Metamodeling and optimisation of a sonic crystal-based noise attenuation device

The present paper takes a first step to the development of a metamodel-based optimisation framework for the design of sonic crystal-based noise attenuation devices. Sonic crystals are peculiar tailored materials, made of rigid inclusions periodically arranged in a fluid medium (air, in this work), which allow to inhibit acoustic wave propagation in certain frequency ranges, depending on their geometric features, relying on a Bragg scattering process. The optimisation process starts by performing a Latin hypercube sampling of the design space to assemble the first training set. For the resulting geometries, finite element simulations compute the acoustic attenuation in terms of insertion loss of the corresponding bidimensional semi-infinite crystals. A metamodel approximates the device response, interpolating the obtained results, and a genetic algorithm is run with the surrogate to find the optimal designs. Cross-validation is applied for metamodel assessment, and error metrics are computed to determine the accuracy of the surrogate predictions. Several designs of the attenuation device are taken into account, varying the scatterers dimensions and arrangement. The objective function of the optimisation process is the mean value of the insertion loss provided by the device in a given frequency range of interest.