基于多种群差分进化算法的火箭弹自力弹射 多目标约束优化设计

宋健; 李超; 佘湖清; 蔡蒨

doi:10.13224/j.cnki.jasp.20210618

基于多种群差分进化算法的火箭弹自力弹射多目标约束优化设计

doi: 10.13224/j.cnki.jasp.20210618

中国船舶集团有限公司宜昌测试技术研究所，湖北宜昌 443000

基金项目: “十三五”预研课题（3020106070501）

详细信息

作者简介:
宋健（1990-），男，博士生，主要研究方向为发射装置总体优化设计

通讯作者:
蔡蒨（1971-），男，研究员，博士，主要研究方向为舷外无源光电对抗总体技术。E-mail：13997656924@139.com

中图分类号: V238；TJ02
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出版历程
- 收稿日期: 2021-10-29
- 网络出版日期: 2023-03-21

Multi-objective constraint optimization design of rocket projectile self-ejection based on multi-population differential evolution algorithm

Yichang Testing Technique Research Institue， China State Shipbuilding Corporation Limited，Yichang Hubei 443000，China

摘要

摘要:
针对火箭弹自力弹射设计中降低低压室压强峰值与提高弹体出筒速度之间的矛盾，开展自力弹射的优化设计工作。建立自力弹射发动机-低压室耦合内弹道求解模型，并开展两种工况共4发实弹的验证试验；提出融合多种差分策略的多种群差分进化算法，并采用“剔除-补足”操作处理优化过程中的约束条件；考虑自力弹射的实际设计约束，以低压室压强峰值和弹体出筒速度为目标建立两目标约束优化模型，并采用多种群差分进化算法进行优化计算。结果表明：计算得到的Pareto前沿近似呈斜率不同的两段线性区间，随低压室压强峰值增大，相同压强增幅带来的出筒速度增量减小；在Pareto前沿上均匀选取12个优化方案并采用逼近理想解排序法进行排序，排序后得到的最终优化方案的低压室压强峰值降低16.11%，弹体出筒速度增加54.55%，自力弹射性能得到提升。
- 火箭弹 /
- 自力弹射 /
- 内弹道模型 /
- 多目标约束优化 /
- 差分进化 /
- 逼近理想解排序法（TOPSIS）
Abstract:
In view of the contradiction between reducing the pressure peak in low pressure chamber and increasing the exit velocity of self-ejection, the optimization design of self-ejection was carried out. A motor-low pressure coupled internal ballistic solution model of self-ejection was developed, physical experiments of two working conditions with four rockets were carried out. The multi-population differential evolution algorithm using differential strategy was proposed, “eliminate-complement operation” was adopted to deal with the constraints in the optimization process. A two-objective self-ejection constraint optimization model was established with the peak of pressure in low pressure chamber and the exit velocity considering the actual constraints of self-ejection, and this optimization model was calculated by the multi-population differential evolution algorithm. Results showed that, the Pareto front was of two segments with different slopes approximately. With the increase of pressure peak of low pressure chamber, the same increment of pressure led to a smaller increment of exit velocity. Twelve schemes were evenly selected in Pareto front and ranked by using technique for order preference by similarity to an ideal solution; the peak of pressure in low pressure chamber of the final optimized scheme of self-ejection decreased by 16.11%, the exit velocity of the final optimized scheme increased by 54.55%, and the performance of rocket projectile self-ejection had been improved.
- rocket projectile /
- self-ejection /
- interior ballistic /
- multi-objective constraint optimization /
- differential evolution /
- technique for order preference by similarity to an ideal solution (TOPSIS)

