Prediction of in-plane mechanical properties of auxetic honeycombs based onmachine learning
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摘要: 负泊松比蜂窝结构具有优良的力学性能，本文开发并对比了两种多输入多输出的人工神经网络模型(ANN)，用于预测不同几何参数下负泊松比蜂窝结构的能量吸收特性。采用蜂窝胞元的胞角$\theta $、直壁长度与胞元高度之比$ L/H $和厚度$ t $作为ANN的输入，输出是蜂窝结构的初始峰值力、平台力和蜂窝结构的总能量吸收。验证集的误差全部在8%内，且验证集和测试集的平均相关系数R2都大于98.2%，说明神经网络可以获得良好的预测效果，这表明ANN有能力学习和捕捉将蜂窝的拓扑结构及其力学性能联系起来的潜在物理机制。开发的两种神经网络中，与ANN1相比，ANN2的网络参数更多，网络结构更复杂，有更好的预测精度和训练速度。通过对给定几何参数的蜂窝结构的力学性能进行快速预测得到了吸能高的蜂窝结构。建立了反向设计网络对蜂窝结构进行反向设计，发现网络对蜂窝结构的胞角$\theta $和壁厚$t$预测效果良好，对$ L/H $的预测效果相对较差，因为$ L/H $对初始峰值力、平台力和总能量吸收影响很小。此外进行了蜂窝几何参数的敏感度分析，结果表明蜂窝结构的几何参数对初始峰值力、平台力和总能量吸收的敏感度趋势一致，蜂窝胞元厚度$t$的敏感度最高，$ L/H $对能量的敏感度最低。对于敏感度高的参数反向设计网络预测效果好，反之敏感度低的参数预测效果相对较差。总之，ANN为蜂窝结构吸能性能的研究提供了一种快速准确的方法，有望加快蜂窝结构的优化和设计进程。Abstract: It is well known that honeycombs with negative Poisson’s ratio have excellent mechanical properties. In this paper, two kinds of multi-input and multi-output artificial neural network models (ANN) were developed and compared to predict the energy absorption characteristics of honeycombs with negative Poisson's ratio under different geometric parameters. The cell angle θ, the ratio of straight wall length to cell height L/H and the thickness t of honeycomb cells are used as the inputs of ANN, and the outputs are the initial peak force, platform force and total energy absorption of honeycombs. The error in the verification set is all within 8%, and the average correlation coefficient R2 of the verification set and the test set is greater than 98.2%, which shows that the neural network can obtain good prediction effect and it has the ability to learn and capture the potential physical mechanism that relates the topology structure and mechanical properties of the honeycombs. Compared with ANN1, ANN2 has more network parameters, more complex network structure and better prediction accuracy and training speed. By quickly predicting the mechanical properties of the honeycomb with given geometric parameters, an optimized honeycomb was obtained. A reversed design network was established to reverse design the honeycomb, and it is found that the network has a good prediction effect on the cell angle θ and wall thickness t of the honeycomb, but the prediction effect of L/H is relatively weak, because the parameter L/H has little effect on the initial peak force, platform force and total energy absorption. In addition, the sensitivity analysis of input parameters was carried out. The results show that the sensitivity trend of geometric parameters of the honeycombs to initial peak force, platform force and total energy absorption is the same, the sensitivity of honeycomb cell thickness t is the highest, and the ratio of straight wall length to cell height L/H is the lowest. The reverse design network has good prediction performance for parameters with high sensitivity, while the prediction performance for parameters with low sensitivity is relatively poor. In a word, ANN provides a fast and accurate method for the study of energy absorption performance of honeycombs, which is expected to accelerate the optimization and design process of honeycomb structures.
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图 1 内凹六边形蜂窝胞元的设计参数
Figure 1. Design parameters of concave hexagonal cellular cells
$L$-Length of the straight wall; $H$-Height of the unit cell; ${\text{t}}$-Thickness of the unit cell; $\theta $- Cell angle
图 10 测试集的预测值与真实值的对比图
Figure 10. Comparison of predicted and true values of the test set
表 1 蜂窝结构参数及其取值范围
Table 1. Structural parameters and their value ranges for the data set
Structural parameters Value range $\theta $/(°) 50-72 $ L/H $ $ 2\sqrt 3 /3 - \sqrt 3 $ $t$/mm 1-2 
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表 2 两种网络的预测效果对比
Table 2. Comparison of the prediction effects of the two networks
R2(ANN1) R2(ANN2) Initial peak force 0.99266 0.99278 Platform force 0.98225 0.99882 Total energy 0.99840 0.99854
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表 3 反向设计网络的验证
Table 3. Verification of the reverse designed network
1 Initial peak force Platform force Total energy Design parameters Target value 24000 7000 350000 $\theta $ 1.20 
Finite element value 24831 7278 365974 
$L/H$ 1.25 Error 3.46% 3.97% 4.56% $t$ 2.05 2 Initial peak force Platform force Total energy Design parameters Target value 19000 4000 220000 $\theta $ 1.05 
Finite element value 18959 3966 216625 $L/H$ 1.54 Error 0.216% 0.85 % 1.53% $t$ 1.76 3 Initial peak force Platform force Total energy Design parameters Target value 15000 2600 150000 $\theta $ 1.02 
Finite element value 14415 2585 151943 $L/H$ 1.42 Error 3.9% 0.58% 1.3% $t$ 1.48
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