Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials

Abstract

Recently, an increasing research effort has been dedicated to analyse the transmission and dispersion properties of periodic acoustic metamaterials, characterized by the presence of local resonators. Within this context, particular attention has been paid to the optimization of the amplitudes and center frequencies of selected stop and pass bands inside the Floquet-Bloch spectra of the acoustic metamaterials featured by a chiral or antichiral microstructure. Novel functional applications of such research are expected in the optimal parametric design of smart tunable mechanical filters and directional waveguides. The present paper deals with the maximization of the amplitude of low-frequency band gaps, by proposing suitable numerical techniques to solve the associated optimization problems. Specifically, the feasibility and effectiveness of Radial Basis Function networks and Quasi-Monte Carlo methods for the interpolation of the objective functions of such optimization problems are discussed, and their numerical application to a specific acoustic metamaterial with tetrachiral microstructure is presented. The discussion is motivated theoretically by the high computational effort often needed for an exact evaluation of the objective functions arising in band gap optimization problems, when iterative algorithms are used for their approximate solution. By replacing such functions with suitable surrogate objective functions constructed applying machine-learning techniques, well-performing suboptimal solutions can be obtained with a smaller computational effort. Numerical results demonstrate the effective potential of the proposed approach. Current directions of research involving the use of additional machine-learning techniques are also presented.

Recent Advances in Acoustic Metamaterials for Simultaneous Sound Attenuation and Air Ventilation Performances

“…However, in the acoustic metamaterial research domain, the utilization of these techniques is at the initial stage. Numerous works have been reported in the acoustic metamaterial field [120][121][122][123][124][125][126][127][128]. Recently, Bianco et al [129] discussed the recent advances and transformative potential of machine learning (ML), including deep learning, in the field of acoustics.…”

Recent Advances in Acoustic Metamaterials for Simultaneous Sound Attenuation and Air Ventilation Performances

“…However, in the acoustic metamaterial research domain, the utilization of these techniques is at the initial stage. Numerous works have been reported in the acoustic metamaterial field [119][120][121][122][123][124][125][126][127]. Recently, Bianco et al [128] has discussed the recent advances and transformative potential of machine learning (ML), including deep learning, in the field of acoustics.…”

Convex combination of data matrices: PCA perturbation bounds for multi-objective optimal design of mechanical metafilters

“…This is the subject of investigation of our ongoing work [3]. So, for the case of the multi-objective optimal design of mechanical metamaterial filters, the application of PCA to the approximation of the sampled gradient field of a suitable associated single-objective function (which represents a proper trade-off between two or more different objectives) can be a valid alternative to the use of surrogate optimization methods (which replace the original objective function with a surrogate function, learned either offline [4] or online [2]), in case a gradient-based optimization algorithm is used to solve the optimization problem. It is also worth mentioning that this particular application of PCA to the multi-objective optimal design of mechanical metamaterial filters, combined with a multi-start optimization approach, has been the source of inspiration for the theoretical investigation made in the present article.…”

“…The theoretical framework considered in Sections 2 and 3 has application, e.g., in the combination of PCA with the so-called weighted sum method, which is used in the context of multi-objective optimization [6]. In the case of two objective functions, this method approximates the Pareto frontier of a multi-objective optimization problem by maximizing 4 , with respect to the column vector p ∈ P ⊆ R n , the trade-off…”