Design and optimization of corrugated multi-cell gradient structures based on machine learning

To address the collision protection requirements in fields such as aeronautics and space, traffic transportation, and civil construction, a novel design method for the corrugated multi-cell gradient hexagonal tube (CMGHT) was proposed. The sinusoidal corrugated ribs were introduced into a conventional hexagonal tube, integrated with the functional gradient design concept to improve the energy absorption performance of the structure. First, the finite element model of the structure was established and numerical simulation analysis was conducted. Results indicate that under the same wall thickness condition, the key energy absorption indicators of CMGHT outperform existing structures significantly. Compared with the hexagonal tube (HT), the energy absorption (E_a), specific energy absorption (E_sa), mean crushing force ( $\overline{F}$), and crushing force efficiency (η) are improved by 390%, 76%, 395%, and 46%, respectively; Compared with the multi-cell hexagonal tube (MHT), the aforementioned indicators are increased by 121%, 58%, 121%, and 97%, respectively; Relative to a corrugated multi-cell hexagonal tube (CMHT), the enhancements are 7%, 7%, 8%, and 33% respectively, while the initial peak crushing force (F_max) is decreased by 18%. These results fully demonstrate its superior energy absorption performance. Subsequently, the geometric parameters of the ribs and outer tube were selected as design variables. A total of 540 sample sets were generated via full factorial experimental design, and a support vector machine (SVM) surrogate model was constructed. Combined with the crested porcupine optimization (CPO) algorithm, model optimization was completed to achieve the accurate prediction of the crashworthiness indicators for CMGHT. Finally, the multi-objective coati optimization algorithm (MOCOA) was adopted for multi-objective optimization to obtain the optimal combination of characteristic parameters. The optimization results show that compared with the CMGHT basic model without parameter optimization (the parameters are initially set based on the common range of engineering: rib thickness of 1 mm, rib amplitude of 3 mm, outer tube gradient thickness of 0.5 mm-1 mm-1.5 mm, outer tube length of 33.3 mm), the E_sa of the optimized structure is increased by 22%, the η is increased by 53%, and the $\overline{F}$ is increased by 270%, which further verifies the effectiveness of the design method.