Multi-objective uncertain optimization with an ellipsoid-based model of a centrally symmetrical square tube with diaphragms for subways

Deterministic optimization has been successfully applied to a series of design problems of square thin-walled energy absorption tubes and to a certain extent has fulfilled great expectations for the application of such structures in subway vehicles. However, most studies have not considered the uncertainty of parameters or the correlation of uncertainty parameters, leaving little or no tolerance and resulting in over-conservative structural design. This research proposes a multi-objective uncertain method with an ellipsoid-based model to address the effects of parametric uncertainties of a centrally symmetrical square tube with diaphragms (CSSTD) on design optimization, in which the ellipsoid model is adopted to describe the related uncertainty parameters. The nonlinear interval number programming method coupled with a reliability-based possibility degree of interval (RPDI) model is introduced to handle the transformation of uncertain optimization problems. Simultaneously, local-densifying technology is adopted to enhance the local accuracy of the approximate model. Finally, the outer layer of the micro multi-objective genetic algorithm ( μ MOGA) combined with the inner layer of the intergeneration projection genetic algorithm (IP-GA) is applied to solve the Pareto optimal solution set of the transformed deterministic optimization. The optimization results indicate that the proposed multi-objective uncertain optimization with an ellipsoid-based model not only guarantees the crashworthiness of the CSSTD, but also improves the design robustness, which means that the proposed method can provide insightful information for crashworthiness design of subways.