Design of locally resonant acoustic coatings using Bayesian inference

A Bayesian approach for the inverse design of acoustic coatings for broadband sound absorption is presented. The acoustic coating comprises a soft viscoelastic material submerged in water and attached to a steel backing plate. The coating is embedded with layers of resonant inclusions corresponding to cavities and hard scatterers yielding monopole and dipole sound scattering, respectively. The acoustic performance of the coating is primarily governed by strong wave scattering at frequencies around the resonance frequency of the inclusions, and enhanced wave scattering due to resonance coupling between adjacent inclusions. Designing an acoustic coating for a targeted performance presents a challenge due to the competing and often conflicting influence of several coating parameters corresponding to the material properties of the coating, the geometric and material properties of the inclusions, and the number of inclusion layers. This challenge is addressed using a dual-level Bayesian inference approach for targeted performance based on sound absorption by the coating. Parameter estimation is employed to determine the geometric dimensions of the inclusions within each layer, while model selection identifies the number of inclusion layers and material of the inclusions within each layer. The dual-level Bayesian approach is validated against coating designs of increasing complexity. By exploiting the resonances associated with different designs, a physics informed design of a coating with high broadband sound absorption is proposed.