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 引用本文: 郝文锐 吕震宙 魏鹏飞. 多项式输出中相关变量的重要性测度分析[J]. 力学学报, 2012, 44(1): 167-173.
Wenrui Hao Zhenzhou Lv Pengfei Wei. Importance measure of correlated variables in polynomial output[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(1): 167-173.
 Citation: Wenrui Hao Zhenzhou Lv Pengfei Wei. Importance measure of correlated variables in polynomial output[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(1): 167-173.

## Importance measure of correlated variables in polynomial output

• 摘要: 为了解决一般工程问题中输出量为多项式情况下相关正态输入变量的贡献识别问题, 以二次不含交叉项的多项输出量为例, 利用多维相关正态分布及其条件分布的性质, 解析地推导了相关正态输入变量对输出量总方差的独立贡献及相关贡献, 采用算例验证了所推导的解析表达式的正确性. 文中所推导的相关正态变量独立贡献和相关贡献的表达式可直接用于输出量为二次不含交叉项多项式或一次多项式情况下的输入变量贡献的识别,并且为其他新的算法提供了对照解, 另外此方法亦可以推广至含交叉项的高阶多项式, 解决更为复杂输出量情况下输入量的贡献识别问题.

Abstract: With the case of the quadratic polynomial outputs withoutcross-term, the correlated and uncorrelated contributions by correlatedinput variables to variance of output response are derived analyticallythrough the properties of the multi-dimensional correlated normaldistribution and conditional distribution. The results of examplesdemonstrate that the derived analytical expressions are correct. The derivedanalytical expressions can be used directly in recognition of thecontribution by input variables in quadratic or one-order polynomial outputwithout cross terms and can be compared for other new algorithms. Thismethod can also be extended to higher order polynomial with cross terms, tosolve the recognition of contribution by input variables in more complicatedoutputs.

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