A Single Number Index to Assess Selected Acoustic Parameters in Churches with Redundant Information

Abstract

The paper presents an innovative approach for the index assessment of the acoustic properties of churches. A new formula for an approximate single number index to assess selected acoustic parameters of church interiors, such as reverberation time (RT), speech intelligibility index (RASTI) and music clarity index (C80), is presented in the paper. The formula is created by means of the Singular Value Decomposition (SVD) method. An innovative approach for calculating the weights of partial indices is shown by solving the problem of redundant information, i.e., the system of overdetermined linear equations, using a computed pseudoinverse matrix. The new procedures for calculating the values of three partial indices and the single number index to assess selected acoustic parameters are presented. The proposed method was verified by measurements in several selected churches.

Singular Vectors in Acoustic Simulation Tests of St. Paul the Apostle Church in Bochnia

“…A much more useful tool for quick single number assessment of the state of any object would be a universal equation, which is easy to apply and does not require knowledge of the SVD technique. The way to obtain such a universal equation for real objects, based on three partial indices, was shown in the article (Kosała, 2011). In this way (like in (Kosała, 2011)), weights necessary for the application of Eq.…”

“…The method is still being improved by using the SVD technique (Kosała, 2007;2008a;2008b;2009;2011). Singular vectors and singular values obtained from Singular Value Decomposition of the Index Observation Matrix (IOM) are used to build the global index.…”

“…The procedure for calculating the weight of partial indices, described and applied in (Kosała, 2011) uses the SVD technique to solve the issue of redundant information, where the number of linear equations is greater than the number of unknowns -weights.…”

“…Calculation procedures of the partial indices W R , W M and W S were described in detail for 6 churches in (Kosała, 2011).…”

Numerical Compensation of Air Absorption of Sound in Scale Model Measurements

“…They can be considered to be a complement to other tools applied for an enclosure analysis and design from an acoustical point of view (see, e.g. Carvalho, Silva, 2010; Kosała, 2011). Thus, the scale models still have a very special position in practice (Gade, 2007).…”