Evaluation of the Effect of Uncertainties on the Acoustic Behavior of a Porous Material Located in a Duct Element Using the Monte Carlo Method

When studying porous materials, most acoustical and geometrical parameters can be affected by the presence of uncertainties, which can reduce the robustness of models and techniques using these parameters. Hence, there is a need to evaluate the effect of these uncertainties in the case of modeling acoustic problems. Among these evaluation methods, the Monte Carlo simulation is considered a benchmark for studying the propagation of uncertainties in theoretical models. In the present study, this method is applied to a theoretical model predicting the acoustic behavior of a porous material located in a duct element to evaluate the impact of each input error on the computation of the acoustic proprieties such as the reflection and transmission coefficients as well as the acoustic power attenuation and the transmission loss of the studied element. Two analyses are conducted; the first one leads to the evaluation of the impacts of error propagation of each acoustic parameter (resistivity, porosity, tortuosity, and viscous and thermal length) through the model using a Monte Carlo simulation. The second analysis presents the effect of propagating the uncertainties of all parameters together. After the simulation of the uncertainties, the 95% confidence intervals and the maximum and minimum errors of each parameter are computed. The obtained results showed that the resistivity and length of the porous material have a great influence on the acoustic outputs of the studied model (transmission and reflection coefficients, transmission loss, and acoustic power attenuation). At the same time, the other physical parameters have a small impact. In addition, the acoustic power attenuation is the acoustic quantity least impacted by the input uncertainties.