Application of principal component analysis to the airborne sound insulation of gypsum board partitions

摘要

In this paper the information lost when a single number rating (Rw or STC) instead of sound reduction index curves are used, is quantified by using a novel statistical technology named Functional Data Analysis. This statistical technique works with observations constituted by a function instead of by discrete values. To describe the functions, Principal Component Analysis is used. The statistical analysis is applied to uncoupled gypsum board partitions. The analysis of principal components shows that is possible to represent one sound reduction index curve by means of only two indices, that are able to retain 99% of the original information (measured like explained variance) of a family of partitions with similar characteristics. The first identified component explains the majority of the variability of the curves family (95% of the total variance). It is a global insulation factor that quantifies the airborne sound insulation of a partition and the correlation with R, and STC ratings is higher than 0.98. The second one is related with the isolation at low frequencies. From these indices, predictive empirical models, based on the physical characteristics of the partitions, can be defined to estimate the sound reduction index curves.