对称性全局统计分析中的定理证明

Proof procedure of some theories in statistical analysis of global symmetry

证明了对称性全局统计分析方法中的几个重要定理,保证了任意系统函数能够进行正交对称分解,确保了系统函数方差分解公式成立,这些是对称性全局统计分析方法的核心基石.通过考察对称函数在整个系统函数中所起作用的大小,达到认识系统函数对称性的目的.实例表明,将贡献率的Monte-Carlo计算值作为全局分析中对称函数的敏感性度量指标,可以较好地刻画系统函数的对称性.

This research guaranteed orthogonal symmetry demonstration to any system function, ensured the formula of demonstration to system function variance. They are the kernel and foundation stone of statistical analysis of global symmetry. By studying how these symmetry functions work in the whole system function, the symmetry of system function can be understood better. As illustrated by the examples, it showed the symmetry of system function clearly by using the Monte-Carlo calculated value of contribution rate as the global sensitivity index of symmetry function.