变量相关情况下方差贡献的参数影响分析

为控制输出方差需进行输入变量对输出方差的贡献分析, 而输入变量对输出方差的贡献由其分布参数决定, 因此研究输入变量的分布参数对方差贡献的影响具有重要意义。该文针对二次不含交叉项的多项式, 将相关变量按照一定的次序变换成独立的变量, 推导了各变量对输出方差主贡献和总贡献对分布参数的灵敏度的解析解, 得到了基本正态相关变量的分布参数对方差贡献的影响的一般规律, 并对这些规律进行了分析解释, 指出了所得规律的应用价值。最后应用数值算例和工程算例验证了所推得解析解的正确性和合理性。

ANALYSIS OF THE INFLUENCE OF DISTRIBUTION PARAMETERS ON VARIANCE DISTRIBUTION

In order to control output variance, the variance contribution of inputs, determined by their distribution parameters, needs to be analyzed, thus the influence of input distribution parameters on variance should be investigated further. Focusing on the classical quadratic polynomial without cross-terms, correlated inputs are transformed into independent ones using the independent-orthogonalisation transformation, then the sensitivity of each input’s variance contribution and of the total variance contribution are derived analytically with respect to each distribution parameter. From the analytical solutions, the basic laws of how distribution parameters affect the variance contribution are developed and some explanations are given. At last, numerical and engineering examples are employed to demonstrate the accuracy and rationality of the analytical solutions.