Multidisciplinary integrated design of long-range ballistic missile using PSO algorithm

doi:10.23919/JSEE.2020.000011

Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (2): 335-349.doi: 10.23919/JSEE.2020.000011

• Systems Engineering • Previous Articles Next Articles

Multidisciplinary integrated design of long-range ballistic missile using PSO algorithm

Xu ZHENG^1,²(), Yejun GAO³(), Wuxing JING^1,*(), Yongsheng WANG⁴()

¹ Department of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001, China
² The 28th Research Institute of China Electronics Technology Group Corporation, Nanjing 210007, China
³ Beijing Aerospace Long-march Flying Vehicle Institute, Beijing 100076, China
⁴ Beijing Aerospace Technology Institute, Beijing 100074, China

Received:2018-02-05 Online:2020-04-30 Published:2020-04-30
Contact: Wuxing JING E-mail:zhengxu_hit@hotmail.com;15311424458@163.com;jingwuxing@hit.edu.cn;wangmeng_ys@qq.com
About author:ZHENG Xu was born in 1988. He received his M.S. and Ph.D. degrees in Department of Aerospace Engineering from Harbin Institute of Technology in 2014 and 2018 respectively. He is currently an engineer in the 28th Research Institute of China Electronics Technology Group Corporation. His research interests include nonlinear guidance and control, multidisciplinary design optimization. E-mail: zhengxu_hit@hotmail.com|GAO Yejun was born in 1968. He received his M.S. degree in Department of Aerospace Engineering from Harbin Institute of Technology. He is currently a senior engineer in Beijing Aerospace Long-march Flying Vehicle Institute. His research interests include guidance and control, multidisciplinary optimization, radio test and control. E-mail: 15311424458@163.com|JING Wuxing was born in 1965. He received hisM.S. and Ph.D. degrees from Harbin Institute of Technology in 1989and 1994, respectively. He was a visiting professor at Universityof Glasgow, UK, from 2000 to 2001. He is currently a professor andPh.D. supervisor in Harbin Institute of Technology. His researchinterests include autonomous navigation, nonlinear guidance, dynamics and control of spacecraft.E-mail: jingwuxing@hit.edu.cn|WANG Yongsheng was born in 1987. He received his M.S degree in Department of Aerospace Engineering, Harbin Institute of Technology. He is currently an engineer in Beijing Aerospace Technology Institute. His research interests include nonlinear guidance and control, and multidisciplinary design optimization. E-mail: wangmeng_ys@qq.com

Abstract

Abstract:

In the case of the given design variables and constraint functions, this paper is concerned with the rapid overall parameters design of trajectory, propulsion and aerodynamics for long-range ballistic missiles based on the index of the minimum take-off mass. In contrast to the traditional subsystem independent design, this paper adopts the research idea of the combination of the subsystem independent design and the multisystem integration design. Firstly, the trajectory, propulsion and aerodynamics of the subsystem are separately designed by the engineering design, including the design of the minimum energy trajectory, the computation of propulsion system parameters, and the calculation of aerodynamic coefficient and dynamic derivative of the missile by employing the software of missile DATCOM. Then, the uniform design method is used to simplify the constraint conditions and the design variables through the integration design, and the accurate design of the optimized variables would be accomplished by adopting the uniform particle swarm optimization (PSO) algorithm. Finally, the automation design software is written for the three-stage solid ballistic missile. The take-off mass of 29~850 kg is derived by the subsystem independent design, and 20 constraints are reduced by employing the uniform design on the basis of 29 design variables and 32 constraints, and the take-off mass is dropped by 1~850 kg by applying the combination of the uniform design and PSO. The simulation results demonstrate the effectiveness and feasibility of the proposed hybrid optimization technique.

Key words: ballistic missile, independent design, multidisciplinary integrated design, uniform design, particle swarm optimization (PSO)

Xu ZHENG, Yejun GAO, Wuxing JING, Yongsheng WANG. Multidisciplinary integrated design of long-range ballistic missile using PSO algorithm[J]. Journal of Systems Engineering and Electronics, 2020, 31(2): 335-349.

