基于PSO-LSTM的负Poisson比材料力学性能预测与参数设计

胡雨涵; 韩芳; 颜芝

doi:10.21656/1000-0887.460118

基于PSO-LSTM的负Poisson比材料力学性能预测与参数设计

doi: 10.21656/1000-0887.460118

胡雨涵^1,,
韩芳^2, ,,
颜芝²

1.
武汉科技大学数学与系统科学学院, 武汉 430065
2.
武汉科技大学物理与力学学院, 武汉 430065

基金项目:

国家自然科学基金青年基金 51108358

详细信息

作者简介:
胡雨涵(1999—)，女，硕士生(E-mail: 1604032064@qq.com)

通讯作者:
韩芳(1980—)，女，副教授，博士(通信作者. E-mail: hanfang@wust.edu.cn)

中图分类号: TB34
计量
- 文章访问数: 142
- HTML全文浏览量: 46
- PDF下载量: 29
- 被引次数: 0
出版历程
- 收稿日期: 2025-06-09
- 修回日期: 2025-08-20
- 刊出日期: 2026-08-01

Mechanical Property Prediction and Parameter Design of Auxetic Materials Based on the PSO-LSTM

Hu Yuhan^1
,,
Han Fang^{2
, ,},
Yan Zhi²

1.
School of Mathematics and Systems Science, Wuhan University of Science and Technology, Wuhan 430065, P.R. China
2.
School of Physics and Mechanics, Wuhan University of Science and Technology, Wuhan 430065, P.R. China

摘要

摘要: 针对负Poisson比蜂窝材料力学性能预测与结构优化设计问题，提出一种融合粒子群优化(PSO)算法与长短期记忆(LSTM)网络的机器学习方法. 通过有限元仿真构建400组包含几何参数(直壁长度、胞元高度、壁厚、胞角)及其对应力学性能(能量吸收、弹性模量、Poisson比)的训练数据集，结合PSO对LSTM模型的超参数进行全局优化，建立多目标力学性能预测模型. 此外，构建基于PSO-LSTM的反向设计框架，通过目标力学性能驱动优化几何参数. 实验结果表明：优化后的PSO-LSTM模型对能量吸收、弹性模量和Poisson比的预测决定系数(R²)分别达到0.983 4，0.974 6和0.970 4，均方误差ε_ms稳定在0.001 2以下；反向设计所得模型的总能量吸收、弹性模量与Poisson比的相对误差分别为0.432%，1.05%和0.327%. 研究成果为负Poisson比材料的智能化设计与工程应用提供理论支持.
- 粒子群优化 /
- 长短期记忆网络 /
- 负Poisson比材料 /
- 几何参数设计
Abstract: To address the challenges of mechanical property prediction and structural optimization design for auxetic honeycomb materials, a machine learning approach integrating the particle swarm optimization (PSO) and the long short-term memory (LSTM) networks was proposed. A training dataset consisting of 400 groups of geometric parameters (including straight wall lengths, cell heights, wall thicknesses, and cell angles) and their corresponding mechanical properties (including energy absorption, Young's moduli, and Poisson's ratios) was constructed through finite element simulation. The PSO algorithm was employed to globally optimize the hyperparameters of the LSTM model, to establish a multi-objective mechanical property prediction model. Furthermore, an inverse design framework based on the PSO-LSTM was developed, enabling the optimization of geometric parameters driven by target mechanical properties. Experimental results show that, the optimized PSO-LSTM model achieves R² values of 0.983 4, 0.974 6, and 0.970 4 for energy absorption, Young's moduli, and Poisson's ratios, respectively, with mean squared errors (MSE) below 0.001 2. The relative errors of total energy absorption, Young's moduli, and Poisson's ratios for the model obtained through inverse design are 0.432%, 1.05%, and 0.327%, respectively. The proposed method provides theoretical support for the intelligent design and engineering application of auxetic materials.
- particle swarm optimization /
- long short-term memory network /
- auxetic material /
- geometric parameter design

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图 1 算法原理图

Figure 1. The principle diagram of the PSO algorithm

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图 2 LSTM结构图

Figure 2. The structure diagram of the LSTM

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图 3 改进PSO-LSTM算法流程图

Figure 3. The flowchart of the improved PSO-LSTM algorithm

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图 4 内凹六边形蜂窝结构胞元的设计参数

Figure 4. Design parameters of the concave hexagonal honeycomb unit cell

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图 5 内凹六边形蜂窝的有限元模型

Figure 5. The finite element model of the concave hexagonal honeycomb

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图 6 PSO-LSTM模型对总能量吸收的预测结果

Figure 6. Prediction results of the PSO-LSTM model for total energy absorption

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图 7 PSO-LSTM模型对弹性模量的预测结果

Figure 7. Prediction results of the PSO-LSTM model for Young’s moduli

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图 8 PSO-LSTM模型对Poisson比的预测结果

Figure 8. Prediction results of the PSO-LSTM model for Poisson's ratios

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图 9 反向设计流程图

Figure 9. The flowchart of the inverse design process

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表 1 蜂窝结构参数的取值范围

Table 1. Ranges of honeycomb structural parameters

structural parameter	value range
θ/(°)	35~60
L/H	1~$\sqrt{3} $
t/mm	1~2

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表 2 各模型对总能量吸收的预测结果

Table 2. Prediction results of various models for total energy absorption

	PSO-LSTM	LSTM	RF	SVM	XGBoost	ANN
R²	0.983 4	0.855 3	0.817 3	0.735 5	0.861 2	0.976 8
ε_ms	0.000 5	0.014 0	0.003 7	0.003 9	0.001 3	0.000 6

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表 3 各模型对弹性模量的预测结果

Table 3. Prediction results of various models for Young's moduli

	PSO-LSTM	LSTM	RF	SVM	XGBoost	ANN
R²	0.974 6	0.764 5	0.717 0	0.616 6	0.846 1	0.890 9
ε_ms	0.000 7	0.003 3	0.004 6	0.006 6	0.002 0	0.001 5

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表 4 各模型对Poisson比的预测结果

Table 4. Prediction results of various models for Poisson's ratios

	PSO-LSTM	LSTM	RF	SVM	XGBoost	ANN
R²	0.970 4	0.828 7	0.781 8	0.692 9	0.818 1	0.947 9
ε_ms	0.001 2	0.003 4	0.004 2	0.007 4	0.002 9	0.001 3

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表 5 三种模型的反向设计结果

Table 5. Reverse design results of 3 models

	PSO-LSTM	GA-LSTM	GA-BPNN
E_{A_pred}	74.676	75.829	75.342
E_pred	22.232	21.972	22.243
ν_pred	-0.220 72	-0.225 44	-0.221 41

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