随机和认知不确定性量化的置信区域法

Confidence Region Method for Quantification of Aleatory and Epistemic Uncertainty

针对非线性机械系统中混合不确定性量化的问题,提出了随机和认知不确定性量化的置信区域法。首先,分别用概率论方法和区间方法来处理混合不确定性中的随机不确定性和认知不确定性,得到混合不确定性的置信区域;然后,为了在时间域内对不确定性进行传播,对传统双层循环蒙特卡罗抽样方法进行了改进;最后,以非线性质量-弹簧-阻尼系统为例讨论了基于混合不确定性分析方法的有效性。结果表明,同时考虑随机不确定性和认知不确定性,有利于提高系统设计的可靠性,为非线性机械系统的设计与精度分析提供了理论依据。

Focusing on the quantification of mixed-uncertainty in nonlinear mechanical systems,a confidence region method for the quantification of aleatory and epistemic uncertainty is presented.In this method,interval analysis is used to represent epistemic uncertainty while probability theory is used to represent aleatory uncertainty,in order to obtain the confidence region of mixed uncertainties.Then,the traditional double-loop Monte Carlo sampling approach is improved to propagate uncertainties during the entire time domain.Finally,a nonlinear mass-spring-damper system is simulated to discuss the validity of the analysis method based on mixed-uncertainty.The results show that it can improve the reliability of the system′s design when both aleatory and epistemic uncertainties of the parameters are considered,and can set a theoretical foundation for the dynamic design and precision analysis of nonlinear mechanical systems.