基于聚类关联规则神经网络组合算法的弹丸初速预测

doi:10.12382/bgxb.2021.0687

摘要/Abstract

摘要：

针对靶场试验中利用初速雷达测试弹丸初速需要重构的情况,选择同时参试的两台雷达的数据进行融合建立神经网络模型,用一台雷达的数据预测出另一台雷达需要重构的数据。由于预测模型预测精度的高低取决于所建模型的好坏,而模型的好坏取决于样本数据的质量,先利用聚类分析和关联规则从大量历史试验数据中挖掘出优质的样本,再建立神经网络进行预测。实验结果表明,与支持向量回归机相比,由聚类分析关联规则神经网络构建的组合算法的预测精度更高,预测历史相似数据误差远小于1‰,预测与历史出入较大的数据的精度也较为理想。两种情况下的预测结果表明,组合算法既保证了预测精度又具有一定的鲁棒性,可以作为弹丸初速的预测模型。

关键词: 初速预测, 聚类分析, 关联规则, 神经网络, 组合算法

Abstract:

In view of the situation that reconstruction is needed for the muzzle velocity of a projectile measured by muzzle velocity radar in the range test, the data of two radars used in the test at the same time are fused to establish a neural network model, and the data of one radar is used to predict the data that needs to be reconstructed by the other radar. Because the prediction accuracy of the prediction model depends on the quality of the model, and the model quality depends on the quality of the sample data, we first use cluster analysis and association rules to mine high-quality samples from a large number of historical test data, and then establish a neural network for prediction. The experimental results show that: compared with support vector regression machine, the prediction accuracy of the combined algorithm constructed by clustering analysis association rules and neural network is higher, the error of predicting similar historical data is far less than 1‰, and the accuracy of predicting data significantly different from historical data is also more reasonable. The prediction results in the two cases show that the combined algorithm not only ensures the prediction accuracy, but also has certain robustness, and can be used as the prediction model of projectile muzzle velocity.

Key words: velocity initial, cluster analysis, association rules, neural network, combined algorithm

中图分类号:

TJ38

田珂. 基于聚类关联规则神经网络组合算法的弹丸初速预测[J]. 兵工学报, 2023, 44(2): 452-461.

TIAN Ke. Prediction of Projectile Muzzle Velocity Based on Neural Network Algorithm Combined with Clustering Association Rules[J]. Acta Armamentarii, 2023, 44(2): 452-461.

图/表 23

图1 3层BP神经网络拓扑图

Fig.1 3-layer BP nurual network topology

图2 两台参试雷达现场布站示意图

Fig.2 Site layout of two test radars

图3 雷达A左正和后正分布曲线

Fig.3 Left positive and rear positive distribution curves of Radar A

图4 雷达A初速和雷达B初速变化曲线

Fig.4 Variation curves of initial velocity of Radar A and Radar B

图5 绝对误差与误差标准变化曲线

Fig.5 Absolute error and error standard variation curves

图6 不同类别数量下类内平方和变化曲线

Fig.6 Variation curve of sum of squares within groups under different numbers of categories

图7 不同类别数量下类间平方和变化曲线

Fig.7 Variation curve of sum of squares between groups under different numbers of categories

图8 分类类别示意图

Fig.8 Schematic diagram of classification category

表1 Apriori关联规则算法挖掘结果

Table 1 Results of Apriori algorithm for association rule mining

左侧规则	右侧规则	支持度	置信度	提升度	样本数量
{A4}	{好}	0.2661290	0.8684211	1.066180	33
{A2}	{好}	0.3145161	1.0000000	1.227723	39

图9 表1所有关联规则频率分布

Fig.9 Frequency distribution of all association rules in Table 1

图10 组合样本中雷达A的左正、后正和初速与雷达B初速之间的相关系数矩阵可视图

Fig.10 Visibility graph of correlation coefficient between left positive, back positive, initial velocity of Radar A and initial velocity of Radar B in combined samples

