Multi-objective optimization design for BFRP/Al hybrid crashworthy device using MOPSO

doi:10.3785/j.issn.1006-754X.2026.05.181

Chinese Journal of Engineering Design

2026, Vol. 33

Issue (1): 106-116 DOI: 10.3785/j.issn.1006-754X.2026.05.181

Optimization Design

Multi-objective optimization design for BFRP/Al hybrid crashworthy device using MOPSO

Youtong LI¹(

),Qinyi LI¹,Qianjie LIU²(

),Yiqing CHEN¹,Chunlin ZHANG^1,³,Hao LI¹

^1.School of Intelligent Manufacturing and Automotive Engineering, Guang'an Vocational & Technical College, Guang'an 638000, China
^2.School of Mechatronics and Vehicle Engineering, East China Jiaotong University, Nanchang 330013, China
^3.College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400030, China

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Abstract

Basalt fiber-reinforced polymer (BFRP) has excellent mechanical properties and melt-recyclability, with broad application prospects in automotive lightweight field. For the aluminum crashworthy device of a certain vehicle, a multi-objective optimization design of BFRP/Al hybrid crashworthy device is carried out. Firstly, mechanical tests were conducted on BFRP laminates, and a finite element model of the crashworthy device was established using HyperMesh software. Subsequently, training samples for the surrogate model were generated via Latin hypercube sampling. Key design parameters were identified through sensitivity analysis, and the prediction accuracy of the surrogate model for response indicators was enhanced by a space-filling sampling method based on the weighted Euclidean distance. Finally, with the objectives of minimizing peak load, total mass and maximum crossbeam displacement of the crashworthy device, the MOPSO (multi-objective particle swarm optimization) algorithm was employed to obtain the Pareto frontier, and the optimal design parameter combination was determined based on the entropy weight-TOPSIS (technique for order preference by similarity to an ideal solution) method. The results demonstrated that the optimized crashworthy device achieved reductions of 36.15% in peak load and 12.23% in total mass, exhibiting significantly improved crashworthiness while meeting the lightweight target. The proposed method can provide a systematic solution for the lightweight design of BFRP/Al hybrid crashworthy devices.

Key words： basalt fiber-reinforced polymer (BFRP) hybrid crashworthy device sensitivity analysis multi-objective particle swarm optimization (MOPSO) crashworthiness

Received: 14 August 2025 Published: 01 March 2026

CLC:

U 465.6

Corresponding Authors: Qianjie LIU E-mail: 859135985@qq.com;734831871@qq.com

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Cite this article:

Youtong LI,Qinyi LI,Qianjie LIU,Yiqing CHEN,Chunlin ZHANG,Hao LI. Multi-objective optimization design for BFRP/Al hybrid crashworthy device using MOPSO. Chinese Journal of Engineering Design, 2026, 33(1): 106-116.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2026.05.181 OR https://www.zjujournals.com/gcsjxb/Y2026/V33/I1/106

基于MOPSO的BFRP/铝混合防撞装置多目标优化设计

玄武岩纤维增强复合材料（basalt fiber-reinforced polymer, BFRP）具有优异的力学性能和可熔融再生特性，在汽车轻量化领域的应用前景广阔。针对某车型的铝制防撞装置，开展BFRP/铝混合防撞装置的多目标优化设计。首先，对BFRP层合板开展力学性能测试，并利用HyperMesh软件建立防撞装置有限元模型；其次，采用拉丁超立方抽样生成代理模型的训练样本，结合敏感度分析识别关键设计参数，并通过基于加权欧式距离的空间填充采样法来提升代理模型对响应指标的预测精度；最后，以防撞装置峰值载荷、总质量及横梁最大位移最小为优化目标，运用MOPSO（multi-objective particle swarm optimization，多目标粒子群优化）算法求解Pareto前沿，并基于熵权- TOPSIS（technique for order preference by similarity to an ideal solution，逼近理想解排序法）确定最优设计参数组合。结果显示：优化后防撞装置的峰值载荷降低了36.15%，总质量减小了12.23%，显著提升了耐撞性能并实现了轻量化目标。所提出的方法可为BFRP/铝混合防撞装置的轻量化设计提供一套系统性的解决方案。

关键词： 玄武岩纤维增强复合材料, 混合防撞装置, 敏感度分析, 多目标粒子群优化, 耐撞性

Fig.1 Test samples and testing equipment

Fig.2 Tensile and compressive stress-strain curves of 1# test sample

Table 1 Material properties of BFRP and aluminum alloy

Fig.3 Schematic of cross-section of key components in crashworthy device and its finite element model

Table 2 Experimental design scheme and solution results

Fig.4 Main effects and interaction effects of design variables

Fig.5 Sensitivity analysis result of design variables

Fig.6 Optimization curve of spread coefficient

Table 3 Error analysis result of surrogate model

Table 4 Weight corresponding to each design variable

Fig.7 Spatial distribution of new sampling points and initial sampling points

Table 5 New sampling points and solution results

Table 6 Error analysis results of surrogate model after supplementary sampling

Fig.8 Fitting accuracy verification result of surrogate model

Fig.9 Multi-objective optimization process based on MOPSO

Fig.10 Pareto frontier for multi-objective optimization of crashworthy device

响应指标	信息熵	差异系数	权重
峰值载荷P	0.988 3	0.011 7	0.199 7
总质量M	0.989 4	0.010 6	0.180 8
横梁最大位移 $δ$	0.963 7	0.036 3	0.619 5

Table 7 Entropy values and weights of response indicators

Table 8 Ranking of relative closeness of Pareto frontier

Fig.11 Comparison between Pareto frontier solution and simulation results of response indicators

Fig.12 Comparison of total energy absorption curves of crashworthy devices before and after optimization

Fig.13 Stress distribution cloud map of crashworthy device after optimization （t=0.095 s）

Fig.14 Comparison of crash performance of crashworthy devices before and after optimization

Table 9 Comparison of response indicators of crashworthy devices before and after optimization


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