Abstract Traditional non-probabilistic methods for uncertainty propagation problems evaluate only the lower and upper bounds of structural responses, lacking any analysis of the correlations among the structural multi-responses. In this paper, a new non-probabilistic correlation propagation method is proposed to effectively evaluate the intervals and non-probabilistic correlation matrix of the structural responses. The uncertainty propagation process with correlated parameters is first decomposed into an interval propagation problem and a correlation propagation problem. The ellipsoidal model is then utilized to describe the uncertainty domain of the correlated parameters. For the interval propagation problem, a subinterval decomposition analysis method is developed based on the ellipsoidal model to efficiently evaluate the intervals of responses with a low computational cost. More importantly, the non-probabilistic correlation propagation equations are newly derived for theoretically predicting the correlations among the uncertain responses. Finally, the multi-dimensional ellipsoidal model is adopted again to represent both uncertainties and correlations of multi-responses. Three examples are presented to examine the accuracy and effectiveness of the proposed method both numerically and experimentally.

中文翻译：

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基于非概率椭球模型的结构不确定性分析相关传播

摘要 传统的不确定性传播问题的非概率方法仅评估结构响应的下限和上限，缺乏对结构多响应之间相关性的任何分析。本文提出了一种新的非概率相关传播方法来有效评估结构响应的区间和非概率相关矩阵。首先将具有相关参数的不确定性传播过程分解为区间传播问题和相关传播问题。然后利用椭球模型来描述相关参数的不确定域。对于区间传播问题，基于椭球模型开发了一种子区间分解分析方法，以低计算成本有效评估响应区间。更重要的是，新推导出非概率相关传播方程，用于从理论上预测不确定响应之间的相关性。最后，再次采用多维椭球模型来表示多响应的不确定性和相关性。提出了三个例子，以从数值和实验上检验所提出方法的准确性和有效性。再次采用多维椭球模型来表示多响应的不确定性和相关性。提出了三个例子，以从数值和实验上检验所提出方法的准确性和有效性。再次采用多维椭球模型来表示多响应的不确定性和相关性。提出了三个例子，以从数值和实验上检验所提出方法的准确性和有效性。