图11 组合样本神经网络残差平方和随迭代次数变化曲线

Fig.11 Variation curve of the residual sum of squares of combined sample neural network with the number of iterations

表2 组合样本神经网络输入层到隐含层权值和阈值

Table 2 Weights and thresholds from input layer to hidden layer of combined sample neural network

神经元	输入1	输入2	输入3	阈值
1	28.1432000	-6.1436770	8.7983940	44.7162829
2	14.5432400	-6.4585750	8.6515020	4.0440836
3	18.5108700	3.5425780	1.7351020	-3.0232857
4	20.6268800	3.0062510	2.6938990	-3.8635498
5	-22.2357100	1.1870900	13.6750550	0.3672449
6	19.0408800	-15.0458720	17.6933350	8.8356581

表3 组合样本神经网络隐含层到输出层权值

Table 3 Weights from hidden layer to output layer of combined sample neural network

神经元	1	2	3	4	5	6
输出层	0.33721577	0.01783879	37.37517928	37.14605252	-18.66516705	0.21881953

图12 BP神经网络对组合样本中雷达B测试的弹丸初速预测值

Fig.12 Prediction value of projectile muzzle velocity measured by radar B in combined samples by BP neural network

表4 雷达B第1~5发实测值与神经网络预测值

Table 4 Measured values and neural network predicted values of the 1st ~ 5th rounds of Radar B

弹序	实测值	神经网络预测值	SVR预测值
1	92.24	92.26248	93.79947
2	91.61	91.56277	93.84397
3	91.95	91.84691	93.81447
4	91.94	91.93622	93.80780
5	91.48	91.27619	93.88130

表5 雷达B第58~62发实测值与神经网络预测值

Table 5 Measured values and neural network predicted values of the 58th ~ 62nd rounds of Radar B

弹序	实测值	神经网络预测值	SVR预测值
58	93.59	93.70422	93.70042
59	93.47	93.58785	93.58933
60	93.38	93.48330	93.49280
61	93.30	93.36240	93.38630
62	93.47	93.48330	93.49280

表6 雷达B第66~70发实测值与神经网络预测值

Table 6 Measured values and neural network predicted values of the 66th~70th rounds of Radar B

弹序	实测值	神经网络预测值	SVR预测值
66	92.90	92.87567	93.09812
67	92.87	92.86936	93.09310
68	92.87	92.86309	93.08815
69	92.82	92.82619	93.06020
70	92.97	92.92084	93.13554

表7 雷达B第104~108发实测值与神经网络预测值

Table 7 Measured values and neural network predicted values of the 104th~108th rounds of Radar B

弹序	实测值	神经网络预测值	SVR预测值
104	92.53	92.59104	92.71547
105	92.78	92.84000	92.84771
106	92.95	93.03365	92.98245
107	92.59	92.69054	92.76176
108	92.82	92.89735	92.88517

图13 v1雷达A与雷达B初速变化曲线

Fig.13 Initial velocity variation curve of v1 Radar A and Radar B

图14 v2雷达A与雷达B初速变化曲线

Fig.14 Initial velocity variation curve of v2 Radar A and Radar B

表8 v1雷达B实测值与BP神经网络预测值

Table 8 Measured values of v1 Radar B and predicted values of BP neural network

弹序	实测值	神经网络预测值	SVR预测值
1	85.30	85.65732	94.20604
2	85.20	85.66622	94.20604
3	85.39	85.65430	94.20604
4	85.38	85.66515	94.20604
5	85.41	85.65885	94.20604

表9 v2雷达B实测值与BP神经网络预测值

Table 9 Measured values of v2 Radar B and predicted values of BP neural network

弹序	实测值	神经网络预测值	SVR预测值
1	84.80	84.31650	94.20603
2	84.86	84.31782	94.20604
3	84.82	84.31676	94.20603
4	84.86	84.31808	94.20603
5	84.86	84.31782	94.20603

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