Structural and Multidisciplinary Optimization

, Volume 58, Issue 5, pp 2291–2308 | Cite as

Crashworthiness optimisation of a composite energy-absorbing structure for subway vehicles based on hybrid particle swarm optimisation

  • Suchao Xie
  • Haihong Li
  • Chengxing Yang
  • Shuguang Yao


To improve the crashworthiness of subway vehicles, a composite energy-absorbing structure (EAS) is designed by coupling a thin-walled metal tube and aluminium honeycomb structures. On this basis, the effectiveness of the composite structure and aluminium honeycomb finite element model (FEM) is validated by conducting trolley impact tests and quasi-static compression experiments. Based on the verified FEM, the surrogate models, including polynomial response surface (PRS), Kriging, radial basis function (RBF) and supported vector regression (SVR), are established to get the relationship between crashworthiness indexes and design variables. Then, the most accurate model is employed for crashworthiness optimisation through comparing the accuracies of these four models. Owing to the mutually effects among components of the composite EAS and the relatively complex mathematical formulae acquired by the high-precision surrogate model, a hybrid particle swarm optimisation (HPSO) algorithm is put forward. The performance of the HPSO is tested by a typical engineering optimisation case. The results indicate that the HPSO algorithm presents various advantages (e.g. strong global search capability, high optimisation accuracy, etc.). By optimising the mathematical model of the composite EAS, the optimal configurations of the structure are obtained, which confirms that the HPSO algorithm has favourable applicability and performance in the crashworthiness optimisation of the EASs for subway vehicles.


Composite energy-absorbing structure Impact test Surrogate model Hybrid particle swarm optimisation Global search 



This research was undertaken at Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, China. The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Grant no. 51775558), the supported by Innovation-Driven Project of Central South University (No. 2018CX023) and the support from the Shenghua Yu-ying Talents Program of the Central South University (Principle Investigator: Prof. Suchao Xie). The corresponding author would like to acknowledge the China Scholarship Council/University of Manchester Joint Scholarship for PhD study (201706370205).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Suchao Xie
    • 1
    • 3
  • Haihong Li
    • 1
    • 3
  • Chengxing Yang
    • 2
  • Shuguang Yao
    • 1
    • 3
  1. 1.Ministry of EducationKey Laboratory of Traffic Safety on Track (Central South University)ChangshaChina
  2. 2.School of Mechanical, Aerospace and Civil EngineeringUniversity of ManchesterManchesterUK
  3. 3.School of Traffic & Transportation EngineeringCentral South UniversityChangshaChina

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