There always exist multiple uncertainties including random uncertainty, interval uncertainty, and fuzzy uncertainty in engineering structures. In the presence of hybrid uncertainties, the hybrid uncertainty propagation analysis can be a challenging problem, which suffers from the computational burden of double-loop procedure when numerical simulation techniques are employed. In this work, a novel method for efficient hybrid uncertainty propagation analysis with the three types of uncertainties is proposed. Generally, multi-fidelity surrogate models, such as Co-Kriging, can greatly improve the computational efficiency by leveraging information from a low-fidelity model to build a high-fidelity approximate model. However, the traditional multi-fidelity surrogate model methods always calculate the hybrid uncertainty propagation result by combining with several numerical simulation techniques. This process can introduce post-processing errors unless unlimited number of samples are used, which is impossible in engineering application. In order to address this issue, the analytical solutions of the output mean and output variance are derived based on the Co-Kriging, and the resulting mean and variance are both random variables. Moreover, a new adaptive framework is established to strengthen the estimation accuracy of the hybrid uncertainty propagation result, by combining the augmented expected improvement function and the derived mean random variable. Several applications are introduced to demonstrate the effectiveness of the proposed method for solving hybrid uncertainty propagation problems.

中文翻译：

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基于多保真代理模型的混合不确定性传播

工程结构中始终存在随机不确定性、区间不确定性和模糊不确定性等多种不确定性。在存在混合不确定性的情况下，混合不确定性传播分析可能是一个具有挑战性的问题，当采用数值模拟技术时，它会受到双循环过程的计算负担的影响。在这项工作中，提出了一种对三种类型的不确定性进行有效混合不确定性传播分析的新方法。通常，多保真代理模型（例如联合克里金法）可以通过利用低保真模型的信息构建高保真近似模型来极大地提高计算效率。然而，传统的多保真代理模型方法总是结合多种数值模拟技术来计算混合不确定性传播结果。除非使用无限数量的样本，否则该过程可能会引入后处理错误，这在工程应用中是不可能的。为了解决这个问题，基于协同克里金法导出了输出均值和输出方差的解析解，得到的均值和方差都是随机变量。此外，通过结合增强的期望改进函数和推导的平均随机变量，建立了一个新的自适应框架，以增强混合不确定性传播结果的估计精度。介绍了几个应用来证明所提出的方法解决混合不确定性传播问题的有效性。