非参数化概率盒下随机与认知不确定性的分离式灵敏度分析

Separating sensitivity analysis of aleatory and epistemic uncertainties in non-parametric probability-box

灵敏度分析(SA)能辨识影响复杂系统响应的关键参数,为系统的稳健设计提供决策依据。非参数化概率盒作为一种典型的不精确概率模型,可以同时量化随机和认知2类不确定性,且在实际工程中应用广泛。由于非参数化概率盒耦合了随机和认知不确定性,非参数化概率盒下灵敏度分析方法能阐明输入概率盒的随机和认知不确定性对系统响应不确定性的影响程度。从随机与认知不确定性分离式角度出发,提出了一种非参数化概率盒下分离式灵敏度分析(SSA)方法。构建了格点法和期望值法分离非参数化概率盒的随机和认知不确定性,采用双层嵌套不确定性传播算法建立输出响应的概率盒,提出了最大方差和面积度量指标分别衡量系统输入的随机、认知不确定性对输出的随机、认知不确定性的影响。以NACA0012翼型升阻比预测为例,分析了来流参数和湍流模型参数的随机、认知不确定性对升阻比的随机、认知不确定性的影响。

Sensitivity Analysis(SA)can identify the most important parameters affecting the complex system output to support robust design of a system.Non-parametric probability-box(P-box),as a typical imprecise probabilistic model,can effectively quantify both aleatory and epistemic uncertainties,therefore extensively used in engineering practices.As aleatory and epistemic uncertainties are coupled in P-boxes,sensitivity analysis under the P-box framework is essential to evaluate their contributions in input P-box variables to output.This study develops a Separating Sensitivity Analysis(SSA)method for aleatory and epistemic uncertainties of non-parametric p-boxes.Two methods,i.e.,grid point method and expectation method,are introduced to separate the input aleatory and epistemic uncertainties in input P-box variables,respectively.A double loop procedure is utilized to propagate the input uncertainties and build the output P-box.Two uncertainty measures,namely,maximum variance metric and area metric,are proposed to evaluate the effects of input aleatory and epistemic uncertainties on the output aleatory and epistemic uncertainties,respectively.The lift-to-drag ratio prediction of the NACA0012 airfoil is exemplified to analyze the contributions of aleatory and epistemic uncertainties of income flow parameters and turbulence model parameters to those of the lift-to-drag ratio prediction result.