A machine learning based optimisation method to evaluate the crushing behaviours of square tubes with rectangular-hole-type initiators

Rui Liang, Fengxiang Xu, Na Liu, Xiang Liu, Christophe Bastien, Cheng Zhang

Research output: Contribution to journalArticlepeer-review


Rectangular-hole-type crush initiators have attracted much attention due to their exceptional advantages in improving crashworthiness performance. Unfortunately, undesired deformation buckling modes, i.e. bifurcation buckling, can occur and challenge optimisation processes. This paper aims remedies to this limitation and proposes a machine learning based optimisation method that removes these undesired deformation modes to effectively evaluate the effect of initiators’ parameters in improving crush response. First, finite element models of square tubes with different numbers and positions of initiators were built and computed. Second, the complex proportional assessment (COPRAS) method was adopted to rank the crashworthiness characteristics. The results demonstrated that square tubes with two sets of four corner holes along the axial direction were the best choice. Finally, the optimisation method based on machine learning was employed to evaluate the influence of the initiator’s size on the crushing behaviours for minimizing the initial peak force (IPF), maximizing the energy absorption (EA), and crushing force efficiency (CFE). The results illustrated that the IPF of the optimised design Pareto front upper limit is about 21.94% lower, with 0.08% and 36.67% higher EA and CFE, respectively, than those of the best choice observed from COPRAS. This study highlights the ability of the proposed machine learning based optimisation method to improve crashworthiness performance.

Original languageEnglish
Pages (from-to)115-131
Number of pages17
JournalInternational Journal of Crashworthiness
Issue number1
Early online date30 Mar 2023
Publication statusPublished - 2024


This paper is supported by the National Natural Science Foundation of China (Grant No. 51605353) and Middle-aged Teachers’ Basic Research Ability Improvement Project (Grant No. 2022KY0781).


  • Machine learning
  • crashworthiness performance
  • deformation mode
  • rectangular-type crush initiator

ASJC Scopus subject areas

  • Transportation
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


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