认知不确定性下可靠性灵敏度分析的新指标

传统的可靠性灵敏度指标只考虑了随机不确定性,当结构中还存在认知不确定性时,该指标难以反映出基本变量中认知不确定性对结构可靠性评估结果的影响程度.针对这一问题,引入概率包络来表达结构中的随机不确定性和认知不确定性,在此基础上建立了可靠性灵敏度分析的新指标——认知灵敏度系数,给出了其定义和代表的意义,并基于证据理论提出了认知灵敏度系数的计算方法.算例分析表明,认知灵敏度系数可以反映出基本变量中认知不确定性对结构可靠性评估结果的不确定性的影响程度,从而为有针对性地提高可靠性评估结果的准确性提供依据.另外,基于证据理论的认知灵敏度系数的计算方法适用于极限状态函数为单调、非单调的结构,以及变量服从正态、非正态的结构,具有普适性.

New Index for Reliability Sensitivity Analysis Under Epistemic Uncertainty

Conventional index for reliability sensitivity analysis considers only aleatory uncertainty, which cannot show the impacts of epistemic uncertainty in basic variables on structural reliability in the condition of epistemic uncertainty. In view of this, probability boxes are introduced to represent aleatory and epistemic uncertainties in structure, on the basis of which a new index for reliability sensitivity analysis, epistemic sensitivity coefficient, is constructed. The meaning and significance of the new index are explained, and a method based on evidence theory is proposed to calculate it. Numerical examples show that the new coefficient can reveal the contribution of each basic variable to the uncertainty of structural reliability, and it provides a direction to improve the accuracy of reliability calculation. The simulation results also show that the proposed method of epistemic sensitivity calculation is applicable to structures with monotonic as well as non-monotonic limit state equations, and with normal as well as non-normal variables.