随机和认知混合不确定系统的全局灵敏度分析方法

Approach to global sensitivity analysis of hybrid uncertain system with aleatory and epistemic uncertainties

为计算具有随机不确定性和认知不确定性的混合不确定系统灵敏度,提出一种基于证据理论和条件概率理论的全局灵敏度分析方法.用证据理论对认知不确定性变量进行表征,并提出两种基于证据理论的随机采样方法,包括一次随机抽样法和二次随机抽样法.运用条件概率理论,提出存在认知不确定性条件下混合不确定系统的Sobol＇全局灵敏度指标,经过理论推导给出一阶灵敏度及总灵敏度的计算公式,并设置单循环的拟蒙特卡罗方法实现灵敏度的近似数值计算.开发了灵敏度分析程序,并给出了典型应用实例.实例表明,新方法的分析结果正确,计算工作量可控.

To compute the sensitivity of the hybrid uncertain system in which both aleatory and epistemic uncertainties are present, a global sensitivity analysis method is proposed on the basis of evidence theory and conditional probability theory. The aleatory uncertain variables are represented by using the evidence theory. For epistemic uncertain variable, two stochastic sampling approaches based on the evidence theory are put forward, which are named one-step and two-step random sampling approach, respectively. With the conditional probability theory and the Sobol＇ method used, the global sensitivity indexes of the hybrid uncertain system are proposed in the presence of epistemic uncertainties, and the formulas of the first-order and total sensitivity indexes are derived. A single-loop quasi-Monte Carlo simulation is developed and it is used to approximately calculate the sensitivity indexes proposed. The sensitivity analysis program based on Matlab is designed. A typical example is presented and its results show that the proposed method is correct and its computational cost is acceptable.