无人作战飞机经济寿命正向设计优化建模与求解研究

doi:10.12305/j.issn.1001-506X.2025.04.14

Abstract

Abstract:

Aiming at the problems of insufficient theoretical model support and deficient cost design method for product life cycle in the economic life design of unmanned combat aircraft, the forward design concept and optimization model of economic life of unmanned combat aircraft are proposed. A mixed integer programming selection model is constructed to assist the decision-making of the selection scheme and system life design of each module of the unmanned combat aircraft system, so that the average life cycle cost of the system in the unit use time is optimized. The conceptual model of economic life is applied to the selection stage of unmanned combat aircraft system through simulation examples, and the forward design of economic life of unmanned combat aircraft is carried out and the economic life selection model is solved. The computation example analysis results show that the proposed optimization model reduces the economic life of the unmanned combat aircraft by 1/5 compared with the design life of the airframe structure and improves the economic efficiency of its life cycle, which verifies the practicability of the proposed model.

Key words: unmanned combat aircraft, forward design, economic life, life cycle, optimization model, economy

CLC Number:

V37
V241.0

Xue YANG, Kailei LIU, Liying YANG, Xinhao CUI, Yiyong XIAO, Rui KANG. Research on modeling and solving of forward design optimization of economic life of unmanned combat aircraft[J]. Systems Engineering and Electronics, 2025, 47(4): 1176-1183.

Figures/Tables 8

Fig.1

Table 1

Fig.2

Table 2

Curve linearization of y=x-1 replacing the tangent set (ε=1%)"

k	x_k	y_k	K_k/β	B_k/β
1	1	1	-1	2
2	1.222 2E+00	8.181 8E-01	-6.694 2E-01	1.636 4E+00
3	1.493 8E+00	6.694 2E-01	-4.481 3E-01	1.338 8E+00
4	1.825 8E+00	5.477 1E-01	-2.999 8E-01	1.095 4E+00
5	2.231 5E+00	4.481 3E-01	-2.008 2E-01	8.962 5E-01
6	2.727 4E+00	3.666 5E-01	-1.344 3E-01	7.333 0E-01
7	3.333 5E+00	2.999 8E-01	-8.999 1E-02	5.999 7E-01
8	4.074 3E+00	2.454 4E-01	-6.024 2E-02	4.908 8E-01
9	4.979 7E+00	2.008 2E-01	-4.032 7E-02	4.016 3E-01
10	6.086 3E+00	1.643 0E-01	-2.699 6E-02	3.286 1E-01
11	7.438 8E+00	1.344 3E-01	-1.807 2E-02	2.688 6E-01
12	9.091 8E+00	1.099 9E-01	-1.209 8E-02	2.199 8E-01
13	1.111 2E+01	8.999 1E-02	-8.098 3E-03	1.799 8E-01
14	1.358 2E+01	7.362 9E-02	-5.421 2E-03	1.472 6E-01
15	1.660 0E+01	6.024 2E-02	-3.629 1E-03	1.204 8E-01
16	2.028 9E+01	4.928 9E-02	-2.429 4E-03	9.857 7E-02
17	2.479 7E+01	4.032 7E-02	-1.626 3E-03	8.065 4E-02
18	3.030 8E+01	3.299 5E-02	-1.088 7E-03	6.599 0E-02
19	3.704 3E+01	2.699 6E-02	-7.287 8E-04	5.399 2E-02
20	4.527 4E+01	2.208 8E-02	-4.878 6E-04	4.417 5E-02
21	5.533 5E+01	1.807 2E-02	-3.265 8E-04	3.614 3E-02
22	6.763 2E+01	1.478 6E-02	-2.186 2E-04	2.957 2E-02
23	8.266 2E+01	1.209 8E-02	-1.463 5E-04	2.419 5E-02
24	1.010 3E+02	9.898 0E-03	-9.797 0E-05	1.979 6E-02
25	1.234 8E+02	8.098 3E-03	-6.558 3E-05	1.619 7E-02
26	1.509 2E+02	6.625 9E-03	-4.390 3E-05	1.325 2E-02
27	1.844 6E+02	5.421 2E-03	-2.938 9E-05	1.084 2E-02
28	2.254 5E+02	4.435 5E-03	-1.967 4E-05	8.871 1E-03
29	2.755 5E+02	3.629 1E-03	-1.317 0E-05	7.258 1E-03
30	3.367 9E+02	2.969 2E-03	-8.816 4E-06	5.938 5E-03
31	4.116 3E+02	2.429 4E-03	-5.901 9E-06	4.858 8E-03
32	5.031 0E+02	1.987 7E-03	-3.950 8E-06	3.975 3E-03
33	6.149 0E+02	1.626 3E-03	-2.644 8E-06	3.252 6E-03
34	7.515 5E+02	1.330 6E-03	-1.770 5E-06	2.661 2E-03
35	9.185 6E+02	1.088 7E-03	-1.185 2E-06	2.177 3E-03
36	1.122 7E+03	8.907 3E-04	-7.933 9E-07	1.781 5E-03
37	1.372 2E+03	7.287 8E-04	-5.311 1E-07	1.457 6E-03
38	1.677 1E+03	5.962 7E-04	-3.555 4E-07	1.192 5E-03
39	2.049 8E+03	4.878 6E-04	-2.380 1E-07	9.757 2E-04
40	2.505 3E+03	3.991 6E-04	-1.593 3E-07	7.983 1E-04
41	3.062 0E+03	3.265 8E-04	-1.066 6E-07	6.531 7E-04
42	3.742 5E+03	2.672 0E-04	-7.139 8E-08	5.344 1E-04
43	4.574 1E+03	2.186 2E-04	-4.779 5E-08	4.372 4E-04
44	5.590 6E+03	1.788 7E-04	-3.199 5E-08	3.577 4E-04
45	6.832 9E+03	1.463 5E-04	-2.141 8E-08	2.927 0E-04
46	8.351 4E+03	1.197 4E-04	-1.433 8E-08	2.394 8E-04
47	1.020 7E+04	9.797 0E-05	-9.598 1E-09	1.959 4E-04

