Multilayer Residual Perceptron as a Surrogate Model in Optimising the Geometry of a Periodic Beam

The paper presents an optimisation workflow for modelling of a periodic mechanical structure in the form of a multi-material, axisymmetric beam. The optimisation objective is to prescribe the positions and widths of selected band gaps within a target frequency range for three basic types of structural vibrations: flexural, longitudinal and torsional. The decision variables were geometric parameters of the unit cell and material properties of selected thermoplastics assigned to successive segments of the cell. The frequency characteristics of the beam were determined using the time-domain spectral finite-element method (TD-SFEM). This model was used to perform a sensitivity analysis using the Morris method, which showed the dominant influence of the beam geometry on the position and width of band gaps, with a relatively smaller role of material variability. Due to high computational costs of the global optimisation based on a FEM solver, a surrogate regression model in the form of a residual MLP network was developed to predict the positions and widths of the first five band gaps for each vibration type. The global search was carried out using a genetic algorithm (GA) with the surrogate model and then the results were refined using a deterministic goal-attainment method with a high-fidelity model.