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

Abstract

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

CLC Number:

TJ413.+6

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.

Figures/Tables 14

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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

Error allocation method of instruction guidance loop based on variance analysis variable reduction

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误差分配项	个体1	个体2	个体3	个体4	优化前
σ_tr/m	10.975 0	8.121 0	7.827 0	8.411 0	6.00
σ_tε/mrad	1.569 0	2.091 0	2.646 0	1.869 0	1.60
σ_tq/mrad	2.106 0	2.191 0	2.060 0	1.377 0	1.40
σ_mr/m	5.075 0	3.860 0	5.050 0	9.502 0	5.00
σ_mε/mrad	1.926 0	1.189 0	1.650 0	2.227 0	1.60
σ_mq/mrad	0.792 1	2.864 6	1.801 5	1.036 0	1.40
h′/m	0.873 0	0.987 0	1.005 0	1.247 0	0.60
M/万元	420.10	383.30	350.70	319.10	523
z_m/m	3.599 0	3.622 0	3.646 0	3.669 0	5.17

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