线性无量纲化方法的结构稳定性分析

Structure Stability Analysis of Linear Dimensionless Methods

针对多种无量纲化方法共存却无统一的优劣甄别标准问题,对几种常用的线性无量纲化方法的稳定性进行分析,在此基础上,提出了一种新的无量纲化方法。界定了稳定性分析视角为噪声干扰,即异常值的出现对于数据无量纲化结果的影响;对无量纲化方法的稳定性测度进行了定义,并基于蒙特卡罗仿真的思想给出了对无量纲化方法稳定性进行测度的标准仿真策略,据此对无量纲化方法的稳定性进行分析及比较,并给出相关结论;在此基础上,提出了一种新的且具有较高稳定性的无量纲化方法。

For the problem of coexistence of multiple dimensionless methods without standard discrimination rule, we study the stability of a few linear dimensionless methods, and propose a new dimensionless method. First, we analyze stability from the aspect of ＂noise interference＂, that is the effect to dimensionless results for ＂extreme value＂ appearing. Then, we define a stability measure and develop the normalized simulation policy for surveying dimensionless methods stability based on Monte Carlo simulation. We use it to analyze and compare dimensionless methods stability and generalize several conclusions. We thus propose a new dimensionless method with higher stability as well.