Forward-backstepping design of phononic crystals with anticipated band gap by data-driven method

Phononic crystals are novel artificial materials characterized by the periodic arrangement of elastic materials within another elastic medium, which imparts exceptional features to the material, including the presence of band gaps. In order to obtain the phononic crystal structure possessing the desired features, standard design approaches typically involve iterative searches within an extensive design space which necessitates significant processing resources and expenses. This study introduces a novel approach, combining a convolutional autoencoder with deep neural network, to extract topological features of phononic crystal samples and conduct forward prediction of band gap distributions. Subsequently, the trained forward prediction model is employed as a substitute for finite element simulations to expedite the computation of the genetic algorithm’s fitness. For the first time, this study introduced a chromosome coding expansion strategy and a fitness gradient strategy which can effectively avoid the issue of stagnation occurring during the initial population evolution. In the on-demand design, the band gap average loss ratio amounts to 5.9%, while the average excess proportion stands at 8.92%. The computation time for this method is 7.5 times shorter than that of method using a genetic algorithm with a finite element model, based on the six cases prediction. The band gap frequency of the optimum structure with proposed method is 2.7 times lower and 73 times broader compared to the classical phononic crystal with square-shaped scatter with almost twice volume fraction, which less degrades the strength. This interactive approach offers a solution to the issue of the nonunique response-to-design mapping problem. This method is not solely restricted to on-demand design, but also has the capability to optimize the band gap of phononic crystals with specific configurations under constrained conditions. This advancement sets the stage for the development of a forward-backstepping interactive design approach for metamaterials.