The acoustic diffusion equation model has been widely applied in various scenarios, but a larger prediction error exists when applied to underground spaces, showing a significantly lower characteristic of the sound pressure level in the later stage compared to field tests since underground spaces have a more closed acoustic environment. Therefore, we analyze the characteristics of underground spaces differentiating from aboveground spaces when applying the model and propose an improved model from the perspective of energy balance. The energy neglected in the calculation of the acoustic diffusion equation model is compensated in long channel underground spaces named "acoustic escape compensation". A simulation and two field experiments are conducted to verify the effectiveness of the proposed compensation strategy in long-channel underground spaces. The mean square error is used to evaluate the differences between the classical model and the improved model, which shows a numerical improvement of 1.3 in the underground field test. The results show that the improved model is more suitable for describing underground spaces. The proposed strategy provides an effective extension of the acoustic diffusion equation model to solve the problem of sound field prediction and management in underground spaces.
Keywords: acoustic diffusion equation model; compensation; long-channel type; underground space.