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

Aug 4, 2026

Upload by Logic

Rectangular-hole-type crush initiators are examined for improving crashworthiness of thin-walled square tubes, while undesired deformation buckling modes such as bifurcation buckling can hinder optimisation. The study proposes a machine learning based optimisation workflow that suppresses these modes and evaluates how initiator parameters affect crushing response. Finite element models are used, COPRAS ranks crashworthiness characteristics, and an ML optimiser estimates optimal initiator size to minimize initial peak force, maximize energy absorption, and improve crushing force efficiency.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages33

Reading Time1 h 23 min

AccessFree to download

Abstract

Introduction

Background on thin-walled square tube crashworthiness

Role of crush initiators and configuration types

Rectangular-type initiators and deformation behavior

A machine learning based optimisation method to evaluate the crushing behaviours of square tubes with rectangular-hole-type initiators Liang, R., Xu, F., Liu, N., Liu, X., Bastien, C. & Zhang, C Author post-print (accepted) deposited by Coventry University’s Repository Original citation & hyperlink: Liang, R, Xu, F, Liu, N, Liu, X, Bastien, C & Zhang, C 2024, 'A machine learning based optimisation method to evaluate the crushing behaviours of square tubes with rectangular-hole-type initiators', International Journal of Crashworthiness, vol. 29, no. 1, pp. 115-131. [https://doi.org/10.1080/13588265.2023.2189000](https://doi.org/10.1080/13588265.2023.2189000) [DOI 10.1080/13588265.2023.2189000](DOI 10.1080/13588265.2023.2189000)[ ](DOI 10.1080/13588265.2023.2189000)[ISSN 1358-8265](ISSN 1358-8265) [ESSN 1754-2111](ESSN 1754-2111) Publisher: Taylor and Francis This is an Accepted Manuscript version of the following article, accepted for publication in International Journal of Crashworthiness. Liang, R, Xu, F, Liu, N, Liu, X, Bastien, C & Zhang, C 2024, 'A machine learning based optimisation method to evaluate the crushing behaviours ofsquare tubes with rectangular-hole-type initiators', International Journal of Crashworthiness, vol. 29, no. 1, pp. 115-131. It is deposited under the terms of the Creative Commons AttributionNonCommercial License ([http://creativecommons.org/licenses/by-nc/4.0/](http://creativecommons.org/licenses/by-nc/4.0/)), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. A machine learning based optimization method to evaluate the crushing behaviors of square tubes with rectangular-hole-type initiators Rui Liang1, Fengxiang Xu2, 3, Na Liu1 *, Xiang Liu1, Christophe Bastien4, Cheng Zhang1 Formatted: French (France) 1. School of Automobile Engineering, Guilin University of Aerospace Technology, Guilin 400054, China; 2. Hubei Key Laboratory of Advanced Technology of Automotive Components, Wuhan University of Technology, Wuhan 430070, China; 3. Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan 430070, China; 4. Centre of Future Transport and Cities, Coventry University, Coventry CV1 2TE, UK Abstract: 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 optimization processes. This paper aims remedies to this limitation and proposes a machine learning based optimization 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 optimization method based on machine learning was employed to evaluate the influence of the initiator's size on the crushing behaviors 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 optimized 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 optimization method to improve crashworthiness performance. Keywords: Machine learning; Rectangular-type crush initiator; Crashworthiness performance; Deformation mode * [Corresponding Author: Email: naliu1989@126.com](Corr

FAQs

Why are rectangular-hole-type crush initiators important for square tubes?

They improve crashworthiness performance by enhancing how thin-walled square tubes deform and absorb energy during impacts.

What challenge does this paper address in the optimisation process?

Unwanted deformation buckling modes, especially bifurcation buckling, can occur and complicate optimisation.

How does the proposed method evaluate and optimise crushing behaviour?

Finite element models generate responses for different initiator numbers and positions, COPRAS ranks crashworthiness characteristics, and a machine learning based optimisation evaluates the initiator size to target IPF, EA, and CFE.

Aug 4, 2026

Upload by Logic