基于随机集理论的相关变量模型不确定性量化

Model Uncertainty Quantification for Dependent Variables Based on Random Set Theory

随机集理论为基于模型的系统分析提供了一种统一的不确定性量化框架。针对现有随机集理论模型不确定性量化研究中缺乏对模型变量相关性的考虑这一不足,提出了一种改进的基于随机集理论的不确定性量化方法。该方法根据模型变量间的相关系数信息,通过Nataf变换产生相关随机样本,进而获取多维空间内焦元的联合基本概率分配。由此所得的不确定性量化结果能够在模型变量间存在相关性的情况下正确反映系统状况。数值仿真证明了所提方法的有效性。

Random set theory provides a uniform mechanism for model uncertainty quantification in system analysis. An improved method was proposed based on random set theory for uncertainty quantification considering the dependence among system variables. The Nataftransformation was used to generate dependent random samples to be consistent with correlation coefficients information, and then the joint basic probability assignments for the multidimensional focal elements were calculated to construct the random set. The result of uncertainty quantification based on the random set can reflect the real system response under dependent variables. Simulation results show the presented method rationality.