Synthesis of Uncorrelated Acoustic Quality Evaluation Indices of Buildings

Abstract

Previous studies and analyses conducted up to now on the indicatory description of the acoustic quality of buildings concerned single value indices based on several selected acoustic parameters that are correlated with each other. Transformation of values, correlated into a new set of independent components for the purpose of their future synthesis, took place using the Singular Value Decomposition (SVD) technique. In this article, it is shown that SVD can also be applied to the determination of the single-value global acoustic quality index in the case where the decomposed index observation matrix contains partial indices that are not only correlated, but also uncorrelated. Alternatively, a statistical method used in econometrics, i.e. Comparative Multivariate Analysis (CMA), was adapted to obtain a single-value index from uncorrelated partial indices. Both proposed methods of synthesis have been veried using the example of a group of buildings Roman Catholic churches.

The Comparative Analysis of Acoustic Properties of Roman Catholic Churches Using the Index Method

“…The correlated indices R, M , and S are reduced using the SVD technique to the single-number RM S index. Next, the weights of each of the uncorrelated indices, RM S, D, and S T , are calculated using the method of Comparative Multivariate Analysis (CMA) described in [11].…”