Stochastic multiscale simulation of porous sound absorbing materials based on a Bayesian approach method

This study describes a method for probabilistically predicting the acoustic properties of porous sound-absorbing materials. Porous materials consist of complex microstructures, and homogenization methods can predict their dynamic properties. However, it is difficult to consider the randomness of the microstructure as in actual porous materials. This randomness affects the acoustic characteristics of the sound-absorbing material. Therefore, we propose a method to consider randomness in the homogenization unit cell and calculate the probability distribution of the sound absorption characteristics. The balance of computational cost with prediction accuracy is essential in predicting stochastic behavior in the multiscale simulation. Thus, we propose a Bayesian approach to achieve both computational cost and prediction accuracy. Random variables are assumed to be the microstructure shape parameters. The product of these probability density functions and the sound absorption coefficient is integrated to calculate the probability distribution of the sound absorption coefficient. The function of the sound absorption coefficient is approximated to calculate this integral by Gaussian process regression. This integral value follows a gauss distribution, and its variance is evaluated as the correctness of the approximation of the integral value. We define this variance as an acquisition function and adaptively obtain additional sampling points where it is minimized. Then, the sound absorption coefficient is recalculated with multiscale simulation at additional points to update the approximate model. Repeating these processes allows the probability distribution to be approximated with reasonable accuracy.