多项式输出中相关变量的结构贡献和相关贡献分析

以二次不含交叉项的多项式为例,解析推导了正态相关输入变量对输出响应量方差贡献的结构贡献部分和相关贡献部分。通过算例验证了解析结果的正确性。将所研究的指标和已有的进行对比,归纳出结构贡献部分和相关贡献部分的侧重与统一。解析解可直接用于极限状态函数不超过两次且不含交叉项的结构和相关贡献的识别,为其他新的数值算法提供了参考对照。

Analysis of structural and correlative contributions by correlated variables in polynomial output

In order to distinguish the structural contribution and the correlative contribution of correlated input variables on the output, the polynomial outputs are investigated. Then for the quadratic polynomial without cross terms outputs, the analytical solutions are derived on the condition of the correlated normal input variables. The numerical results of several examples validate the correctness of analytical solutions. Comparing the presented indices with the existent indices, some general conclusions are drawn and the differences of them are identified. The analytical solutions derived in this work can be conveniently used to identify the structural contribution and the correlative contribution of the quadratic polynomial without cross-terms, which offer the comparison for the novel numerical algorithm.