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摘要:
填充式防护结构的显式弹道极限方程在对弹丸进行超高速撞击损伤预测时，由于填充材料、填充方式的不同，会导致预测结果与实测数据存在一定偏差。对此，采用机器学习方式将该问题转化为二分类问题，以碰撞过程中的弹丸撞击参数、防护结构参数作为分类特征，构建了基于Adaboost的填充式防护结构超高速撞击损伤预测模型。该模型以分类回归树（CART）作为弱分类器，通过对一系列弱分类器的加权组合生成强分类器，并通过对训练样本的循环使用，实现了小样本集下的撞击损伤预测。实验结果表明，建立的Adaboost预测模型对填充式防护结构的超高速撞击损伤具有良好的预测效果，总体预测率与安全预测率相比于NASA的弹道极限方程均提高了14.3%，具有更强的通用性。通过不同训练样本规模下的交叉检验，证明了该模型具有良好的鲁棒性与准确性。
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关键词:
- 填充式防护结构 /
- 损伤研究 /
- Adaboost算法 /
- 总体预测率 /
- 安全预测率
Abstract:The explicit ballistic limit equation of stuffed Whipple shield may cause some deviations between the prediction results and the measured data when the projectile is subjected to hypervelocity impact damage prediction because of different filling materials and filling methods. In this regard, the machine learning method is used to transform the problem into a binary problem. The projectile impact parameters and protective structure parameters in the collision process are used as the classification features to construct a hypervelocity impact damage prediction model of stuffed Whipple shield based on Adaboost. The model uses the classification and regression tree (CART) as a weak classifier to generate a strong classifier by weighted combination of a series of weak classifiers. Through the cyclic use of training samples, the impact damage prediction under a small sample set is achieved. The experimental results show that the established Adaboost prediction model has good prediction effect on the hypervelocity impact damage of stuffed Whipple shield. Both the totality prediction rate and the safety prediction rate of Adaboost prediction model increase by 14.3% compared with NASA's ballistic limit equation, and the established model has more versatility. Cross check under different training sample sizes proves that the model has good robustness and accuracy.
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图 5 基于Adaboost的超高速撞击损伤的预测流程
Figure 5. Hypervelocity impact damage prediction process based on Adaboost
图 6 Adaboost预测模型预测误差和训练误差
Figure 6. Prediction error and training error of Adaboost prediction model
图 7 10折交叉检验预测误差和训练误差
Figure 7. Prediction error and training error of 10-fold cross check
图 8 NASA弹道极限方程在总体数据中的预测效果
Figure 8. Prediction effect of NASA ballistic limit equation on all data
表 1 超高速撞击实验预测结果
Table 1. Prediction results of hypervelocity impact experiment
编号 实际弹丸直径/cm 弹丸撞击速度/(km·s-1) 穿透结果 临界弹丸直径/cm 预测结果 1 0.635 3.42 yes 0.5291 √ 2 0.635 3.99 no 0.6231 × 3 0.635 4.153 no 0.65 √ 4 0.635 4.21 no 0.6593 √ 5 0.635 3.87 yes 0.6033 √ 6 0.635 3.75 yes 0.5855 √ 7 0.635 3.82 no 0.597 × 8 0.635 1.24 yes 0.65 × 9 0.635 1.04 no 0.7308 √ 10 0.794 4.54 yes 0.7151 √ 11 0.794 2.1 yes 0.4575 √ 12 0.794 1.53 yes 0.565 √ 13 0.794 0.7645 no 0.8972 √ 14 0.794 1.3085 yes 0.6271 √ 15 0.794 1.81 yes 0.5047 √ 16 0.794 0.801 no 0.8692 √ 17 0.794 0.595 no 1.0597 √ 18 0.635 4.06 yes 0.6362 × 19 0.635 4.237 yes 0.6653 × 20 0.635 4.425 no 0.6961 √ 21 0.635 4.345 yes 0.683 × 22 0.635 1.404 yes 0.5979 √ 23 0.635 1.16 yes 0.679 × 24 0.635 1.12 no 0.6951 √ 25 0.635 2.97 yes 0.4572 √ 26 0.635 0.871 no 0.822 √ 27 0.635 0.801 no 0.8692 √ 28 0.635 1.062 no 0.7202 √ 29 0.635 1.31 yes 0.6262 √ 30 0.635 3.97 yes 0.6214 √ 31 0.635 2.2 yes 0.4432 √ 32 0.635 3.87 no 0.605 × 33 0.635 3.92 yes 0.6132 √ 34 0.635 4.3941 yes 0.691 × 35 0.635 4.46 yes 0.7019 × 
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表 2 填充式防护结构的超高速撞击实验数据源
Table 2. Hypervelocity impact experimental data source of stuffed Whipple shield
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表 3 填充式防护结构的超高速撞击实验预测对比
Table 3. Predictive comparison of hypervelocity impact experiment of stuffed Whipple shield
% 模型 总体(35组) 低速段(17组) 中速段(18组) Ptotal Psafe Ptotal Psafe Ptotal Psafe NASA弹道极限方程 71.4 80.0 88.2 88.2 55.6 72.2 Real Adaboost 85.7 94.3 100 100 72.2 88.9 Modest Adaboost 85.7 94.3 100 100 72.2 88.9 Gentle Adaboost 85.7 94.3 100 100 72.2 88.9
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表 4 十次10折交叉检验结果
Table 4. Ten 10-fold cross check results
检验标准 Real Adaboost Gentle Adaboost Modest Adaboost 预测误差/% 12.15 11.83 13.85 9.53 8.53 11.32 13.32 14.09 14.61 9.35 10.26 9.43 12.30 12.49 11.49 11.72 10.29 11.12 13.22 13.22 13.22 11.27 8.73 11.27 12.40 12.08 13.51 12.61 11.38 13.61 平均预测准确率/% 88.21 88.71 87.66
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表 5 不同规模训练样本的预测准确率
Table 5. Prediction accuracy of training samples with different scales
检验标准 Real Adaboost Gentle Adaboost Modest Adaboost 5折 3折 5折 3折 5折 3折 预测误差/% 12.61 15.81 13.17 15.78 12.61 14.88 13.14 10.68 12.09 9.57 12.09 12.01 12.98 15.44 12.98 15.44 10.96 15.44 14.40 13.07 13.84 12.00 16.15 12.00 12.39 13.12 11.44 12.17 11.56 10.32 平均预测准确率/% 86.90 86.38 87.30 87.01 87.33 87.07
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