随机-认知不确定性的相关性分析模型及可靠性计算方法

针对工程中同时存在随机和认知不确定性的问题，提出了一种考虑相关性的概率-证据混合不确定性模型及相应的结构可靠性分析方法。首先引入样本相关系数来描述概率变量之间、证据变量之间以及概率和证据变量之间的相关性，通过一个转换矩阵将原问题中相关的变量转换为相互独立的变量，并构建了一个等效的概率-证据混合可靠性模型。然后将其转化为一系列概率-区间混合可靠性分析模型，并总结了嵌套优化分析迭代格式来求解失效概率区间。最后提供了三个数值算例验证该方法的有效性。

An Aleatory and Epistemic Mixed Uncertainty Model Considering Parametric Correlation and Its Reliability Analysis

A  probability and evidence hybrid uncertainty model considering parametric correlation was proposed and a corresponding reliability analysis method for problems  with both aleatory and epistemic uncertainties was studied.Firstly,sample correlation coefficients were introduced to describe the correlation among probability variables,evidence variables as well as probability and evidence variables. Correlated parameters were transformed into independent ones through a matrix transformation and an equivalent probability-evidence hybrid model was built. Then the hybrid model was transformed into a series of probability-interval models in subspaces and a nested optimization analysis iterative format was summarized to obtain the failure probability interval. At last, three numerical examples were provided to verify the validity of the proposed method.