Efficient dataset generation for inverse design of micro-perforated sonic crystals

Abstract

Micro-perforated panels (MPPs) used as scatterers in sonic crystals (SCs) provide design flexibility for acoustic applications. Achieving the sound attenuation within a specified frequency range requires an inverse design procedure that refines the geometric parameters of MPP-SCs. Although data-driven methods show considerable promise for solving such inverse design problems, the generation of a large, well-labeled dataset of MPP-SCs remains computationally intensive, posing a critical bottleneck in deep learning-assisted design of periodic structures. To evaluate the acoustic attenuation properties of MPP-SCs, their complex band structures are computed using the Finite Element Method (FEM). In order to enhance computational efficiency, an Interpolated Bloch Mode Synthesis (Interpolated BMS) method is developed within the FEM framework. This method integrates conventional BMS with the matrix interpolation technique. Specifically, the Craig-Bampton method is employed to reduce interior degrees of freedom (DOFs), while a B-spline-based approach is proposed for reducing boundary DOFs. Both steps decrease the dimensionality of the eigenvalue problem involved in calculating the complex band structure, thereby reducing the computational time from 14.86 s to 1.11 s without sacrificing numerical accuracy. Subsequently, matrix interpolation is applied to estimate the reduced global matrices, thereby eliminating the need for re-meshing and re-assembling the matrices when the geometric parameters of the MPP-SCs are adjusted. As a result, the efficiency of training sample generation is enhanced by a factor of 14.4 compared to commercial software. The dataset generated by the proposed method is then utilized to determine the geometric parameters of the MPP-SCs through either meta-heuristic algorithms or a conditional generative neural network. Experiments are also conducted to verify the numerical results and the inverse design results.