Differential evolution optimization for stuffed Whipple shield ballistic limit equations
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摘要:
综合建模形式弹道极限方程中存在11个待定参数，从理论上讲，采用穷举法可以获得其数值大小，但需要的计算时间过长，储存空间巨大，不宜实现，为解决此问题，改用差异演化算法。基于填充式实验数据，采用差异演化算法对综合建模形式弹道极限方程的11个待定参数进行了多目标优化计算。结果显示，方程的总体预测率为82.35%，安全预测率为100%，平均相对误差平方和为0.001 3。该方程对其他来源的49个实验数据的预测结果显示，总体预测率提升了1.32%，安全预测率降低了4.08%，平均相对误差平方和增加了0.007 3，表明差异演化算法适用于解决多参数多目标的弹道极限方程建模问题。
Abstract:There are 11 parameters in the form of domestic integrated modeling of ballistic limit equations. Theoretically, the exhaustion method can be used to obtain the numerical value, but the computation time is too long and the storage space is huge, so it is not suitable to realize. To solve this problem, differential evolution algorithm is used. Based on the domestic data of stuffed Whipple shield, the differential evolution algorithm is applied to optimize 11 undetermined parameters of the formal ballistic limit equation of the integrated modeling. The optimization results show that the totality predicted rate is 82.35%, the safety predicted rate is 100%, and the average sum of squared prediction relative errors is 0.001 3. Based on 49 experimental data from other sources for predictive testing, the prediction test shows that the totality predicted rate is raised by 1.32%, the safety predicted rate is reduced by 4.08%, and the average sum of squared prediction relative errors is increased by 0.007 3. It shows that the differential evolution algorithm is suitable for solving the ba-llistic limit equation modeling of multiple parameters and multiple targets.
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图 1 各函数最优个体的变量绝对值之和与适应度随演化代数变化曲线
Figure 1. Changing curves of sum optimal individual absolute variables and fitness with generation for each function
图 2 最优个体的变量绝对值之和随演化代数变化曲线
Figure 2. Changing curve of sum of optimal individual absolute variables with algebra
图 3 最优个体的预测率随演化代数变化曲线
Figure 3. Changing curves of predicted rate of optimal individual with algebra
图 4 最优个体的平均相对误差平方和随演化代数变化曲线
Figure 4. Changing curve of average sum of squared relative errors of optimal individual with algebra
图 5 优化后方程对实验数据的预测效果
Figure 5. Experimental data prediction results using optimized equation
表 2 优化前后变量的数值比较
Table 2. Comparison of variable values before and after optimization
变量 初始值 优化值 x1 0.6 0.457 x2 0.3 0.4 x3 0.2 0.1 x4 -0.3 -0.311 x5 1 1.05 x6 0.3 0.25 x7 0.4 0.284 x8 1.2 1.5 x9 0.3 0.21 x10 0.2 0.11 x11 -0.25 -0.339 
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