Table 2

Table 3

Table 4

Table 5

Fig.3

References 29

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参数	定义
N	构成装备的模块的集合，i∈N
a_i	模块i的装机数量
L_i	模块i的可选方案集合，j∈L_i
f_ij	方案j的研制费用
g_ij	方案j的生产费用
p_ij	选择方案j后是否可更换，0/1参数
q_ij	选择方案j后是否可维修，0/1参数
λ_ij	方案j的可靠性(1/MTBF)
x_ij	方案j的设计寿命
c_ij	方案j的故障修复费用
C_ij	方案j的到寿更换费用
b	无人作战飞机的生产量
M	一个大正数
X	非负连续变量，整机设计寿命(使用小时)
s_ij	0/1变量，表示模块i是否选择方案j
R_i	非负连续变量，模块i在X内的更换次数
F_i	非负连续变量，模块i的每飞行小时研制费用
G_i	非负连续变量，模块i的每飞行小时生产费用
H′_i	非负连续变量，模块i的每飞行小时修复费用
H″_i	非负连续变量，模块i的每飞行小时更换费用

序号	模块名称	组成数量	方案数量
1	机体结构	1	2
2	发动机	2	3
3	雷达	4	2
4	航电	1	4
5	导航	1	2
6	起落装置	1	2
7	机载1	10	3
8	机载2	2	3
9	机载3	4	2

模块名称	方案	研制成本f_ij	生产成本g_ij	是否可更换p_ij	是否可维修q_ij	故障率λ_ij	设计寿命x_ij/h	故障维修成本c_ij	到寿更换成本C_ij
机体结构	方案1	3 650	968	0	1	0.001 0	6 000	234.4	0
机体结构	方案2	2 780	557	0	1	0.001 2	3 500	109.5	0
发动机	方案1	1 189	225	1	1	0.001 0	1 500	49.5	486.0
	方案2	1 215	221	1	1	0.001 3	1 800	22.1	654.2
	方案3	1 524	259	1	1	0.000 9	2 100	72.5	676.0
雷达	方案1	560	24	1	1	0.001 0	1 200	2.4	70.1
雷达	方案2	780	25	1	1	0.002 0	1 400	5.3	44.0
航电	方案1	470	23	1	1	0.001 0	1 500	5.8	62.1
	方案2	580	21	1	1	0.000 8	1 300	4.6	46.6
	方案3	680	28	1	1	0.001 0	2 800	4.8	48.2
	方案4	980	31	1	1	0.000 9	2 000	9.3	75.9
导航	方案1	1 450	81	1	1	0.001 0	1 600	17.8	160.4
导航	方案2	1 570	90	1	1	0.000 8	1 400	17.1	266.4
起落装置	方案1	1590	55	1	1	0.001 0	1200	11.0	119.4
起落装置	方案2	1 200	61	1	1	0.001 0	1 400	15.3	170.2
机载1	方案1	2140	140	1	1	0.001 0	2 800	35.0	411.6
	方案2	2 570	180	1	1	0.002 0	3 000	46.8	446.4
	方案3	3 500	250	1	1	0.000 5	4 000	55.0	750.0
机载2	方案1	2 640	58	1	1	0.001 0	600	16.8	160.1
	方案2	2 850	62	1	1	0.001 0	500	10.5	114.1
	方案3	2 950	70	1	1	0.002 0	800	9.8	174.3
机载3	方案1	1 300	130	1	1	0.001 0	1 500	31.2	331.5
机载3	方案2	1 800	180	1	1	0.001 0	1 900	50.4	354.6

序号	模块名称	最佳选型方案	期望故障次数	更换次数
1	机体结构	方案2	3.4	0
2	发动机	方案1	5.6	2
3	雷达	方案2	22.4	4
4	航电	方案3	2.8	0
5	导航	方案1	2.8	1
6	起落装置	方案2	2.8	1
7	机载1	方案1	28	0
8	机载2	方案3	11.2	6
9	机载3	方案1	11.2	4

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Research on modeling and solving of forward design optimization of economic life of unmanned combat aircraft

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