Correction of the Eyring Reverberation Time Formula Using an Artificial Neural Network: A One-Solution Approach

The first part of this paper presents the classical Eyring formula used for estimating the reverberation time T<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60</inf> of a room. An experimental study to assess T<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60</inf> using the classical Eyring formula was performed. The Schroeder algorithm to estimate T<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60</inf> from the Room Impulse Response (RIR) was also applied. The second part of the paper introduces a corrected Eyring formula obtained by multiplying the original Eyring formula by a correction coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{\text{Eyr}}$</tex>, parameterized by the coefficients <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta, \gamma$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${\delta}$</tex>. Using an Artificial Neural Network (ANN), the parameters <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${\beta}, {\gamma}$</tex>, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${\delta}$</tex> were computed. An ANN training procedure on the dataset <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{D}_{\text {train }}$</tex>, consisting of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N=25401$</tex> RIRs, was performed. The corrected Eyring formula to test on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M=10887$</tex> RIRs was then applied. The mean absolute error <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\overline{{e}}$</tex> and the mean squared error MSE <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${ }_{\text {Eyr }}$</tex> as evaluation metrics for reverberation time estimation were used. The experimental results with graphs and a table are presented. A detailed comparative analysis shows that the corrected Eyring formula improves the precision of reverberation time estimation by 51.38 % compared to the classical Eyring formula was performed.