大系统建模中的主成分分析法

Analytical Method of Principal Components in Large-scale Systems Modelling

大系统、尤其是社会经济大系统建立数学模型是困难的,难点在于大系统中变量多,变量之间关系复杂,而且对大系统运行机制也不完全了解。而目前由观测数据直接建立数学模型的方法还基本上属于尝试法,即便最简单的多项式模型种类在次数不变的情况下也随变量的增加而惊人地增加,计算工作量迅速达到无法忍受的程度。因此努力将系统划分成较小的部分分别建立数学模型,再加以拼装调整一直是大系统建模的一个主要方法。但既能把大系统分解成若干个关联较少的子系统,而又不借助于定性知识的方法还不成熟。

While retaining principal informmation ,the analytical method of principal cornpo-nents(AMPC)has the function of compressing the number of variables. This paper proves that AMPC describes the distribution of the sample points in sammple space. Therefore AMPC can be widely applied to the large-scale systems modelling, especially to modelling for analysis and evaluation.In addition the paper presents two successful examples in the analysis and evaluation of scientific and technical statistics by applying AMPC.