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References 32

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Constraint	Boundary	Value
$g_1 $	$\mu _{F\min 1} $	0.89
$g_2 $	$\Delta \alpha _{\max 1} $/($^\circ$)	12.0
$g_3 $	$\mu _{dD\max1}$	1
$g_4 $	$k_{ld\max 1} $	5.0
$g_5 $	$k_{ld\min 1} $	3.5
$g_6 $	$\mu _{F\min 2} $	0.89
$g_7 $	$\Delta \alpha _{\max 2} $/($^\circ$)	12.0
$g_8 $	$\mu _{dD\max2} $	1
$g_9 $	$k_{ld\max 2} $	4.0
$g_{10} $	$k_{ld\min 2} $	2.0
$g_{11} $	$\mu _{F\min 3} $	0.89
$g_{12} $	$\Delta \alpha _{\max 3} $/($^\circ$)	12.0
$g_{13} $	$\mu _{dD\max3} $	1
$g_{14} $	$k_{ld\max 3} $	2.0
$g_{15} $	$k_{ld\min 3} $	1.0
$g_{16} $	$N_{01\max } $	2.2
$g_{17} $	$N_{01\min}$	2.7
$g_{18} $	$k_{p\min } $	3.0
$g_{19} $	$\mu _{bD\max}$	0.1
$g_{20} $	$\theta _{d\max } $/($^\circ$)	15.0
$g_{21} $	$\theta _{d\min } $/($^\circ$)	8.0
$g_{22} $	$k_{LD\max } $	14.0
$g_{23} $	$k_{LD\min } $	8.0
$g_{24} $	$n_{x\max } $	14.0
$g_{25} $	$n_{y\max } $	2.0
$g_{26} $	$\alpha _{Ma\max } $/($^\circ$)	0.5
$g_{27} $	$q_{\max } $/MPa	0.1
$g_{28}$	$H_{12\min}$/km	30.0
$g_{29} $	$\theta _{e\max }$/($^\circ$)	-5.0
$g_{30} $	$\theta _{e\min } $/($^\circ$)	-35.0
$g_{31} $	$\Delta L_{\max }$/km	10.0
$g_{32} $	$\Delta Z_{\max }$/km	10.0

Engineparameter	Stage 1	Stage 2	Stage 3
$D_{ci}$/m	1.67	1.32	1.32
$L_{ci}$/m	4.72	3.10	0.73
$p_{ci}$/MPa	7	4.7	4.5
$\varepsilon _{Ai}$	14.47	19.64	23.57
$t_{ai}$/s	67.6	68.6	63.8
$\alpha _{Mi}$/($^\circ$)	23	23	23
$\alpha _{ei}$/($^\circ$)	12	12	12

Parameter	Value
$r_b$/m	0.132
$l_m$/m	2.73
$A_0$/($^\circ$)	-55.3
$t_1$/s	5.16
$a$	0.35
$\alpha _m$/($^\circ$)	10
$\dot {\varphi }_{cx2}$/($^\circ$/s)	0.15
$\dot {\varphi }_{cx3}$/($^\circ$/s)	0.2

Constraint function	Mean value	Standard deviation	$P(g_i > 0)$	Ordering
$g_1 $	-0.01	0.00	3.42e-7	22
$g_2 $	-0.10	0.09	0.13	9
$g_3 $	-0.55	0.06	0.00	29
$g_4 $	-1.04	0.13	6.66e-16	27
$g_5 $	-0.46	0.13	2.21e-4	16
$g_6 $	-0.02	0.00	0.00	30
$g_7 $	-0.10	0.09	0.13	8
$g_8 $	-0.35	0.05	4.43e-14	26
$g_9 $	-0.76	0.13	2.81e-9	24
$g_{10} $	-1.24	0.13	0.00	31
$g_{11} $	-0.03	0.01	1.97e-6	21
$g_{12} $	-0.10	0.10	0.14	7
$g_{13} $	-0.70	0.07	0.00	32
$g_{14} $	-0.47	0.10	2.11e-6	20
$g_{15} $	-0.53	0.10	6.94e-8	23
$g_{16} $	-0.16	0.08	0.03	12
$g_{17} $	-0.34	0.08	2.33e-5	17
$g_{18} $	-0.13	0.04	0.00	15
$g_{19} $	-0.02	0.02	0.10	10
$g_{20} $	-0.05	0.04	0.07	11
$g_{21} $	-0.07	0.04	0.03	13
$g_{22} $	-2.31	0.54	8.76e-6	18
$g_{23} $	-3.69	0.54	3.78e-12	25
$g_{24} $	-6.05	0.74	1.11e-16	28
$g_{25} $	-1.05	0.43	0.01	14
$g_{26} $	1.22e4	8.42e3	0.93	2
$g_{27} $	0.00	0.01	0.79	4
$g_{28} $	-2.06e3	3.06e3	0.25	6
$g_{29} $	-0.52	0.12	5.98e-6	19
$g_{30} $	0.01	0.12	0.52	5
$g_{31} $	6.37e5	3.76e5	0.95	1
$g_{32} $	5.59e4	4.91e4	0.87	3

