不确定性参数灵敏度分析的随机响应面法

动力学和控制系统中往往包含有不确定性参数,为此提出了一种基于随机响应面的不确定性参数灵敏度分析方法,以量化参数不确定性对响应变异性的影响.文中首先利用随机响应面建立不确定性参数和响应之间的表达式,然后通过求偏导方式推导参数的灵敏度系数,该系数综合反映了参数均值和标准差的影响.最后通过一根包含几何、材料不确定参数的数值梁来验证所提出方法,并与方差分析法结果进行了比较.

Stochastic response surface based sensitivity analysis of uncertain parameters

Dynamic and control systems often contain uncertain parameters that may result in uncertain predictions. In the interest of quantifying the effects of parameter uncertainties on response variability, this paper develops a stochastic response surface based method for the sensitivity analysis of uncertain parameters. Stochastic response surfaces were firstly constructed to describe the explicit relationships between uncertain parameters and responses. Then partial derivations were performed on the mathematical expressions of stochastic response surfaces in order to obtain sensitivity indices that simultaneously embody the effects of parameter means and standard deviations. Lastly, the developed method has been verified against a numerical cantilever beam containing uncertain geometric and material parameters. The sensitivity analysis results were compared with those given by the analysis of variance method.