Analyses for lower and upper bounds of sobol' total sensitivity index based on derivative

Abstract

以Sobol’主测度指标Si作为总测度指标Stoti的下限,建立并推导了基于偏导数的测度指标作为Stoti的新上限。基于泛函和Euler-Lagrange等式,进行了不同变量分布形式下(均匀、正态、指数、Beta、三角分布等),Sobol’总测度指标Stoti的基于偏导数的上限分析,并给出了新上限详细的推导过程和具体的计算公式。通过简单数值和工程算例,验证了新上限的精度及效率,为更准确地界定总测度指标Stoti的取值区间提供了参考。 A main sensitivity index Si was set as the lower bound of Sitot and the new upper bound of Sitot was built based on the derivative. On the basis of functional analysis and Euler-Lagrange equation, the new upper bound of Sitot based derivative was analyzed for different variable distribution types, such as uniform, normal, exponential, triangular, Beta distribution etc. The derived process and formulas were presented in detail. Several numerical and engineering examples were used to verify the precision and efficiency of the presented bounds, which may provide the accurate bounds of Sitot.