${\partial f} / {\partial X_i }$	Mean value	Standard value	$P(\|{\partial f} / {\partial X_1 }\| \!>\! b)$	Ordering
${\partial f} / {\partial X_1 }$	1.13e5	4.47e3	1	1
${\partial f} / {\partial X_2 }$	9.12e3	6.17e2	0.78	4
${\partial f} / {\partial X_3 }$	1.35e2	7.88	1.00	2
${\partial f} / {\partial X_4 }$	0.62	0.08	3.92e-10	10
${\partial f} / {\partial X_5 }$	0.59	0.06	4.36e-6	8
${\partial f} / {\partial X_6 }$	-4.15e2	68.66	8.97e-16	15
${\partial f} / {\partial X_7 }$	-1.38e2	22.91	8.28e-16	16
${\partial f} / {\partial X_8 }$	5.14e4	3.14e3	0.99	3
${\partial f} / {\partial X_9 }$	5.34e3	4.75e2	2.96e-3	6
${\partial f} / {\partial X_{10} }$	47.37	3.80	0.06	5
${\partial f} / {\partial X_{11} }$	0.11	0.02	1.99e-12	13
${\partial f} / {\partial X_{12} }$	0.26	0.04	1.41e-12	12
${\partial f} / {\partial X_{13} }$	-1.51e2	26.70	3.43e-17	17
${\partial f} / {\partial X_{14} }$	-50.28	8.91	3.23e-17	18
${\partial f} / {\partial X_{15} }$	1.57e4	2.00e3	4.25e-10	9
${\partial f} / {\partial X_{16} }$	5.78e3	5.18e2	2.25e-3	7
${\partial f}/ {\partial X_{17} }$	3.29	0.65	1.95e-81	21
${\partial f} / {\partial X_{18} }$	0.03	0.00	4.29e-11	14
${\partial f}/ {\partial X_{19} }$	0.20	0.03	6.70e-13	11
${\partial f} / {\partial X_{20} }$	-50.83	10.85	6.01e-21	19
${\partial f}/ {\partial X_{21} }$	-16.94	3.62	5.72e-21	20
${\partial f}/ {\partial X_{22} }$	0	0	-	-
${\partial f} / {\partial X_{23} }$	0	0	-	-
${\partial f} / {\partial X_{24} }$	0	0	-	-
${\partial f}/ {\partial X_{25} }$	0	0	-	-
${\partial f}/ {\partial X_{26} }$	0	0	-	-
${\partial f}/ {\partial X_{27} }$	0	0	-	-
${\partial f} / {\partial X_{28} }$	0	0	-	-
${\partial f} / {\partial X_{29} }$	0	0	-	-
-	-	-	-	-

Multidisciplinary integrated design of long-range ballistic missile using PSO algorithm