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图 1 自力弹射装置示意图

Figure 1. Schematic diagram of self-ejection device

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图 2 火箭弹自力弹射高速摄像照片

Figure 2. High-speed photograph of rocket projectile self-ejection

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图 3 试验数据与仿真数据对比

Figure 3. Data comparison of experiment and simulation

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图 4 种群的“剔除-补足”操作

Figure 4. “Eliminate-complement” operation of population

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图 5 测试函数的Pareto前沿

Figure 5. Pareto front of test function

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图 6 火箭弹自力弹射优化得到的Pareto前沿

Figure 6. Pareto front of rocket projectile self-ejection optimization

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图 7 Pareto前沿不同方案的低压室压强

Figure 7. p_l of different scheme on Pareto front

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图 8 Pareto前沿不同方案的弹体速度

Figure 8. v_r of different scheme on Pareto front

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表 1 实弹试验数据与计算数据对比

Table 1. Data comparison of livefiring experimrnt and calculation

参数	工况	计算结果	试验结果		最大误差/%
参数	工况	计算结果	实弹试验1	实弹试验2	最大误差/%
p_lmax/ MPa	1	1.314 01	1.359 72	1.364 62	3.85
p_lmax/ MPa	2	0.996 632	1.036 795	1.027 075	4.03
v_r0/ （m/s）	1	29.56	28.49	28.17	4.7
v_r0/ （m/s）	2	25.79	24.94	25.32	3.295

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表 2 自力弹射优化设计参数

Table 2. Parameters of optimization model of self-ejection

序号	参数描述	取值范围	初始值
1	发动机喉部直径D_t/mm	10～20	12.5
2	发动机喷管扩张比R_n	3～6	4
3	推进剂长度L_p/mm	160～180	170
4	推进剂数量n_p	2～6	2
5	低压室开孔数量n_h	1～6	2
6	低压室开孔直径D_h/mm	5～20	15
7	燃烧室长度L_c/mm	170～200	190
8	低压室直径D_l/mm	165～195	173
9	低压室初始长度L_l0/mm	100～500	300
10	发射筒长度L_t/mm	1 500～2 000	1 700
11	火箭弹质量m_r/kg	40～70	70

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表 3 自力弹射优化方案TOPSIS排序结果

Table 3. TOPSIS ranking result of the self-ejection optimization schemes

序号	优化目标值		规范后优化目标		与正理想解的欧氏距离	与负理想解的欧式距离	方案评价指标	排序结果
序号	p_lmax/MPa	v_r0/（m/s）	p_lmax	v_r0	与正理想解的欧氏距离	与负理想解的欧式距离	方案评价指标	排序结果
1	4.115	65.269	0.334 083	0.149 868	0.308 347	0.103 203	0.250 8	12
2	3.538	64.411	0.287 238	0.147 898	0.261 509	0.111 546	0.299 0	11
3	3.016	63.395	0.244 859	0.145 565	0.219 165	0.133 198	0.378 0	10
4	2.450	61.585	0.198 907	0.141 409	0.173 377	0.165 072	0.487 8	9
5	1.896	58.965	0.153 929	0.135 393	0.129 008	0.200 818	0.608 9	8
6	1.583	53.725	0.128 518	0.123 361	0.106 145	0.219 406	0.674 0	7
7	1.275	48.297	0.103 513	0.110 897	0.086 994	0.239 349	0.733 5	6
8	1.015	43.267	0.082 404	0.099 348	0.075 918	0.257 133	0.772 1	3
9	0.794	37.549	0.064 462	0.086 221	0.074 503	0.272 507	0.785 3	1
10	0.623	32.358	0.050 579	0.074 299	0.079 548	0.284 847	0.781 7	2
11	0.439	26.244	0.035 641	0.060 260	0.090 153	0.298 751	0.768 2	4
12	0.317	20.323	0.025 736	0.046 665	0.103 203	0.308 347	0.749 2	5

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表 4 自力弹射优化方案的参数

Table 4. Parameters of self-ejection optimization scheme

参数	数值
D_t/mm	14.4
R_n	4.89
L_p/mm	180
n_p	4
n_h	5
D_h/mm	19.4
L_c/mm	200
D_l/mm	200
L_l0/mm	500
L_t/mm	1 997.4
m_r/kg	40.01

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表 5 初始方案与优化方案指标对比

Table 5. Indicator comparison of initial scheme and optimization scheme

参数	初始方案	优化方案	变化率/%
p_lmax/MPa	0.946 7	0.794 2	−16.11
v_r0/（m/s）	24.296	37.55	54.55
p_c/MPa	7.5	14.5	93.33
$ {\dot m_{\text{t}}} $/（kg/s）	0.75	1.85	146.67
t_e/ms	134.2	109.8	−18.18
L_a/mm	2 000	2 497.4	24.87

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