On data-driven optimization design of protective structures for vehicles against explosion
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摘要: 针对车辆爆炸防护结构优化中数据来源匮乏、代理模型精度低、优化效率低和可靠性不足的问题，提出了一种数据增广方法结合半监督回归的数据驱动方法。通过改进生成对抗网络（generative adversarial network，GAN），提出了Gaussian密度估算-对抗生成网络（Gaussian density estimation-Wasserstein generative adversarial network，GDE-WGAN）；分别采用GDE-WGAN、Gaussian模型、最优拉丁超立方方法，并结合半监督支持向量回归，对原始数据集进行增广，通过对比不同方法的数据增广效果，验证了GDE-WGAN的可行性和优越性；通过多目标优化分别求解数据增广前后代理模型的最优解，并通过有限元仿真验证比较。结果表明，GDE-WGAN结合半监督回归的方法可以显著提升代理模型的拟合精度，2个输出变量的决定系数R2分别提升了16.7%和4.2%。结合半监督回归的数据增广优化方法在准确性和优化效率方面具有较大提升。Abstract: In order to address the needs of modern combat vehicles for both personnel protection and lightweight design, optimizing their blast-resistant structures is necessary. Due to the high cost of physical experiments, finite element simulation has been commonly used instead. However, simulations of explosion and vehicle responses require extensive computational resources and incur high computational costs, leading to limited data availability for the optimization of explosion-proof structures. Since structural optimization demands sufficient data support, larger amount of valid data can improve the accuracy of the surrogate model and the precision of the optimal solution, yielding better optimization results. To overcome these challenges, a data-driven optimization method for vehicle’s explosion-proof structures was proposed, integrating data augmentation and semi-supervised regression. To address the limitations of generative adversarial networks (GANs) in handling numerical data, an improved model, a Gaussian density estimation-Wasserstein generative adversarial network (GDE-WGAN), was developed by modifying both the generator and discriminator of the WGAN model, a variant of the GANs. The feasibility of the proposed method was demonstrated based on the principle of information gain. The data generated by the GDE-WGAN were incorporated into a self-training framework, where an adaptive confidence assessment mechanism dynamically adjusted the way that the semi-supervised support vector regression model utilizes the generated data. The feasibility and superiority of the method were validated by comparing the enhanced performance of the semi-supervised regression model using different numerical data expansion techniques. Finally, multi-objective optimization was performed to obtain the optimal solutions of the data-augmented semi-supervised regression model and the initial model, followed by verification and comparison with finite element simulation results. It shows that the GDE-WGAN significantly enhances the performance of the semi-supervised regression model, and the generated data exhibit greater randomness and diversity through the network structure of the GANs, which benefits semi-supervised learning. When handling semi-supervised regression for high-dimensional nonlinear numerical data, both global and local data distribution similarities play a crucial role. Furthermore, finite element simulations indicate that the improved model predicts results more accurately than the initial model and achieves superior optimization outcomes.
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图 1 某轻型车身底部爆炸案例有限元模型
Figure 1. Finite element model of a light vehicle subjected to a bottom explosion
图 2 轻型车身底部爆炸案例ATD下Z向胫骨力响应实验结果与仿真数据的比较
Figure 2. Experimental and simulated results of the Z-direction force response of the lower tibia in ATD of a light vehicle subjected to a bottom explosion
图 4 GAN生成数据与原始数据对比的可视化散点图
Figure 4. Visualization of scatter plots of GAN-generated data compared with raw data
图 6 GDE-WGAN生成数据与原始数据对比可视化散点图
Figure 6. Visualization of scatter plots comparing GDE-WGAN generated data with raw data
图 7 最优拉丁方采样生成数据与原始数据对比可视化散点图
Figure 7. Comparison of the data generated by the optimal Latin sampling and the original data to visualize the scatter plot
图 8 Gaussian模型生成数据与原始数据对比可视化散点图
Figure 8. Comparison of Gaussian model generated data with raw data and visual scatter plots
图 9 生成数据整体分布与局部分布相似性评价示意图
Figure 9. Schematic diagram of the similarity evaluation of the global distribution and local distribution of the generated data
图 10 自训练框架下半监督回归算法流程
Figure 10. Flowchart of semi-supervised regression algorithm under self-training framework
图 11 初始模型与半监督训练后模型性能对比
Figure 11. Comparison of the performance of the initial model with one of the model after semi-supervised training
图 12 不同生成数据数量下半监督回归模型性能随迭代次数的变化
Figure 12. Variation of semi-supervised regression model performance with the number of iterations for different numbers of generated data
图 13 利用不同未标记样本集进行半监督学习代理模型性能指标
Figure 13. Performance indicators of semi-supervised learning model using different unlabeled sample sets
图 14 初始模型和最终模型的Pareto前沿解集
Figure 14. Pareto frontier solution sets of initial model and final model
表 1 最优拉丁超立方实验采样样本
Table 1. Optimal Latin hypercube experimental sampling samples
No. X1/mm X2/mm X3/mm X4/mm X5/mm 1 5.240 9.380 3.340 4.720 0.531 $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ 15 5.450 5.860 3.000 6.620 0.345 16 6.900 10.000 5.760 6.100 0.738 $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ 29 9.590 8.970 4.550 4.210 0.593 30 8.140 6.280 5.590 7.830 0.262 
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表 2 传统优化流程代理模型性能指标
Table 2. Performance metrics of the surrogate model in the traditional optimization process
预测目标 R2 eMS εMAP 假人左胫骨力 0.61 168365 N20.0557 爆炸防护结构总体质量 0.87 9.74×10−5 t2 0.0199
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表 3 生成器和判别器网络的结构参数
Table 3. Structure parameters for generator and discriminator networks
模型类型 层类型 输入维度 输出维度 激活函数 生成器 全连接层 105 128 无 128 256 ReLU 256 128 ReLU 128 5 无 判别器 全连接层 11 512 无 512 256 ReLU 128 64 ReLU 64 1 Sigmoid
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表 4 GDE-WGAN超参数设定
Table 4. GDE-WGAN hyperparameter settings
超参数 对应符号 赋值 总训练轮数 nepoches 10000 批大小 B 64 判别器更新次数 ncritic 5 权重剪切限制 λgp 5 Adam优化学习率 c 0.01 Adam优化器指数衰减率 (β1, β2) (0.5, 0.9) 特征标准差 f(G(s)) 特征范围的$ \dfrac{1}{4} $
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表 5 初始模型与最终模型预测帕累托最优解及对应优化结构参数
Table 5. Pareto optimal solutions predicted by the initial and final models and corresponding optimized structural parameters
模型 X1/mm X2/mm X3/mm X4/mm X5/mm $ {Y}_{1} $/N $ {Y}_{2} $/t 初始模型 9.7 8.0 5.7 5.6 0.60 4574.1 0.595 最终模型 9.9 7.7 5.6 5.1 0.57 4438.0 0.593
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表 6 初始模型和最终模型预测结果与仿真计算结果的对比
Table 6. Comparison of errors between predicted results of the initial and final models and simulation results
模型 Y1 Y2 预测
结果/N计算
结果/N误差/% 预测
结果/t计算
结果/t误差/% 初始模型 4574.1 5174.0 11.6 0.595 0.566 5.12 最终模型 4438.0 4756.0 6.7 0.593 0.574 3.31
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