Abstract

Dimensional analysis transforms a dimensionally homogeneous model into its simplest form; the number of input variables can be reduced. Such a reduction is very helpful in statistical design and analysis. Although the Buckingham π theorem provides a method of transforming the model based on the basis quantities (BQ’s), the choice of the BQ’s in general is not unique. In practice, a different choice of the BQ’s may lead to a different performance in statistical analysis. A new criterion, based on the BQ’s with a small coefficient of variation, is proposed to choose the optimal BQ’s. It is anticipated that such a criterion will be popularly used in practice. The distribution of the newly proposed criterion is derived to statistically differentiate the performance via different choices of the BQ’s. Three case studies are provided for illustration.

摘要

维数分析将维同质模型转化为最简单的形式；可以减少输入变量的数量。这种减少对统计设计和分析非常有帮助。虽然白金汉π定理提供了一种基于基本量 (BQ) 的模型转换方法，BQ 的选择通常不是唯一的。在实践中，BQ 的不同选择可能会导致统计分析中的不同性能。提出了一种基于变异系数较小的 BQ 的新标准来选择最佳 BQ。预计这种标准将在实践中广泛使用。推导出新提出的标准的分布，以通过 BQ 的不同选择在统计上区分性能。提供了三个案例研究以供说明。