基于概率盒演化的时变系统不确定性量化方法

针对时变系统的不确定性量化和传递问题,提出一种概率盒演化方法.根据系统的时变规律,获取系统响应的累积分布函数随时间变化的规律.将认知不确定性参数和随机不确定性参数分离在外层和内层,用蒙特卡洛法量化外层的认知不确定性参数,用基于随机配点的非嵌入式混沌多项式法量化内层的随机不确定性参数,通过求取不同时刻系统响应的累积分布函数的上下边界创建时变概率盒.最后,通过一延时电路性能退化算例验证所提出方法的有效性.研究表明,时变概率盒不仅可以表征系统特定时刻的混合不确定性,而且反映了输出响应的时变规律和输出不确定性随时间变化的趋势.

Uncertainty quantification for time-variant system based on probability box evolution

A probability evolution method is proposed to quantify time-variant systems with mixed uncertainty based on a probability box. The cumulative distribution function(CDF) evolution is obtained from time-variant system response. The double-loop sampling method is used to separate for the epistemic uncertainties from the sampling of the aleatory uncertainties. The outer loop is for sampling of the epistemic uncertainties by Monte Carlo, and the inner loop is for sampling the aleatory uncertainties by a point-collocation non-intrusive polynomial chaos method. A time-variant probability box for system response can be obtained by the CDF boundary calculating at different time. The proposed method is verified through a delay performance degradation circuit. The studies demonstrate that the time-variant probability box not only quantifies the mixed uncertainty at each time, but also reflects the system response and uncertainty changing with time.