率积分法的静态和动态结构可靠性统一分析框架

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摘要

Generally, the static and dynamic reliabilities of structures are addressed separately in the existing methods except the computationally expensive stochastic sampling-based approaches. This study establishes a unified framework of reliability analysis for static and dynamic structures based on the direct probability integral method (DPIM). Firstly, the probability density integral equations (PDIEs) of performance functions for static and dynamic structures are presented based on the principle of probability conservation. The DPIM decouples the physical mapping (i.e., performance function) of structure and PD1E, and involves the partition of probability space and the smoothing of Dirac delta function. This study proposes a new adaptive formula of smoothing parameter based on kernel density estimation. Then, the improved DPIM is utilized to obtain the probability density function (PDF) of performance functions by solving the corresponding representative values and the PDIE successively. Furthermore, the reliability of static structure is calculated by integrating the PDF of performance function within safety domain. To overcome the difficulty of evaluating first passage dynamic reliability, the two approaches, namely the DPIM-based absorbing condition (DPIM-AC) and the DPIM-based extreme value distribution (DPIM-EVD), are also proposed. Finally, three engineering examples with stochastic parameters and random excitation indicate the desired efficiency and accuracy of the established framework for unified reliability analysis. Specifically, the challenging issue of dynamic reliability assessment for nonlinear structural system is attacked based on DPIM rather than Monte Carlo simulation or other sampling-based method. The proposed method is beneficial for propagation analysis of aleatory or/and epistemic uncertainties, as well as for stochastic model updating.
机译：通常，除了基于计算昂贵的随机采样的方法之外，结构的静态和动态可靠性在现有方法中分别解决。本研究建立了基于直接概率积分法（DPIM）的静态和动态结构可靠性分析统一框架。首先，基于概率节约原理，提出了静态和动态结构的性能函数的概率密度整体方程（PDIE）。 DPIM将结构和PD1E的物理映射（即，性能函数）解耦，涉及概率空间的分区和DIRAC DELTA功能的平滑。本研究提出了一种基于内核密度估计的平滑参数的新自适应公式。然后，利用改进的DPIM来通过求求相求解相应的代表值和PDIE来获得性能功能的概率密度函数（PDF）。此外，通过将性能函数的PDF集成在安全域内来计算静态结构的可靠性。为了克服评估第一通道动态可靠性的难度，还提出了两种方法，即DPIM的吸收条件（DPIM-AC）和基于DPIM的极值分布（DPIM-EVD）。最后，具有随机参数和随机励磁的三个工程示例表示统一可靠性分析的既定框架的所需效率和准确性。具体地，非线性结构系统动态可靠性评估的具有挑战性问题基于DPIM而不是蒙特卡罗模拟或其他基于样品的方法攻击。所提出的方法有利于杀菌或/和认知的不确定性的传播分析，以及随机模型更新。

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