Reliability analysis of dynamic structural systems and its implications for structural design have garnered increasing attention. Sample-based methods prove insensitive to the dimension of the probability integral. Nontheless, a substantial number of realizations is necessary for estimating small failure probabilities, resulting in time-consuming computations. Recently, the Directional Importance Sampling (DIS) was introduced for linear structural systems subjected to Gaussian loads, showcasing the ability to accurately estimate small failure probabilities with a reduced number of simulations. However, this Gaussian assumption on the load makes the method inapplicable for realistic loading scenarios as they might be of non-Gaussian nature. This contribution develops the DIS method for linear structural systems subjected to loading characterized as non-Gaussian white noise. To take the advantage of both linearity in physical space and simplicity of Gaussian space, directional importance sampling is conducted in Gaussian space and the failure probability is estimated with the aid of physical space. The information is dynamically exchanged between physical and Gaussian spaces with the aid of normal and inverse-normal transformation techniques. The whole procedure of the developed DIS method is straightforward, and it provides an explicit estimator of the failure probability. The application of the developed DIS method is presented through three examples, illustrating its accuracy and efficiency for dynamic reliability analysis.

中文翻译：

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非高斯白噪声激励下线性结构动态可靠性的方向重要性采样


动态结构系统的可靠性分析及其对结构设计的影响越来越受到关注。基于样本的方法被证明对概率积分的维度不敏感。尽管如此，估计较小的故障概率需要大量的实现，从而导致耗时的计算。最近，针对承受高斯载荷的线性结构系统引入了方向重要性采样 （DIS），展示了以较少的仿真次数准确估计小失效概率的能力。然而，这种对载荷的高斯假设使得该方法不适用于实际载荷场景，因为它们可能具有非高斯性质。这一贡献为承受非高斯白噪声特征的载荷的线性结构系统开发了 DIS 方法。为了充分利用物理空间的线性和高斯空间的简单性，在高斯空间中进行方向重要性采样，并借助物理空间估计失效概率。借助法向和逆法态变换技术，信息在物理空间和高斯空间之间动态交换。开发的 DIS 方法的整个过程很简单，它提供了失效概率的显式估计器。通过三个实例介绍了所开发的 DIS 方法的应用，说明了其在动态可靠性分析中的准确性和效率。