Reconstruction of the interior sound pressure of a room using the probabilistic approach

In this paper, a probabilistic approach is introduced and used to find the optimal values assigned to the uncertain parameters of a room acoustic model, which is used for the reconstruction of the interior sound pressure distribution. The acoustic model selected here to examine the capacity of the probabilistic approach is a rectangular room with two air leakages that is subject to an external uniform noise. The model is set up using the modal analysis method. The values of the uncertain parameters of the model are identified using the time domain sound pressure responses at selected measurement points. In the simulation results, the comparisons between the proposed approach and the typical least error square method show that the former clearly assigns optimal values to the uncertain model parameters for the best prediction, while the latter generates a set of values for which the prediction errors are very similar and close to the minimum (in other words, it is difficult to identify the optimal values using the least error square method). Moreover, the optimal values for the uncertain parameters can be found individually, unlike those from the least error square method. It is also found that the measurement points should not be located at the nodal points of the dominant acoustic modes; otherwise, the identification process becomes unidentifiable. For cases in which large modal truncation errors (or modeling errors) exist, the identification process also becomes unidentifiable.