基于方差分析变量约减的指令制导回路误差分配方法

doi:10.3969/j.issn.1001-506X.2020.05.21

摘要/Abstract

摘要：

针对引入惯导设备的指令制导系统中的误差分配问题,构建了指令制导回路误差优化分配的数学模型,利用方差分析法进行了变量约减,改善了传统优化设计中优化参数过多的问题。采用基于带精英策略的非支配排序遗传算法的Pareto多目标遗传算法,并利用动态罚函数法处理多约束情况,改善了优化求解过程仿真时间过长和局部收敛的问题。以某指令制导系统和惯导设备的误差参数为例,用此方法对制导精度和总费用两项指标进行优化。结果表明,优化方案的各项性能指标均满足设计要求,与优化前方案相比,优化目标有很大程度的改观,制导精度提高近30%,总费用降低近40%。该优化方法有效且通用性强,可为其它制导方式的误差优化分配问题提供设计依据。

关键词: 指令制导, 误差优化分配, 遗传算法, 方差分析, 罚函数

Abstract:

Aiming at the error distribution problem in the instruction guidance system of the inertial navigation device, the mathematical model of the error distribution of the instruction guidance loop error is constructed. The analysis of variance is carried out to reduce the decision variables and the optimization parameters is improved.And then the Pareto multi-objective genetic algorithm based on the non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ) is adopted, the dynamic penalty function is used to handle multi-restriction, thereby, the simulation time is reduced and the local convergence in the traditional optimization design is improved. Taking the error parameters of a command guidance system and inertial navigation equipment as an example, this method is used to optimize the guidance precision and the total cost. The results show that the performance indicators of the optimization scheme meet the design requirements. Compared with the pre-optimization scheme, the optimization objectives have been greatly improved, the guidance precision is improved by nearly 30%, and the total cost is reduced by nearly 40%. The optimization method is effective and general-purpose, and can provide the design basis for error-optimized allocation problems of other guidance methods.

Key words: instruction guidance, error optimization allocation, genetic algorithm, analysis of variance, penalty function

中图分类号:

TJ413.+6

卢发兴, 姚鸿鹤, 史浩然. 基于方差分析变量约减的指令制导回路误差分配方法[J]. 系统工程与电子技术, 2020, 42(5): 1131-1138.

Faxing LU, Honghe YAO, Haoran SHI. Error allocation method of instruction guidance loop based on variance analysis variable reduction[J]. Systems Engineering and Electronics, 2020, 42(5): 1131-1138.

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序号	误差参数	误差范围	误差水平
1	σ_tr/m	2~12	2, 4, 6, 8, 10
2	σ_tε/mrad	0.2~3	1.2, 1.4, 1.6, 1.8, 2.0
3	σ_tq/mrad	0.2~3	1.0, 1.2, 1.4, 1.6, 1.8
4	σ_mr/m	2~12	1, 3, 5, 7, 9
5	σ_mε/mrad	0.2~3	1.2, 1.4, 1.6, 1.8, 2.0
6	σ_mq/mrad	0.2~3	1.0, 1.2, 1.4, 1.6, 1.8
7	Δh/m	0.2~2	0.2, 0.6, 1.0, 1.4, 1.8
8	h′/(m/s)	0.1~2	0.2, 0.4, 0.6, 0.8, 1.0
9	σ_n/m	2~10	2, 4, 6, 8, 10
10	p	-0.1~-0.5	-0.1, -0.2, -0.3, -0.4, -0.5
11	μ/m	0~5	1, 2, 3, 4, 5
12	σ_r/m	0~10	2, 4, 6, 8, 10
13	T₀/ms	0~50	10, 20, 30, 40, 50

序号	误差水平
序号	2	4	6	8	10
1	5.944 5	5.997 2	6.072 0	6.127 2	6.256 6
2	5.781 7	6.123 6	6.095 2	6.164 3	6.264 6
3	5.835 9	5.998 5	6.135 9	6.112 5	6.270 1
4	5.896 0	5.988 5	6.210 7	6.187 0	6.103 0
5	5.966 7	5.883 4	6.081 3	6.200 3	6.209 1
6	5.851 2	5.998 4	6.153 2	6.067 7	6.281 2
7	5.767 1	5.963 7	5.984 6	6.148 3	6.185 3
8	5.765 4	5.967 9	6.050 2	6.208 7	6.267 0
9	5.936 1	5.958 0	6.141 1	6.214 6	6.267 4
10	5.778 3	5.950 6	6.061 6	6.224 1	6.313 7
11	5.939 7	5.839 6	6.172 3	6.326 6	6.166 0
12	5.864 4	5.895 1	6.055 1	6.248 0	6.283 9
13	5.784 6	5.955 1	6.061 1	6.195 3	6.340 7

差异源	平方和	自由度	均方差	F	P	F临界值
组间	0.585 7	4	0.146 4	6.631	0.000 2	4.016 0
组内	1.325 6	60	0.022 1	—	—	—
总和	1.911 3	64	—	—	—	—

序号	误差参数	F值
1	σ_tε	129.423 0
2	σ_tq	522.371 1
3	σ_mr	6.412 1
4	σ_mε	106.168 1
5	σ_mq	82.792 1
6	Δh	5.023 5
7	h′	15.453 2
8	σ_n	2.145 2
9	p	1.235 4
10	μ	5.068 9
11	σ_r	1.023 5
12	T₀	4.016 0

参数	参数名称	初值
误差源参数	惯导设备误差	Δh=1.5, σ_n=5 m, p=-0.2
	起控点散布误差	μ=2, σ_r=5 m
	延时误差	T₀=20 ms
遗传算法参数	最大进化代数	Gen=100
	种群大小	N=100
	交叉概率	P_c=0.8
	变异概率	P_m=0.1
	最优前端个体系数	O_p=0.1