In the response analysis of uncertain structural models with limited information, probability-boxes can be effectively employed to address the aleatory and epistemic uncertainty together. This paper presents a copula-based uncertainty propagation method which can accurately perform uncertainty propagation analysis with correlated parametric probability-boxes. Firstly, the parameter estimation and Akaike information criterion analysis are utilized to select an optimal copula based on available samples, by which the joint cumulative distribution function is constructed for the correlated input variables. Then, using the obtained joint cumulative distribution function, the correlated parametric probability-boxes are transformed into independent normal variables, and an efficient method based on sparse grid numerical integration is proposed to calculate the bounds on statistical moments of a response function. Finally, numerical examples and an engineering application are provided to verify the effectiveness of the presented method.

在信息有限的不确定结构模型的响应分析中，可以有效地使用概率盒来解决偶然性和认知性的不确定性。本文提出了一种基于copula的不确定性传播方法，该方法可以通过相关参数概率盒准确地进行不确定性传播分析。首先，利用参数估计和Akaike信息判据分析，根据可用样本选择最优Copula，构建相关输入变量的联合累积分布函数。然后，使用获得的联合累积分布函数，将相关的参数概率框转换为独立的正态变量，提出了一种基于稀疏网格数值积分的计算响应函数统计矩界的有效方法。最后，通过数值算例和工程应用验证了所提出方法的有效性。