Global index of the acoustic quality of sacral buildings at incomplete information

Abstract

The global assessment of acoustic quality of sacral building was, up to the present, performed when the full information about the object - determined by partial indices calculated from the measurements of acoustic parameters - was known. The formula for calculating the global index of acoustic quality at incomplete information by means of the Singular Value Decomposition (SVD) is given in the paper. Having only one of the indices - the reverberation index - it is possible to approximately assess the acoustic quality of the church. Application of the SVD method required certain modifications of the previously proposed index method. The technique of decomposition into singular values enabled the transformation of initial variables being in the form of correlated indices - into mutually orthogonal new variables. The decomposition versus singular values was done on the previously built empirical model of the index observation matrix of sacral objects. Due to this operation the weight values, which were applied in the global assessment of acoustic quality of sacral objects, were obtained. The approximate theoretical models containing information on interdependency of partial indices - were developed. The developed formula for the global assessment of acoustic quality - at incomplete information on the sacral object - was applied for comparing acoustic qualities of ten churches.