无量纲化方法选择及最优无量纲化方法构建  

Selection of Dimensionless Method and Construction of Optimal Dimensionless Method

作　　者：高晓红[1] 李兴奇[2] Gao Xiaohong;Li Xingqi(School of Mathematics and Computer Science,Chuxiong Normal University,Chuxiong Yunnan 675000,China;School of Management and Economics,Chuxiong Normal University,Chuxiong Yunnan 675000,China)

机构地区：[1]楚雄师范学院数学与计算机科学学院,云南楚雄675000 [2]楚雄师范学院管理与经济学院,云南楚雄675000

出　　处：《统计与决策》2024年第4期44-49,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(11261001);云南省地方本科高校基础研究联合专项面上项目(202301BA070001-054,202301BA070001-059)。

摘　　要：文章针对综合评价过程中无量纲化方法难以选择的问题,首先,基于分布特征不变性和变异特征不变性对无量纲化方法进行初步筛选,结果发现,只有伸缩法能同时保持指标的分布特征和变异特征不变;其次,构建无量纲化有效性的统计检验方法,并检验各种伸缩法的有效性,结果发现,并非所有的伸缩法都能有效消除指标间的量纲差异;然后,建立无量纲化信息损失速率的度量模型,提出无量纲化方法选择的主要步骤,并以无量纲化应在有效消除指标间量纲差异的情况下尽可能减小指标内的信息损失速率为原则,构建一种最优无量纲化模型;最后,通过大量的数值模拟实验来进行无量纲化方法选择,并求解最优无量纲化模型。结果发现,基于以上步骤能更加科学准确地进行无量纲化方法选择;构建的最优无量纲化方法不同于任何一种现有的无量纲化方法,其不仅可以有效消除指标间的量纲差异,而且可以防止对数据的过度处理,造成不必要的信息损失。In order to solve the problem that it is difficult to select the dimensionless method in the comprehensive evaluation process,firstly,the dimensionless methods are preliminarily screened based on the distribution characteristic invariance and variation characteristic invariance,only to find that only the scaling methods can keep the distribution characteristics and variation characteristics unchanged at the same time.Secondly,a statistical test method for the effectiveness of the dimensionless methods is constructed,and the effectiveness of various scaling methods is tested,the results show that not all scaling methods could effectively eliminate the dimensional difference between indicators.Then,the measurement model of the dimensionless information loss rate is established;the main steps of dimensionless methods selection are proposed,and an optimal dimensionless model is established based on the principle that the dimensionless methods should reduce the information loss rate within the indicator while effectively eliminating the dimensional difference between indicators.Finally,a large number of numerical simulation experiments are carried out to select the dimensionless method and solve the optimal dimensionless model.The research results indicate that based on the above steps,the dimensionless method selection can be carried out more scientifically and accurately,that the optimal dimensionless method constructed is different from any existing dimensionless methods,which can not only effectively eliminate the dimensional difference between indicators,but also prevent the excessive processing of data from resulting in unnecessary information loss.

关 键 词：无量纲化 有效性检验 信息损失速率 数值模拟实验 

分 类 号：C812[社会学—统计学] O213.9[理学—概率论与数理统计]