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${\partial C} / {\partial X_i }$	Mean value	Standard deviation	$P(\|{\partial f} / {\partial X_1 }\|\!>\!b)$	Ordering
${\partial C} / {\partial X_1 }$	-2.06	2.34	0.28	11
${\partial C}/ {\partial X_2 }$	-0.23	0.22	0.33	9
${\partial C} / {\partial X_3 }$	-7.60e3	0.02	0.17	20
${\partial C} / {\partial X_4 }$	2.05e-3	1.64e-3	0.40	8
${\partial C} / {\partial X_5 }$	8.22e-4	3.86e-3	0.14	28
${\partial C} / {\partial X_6 }$	1.72	1.07	0.54	5
${\partial C} / {\partial X_7 }$	-0.11	0.40	0.15	24
${\partial C} / {\partial X_8 }$	0.38	2.27	0.14	27
${\partial C} / {\partial X_9 }$	0.06	0.25	0.14	26
${\partial C} / {\partial X_{10} }$	4.59e-3	9.17e-3	0.18	19
${\partial C} / {\partial X_{11} }$	1.76e-4	1.01e-4	0.59	4
${\partial C} / {\partial X_{12} }$	1.14e-4	1.79e-4	0.21	16
${\partial C} / {\partial X_{13} }$	1.41	0.69	0.71	1
${\partial C} / {\partial X_{14} }$	-0.15	0.21	0.23	14
${\partial C} / {\partial X_{15} }$	0.34	0.80	0.17	21
${\partial C} / {\partial X_{15} }$	0.02	0.32	0.13	29
${\partial C} / {\partial X_{17} }$	2.81e-3	3.62e-3	0.25	12
${\partial C} / {\partial X_{18} }$	-3.7e-5	1.36e-4	0.15	25
${\partial C} / {\partial X_{19} }$	1.35e-4	2.25e-4	0.20	17
${\partial C}/ {\partial X_{20} }$	1.26	0.64	0.68	2
${\partial C} / {\partial X_{21} }$	-0.19	0.14	0.44	7
${\partial C}/ {\partial X_{22} }$	5.93	3.27	0.62	3
${\partial C} / {\partial X_{23} }$	-3.9e-3	1.09e-2	0.16	23
${\partial C} / {\partial X_{24} }$	-21.57	58.65	0.16	22
${\partial C} / {\partial X_{25} }$	-0.07	0.11	0.21	15
${\partial C} / {\partial X_{26} }$	-9.05	6.15	0.49	6
${\partial C} / {\partial X_{27} }$	18.23	19.22	0.30	10
${\partial C} / {\partial X_{28} }$	-1.40e5	2.55e5	0.19	18
${\partial C} / {\partial X_{29} }$	-4.55e4	6.03e4	0.24	13
-	-	-	-	-

Design variable		Lower boundary	Upper boundary	Nominal value	Optimization value
$X_1 $	$D_{c1} $/m	1.60	1.80	1.67	1.643
$X_2 $	$D_{c2} $/m	1.20	1.40	1.32	1.356
$X_3 $	$D_{c3} $/m	1.20	1.40	1.32	1.200
$X_4 $	$L_{c1} $/m	4.80	5.20	4.93	4.800
$X_5 $	$L_{c2} $/m	2.70	3.10	2.87	2.707
$X_6 $	$L_{c3} $/m	0.50	0.90	0.70	0.900
$X_7 $	$p_{c1} $/MPa	6.50	7.50	7.00	6.500
$X_8 $	$p_{c2} $/MPa	4.00	5.00	4.70	5.000
$X_9 $	$p_{c3} $/MPa	4.00	5.00	4.50	4.000
$X_{10} $	$t_{a1} $/s	60.00	65.00	62.56	65.000
$X_{11} $	$t_{a2} $/s	65.00	70.00	67.58	65.000
$X_{12} $	$t_{a3} $/s	60.00	65.00	63.09	60.000
$X_{13} $	$\varepsilon _{A1} $	13.00	17.00	14.47	13.000
$X_{14} $	$\varepsilon _{A2} $	18.00	23.00	19.64	23.000
$X_{15} $	$\varepsilon _{A3} $	20.00	26.00	23.56	25.775
$X_{16} $	$\alpha _{M1} $/($^\circ$)	20.00	26.00	23.00	20.000
$X_{17} $	$\alpha_{M2} $/($^\circ$)	20.00	26.00	23.00	20.000
$X_{18} $	$\alpha_{M3} $/($^\circ$)	20.00	26.00	23.00	25.880
$X_{19} $	$\alpha_{e1} $/($^\circ$)	8.00	26.00	12.00	8.273
$X_{20} $	$\alpha_{e2} $/($^\circ$)	8.00	26.00	12.00	8.018
$X_{21} $	$\alpha_{e3} $/($^\circ$)	8.00	26.00	12.00	14.932
$X_{22} $	$r_b$/m	0.07	0.14	0.11	0.106
$X_{23} $	$l_m$/m	2.00	3.50	2.83	2.702
$X_{24} $	$A_0$/($^\circ$)	-57.34	-54.34	-55.84	-56.047
$X_{25} $	$t_1$/s	4.80	5.50	5.16	4.800
$X_{26} $	$a$	0.30	0.40	0.35	0.400
$X_{27} $	$\alpha _m $/($^\circ$)	10.00	15.00	14.00	10.002
$X_{28} $	$\dot {\varphi }_{cx2}$/($^\circ$/s)	-0.20	0.00	-0.10	-0.080
$X_{29} $	$\dot {\varphi }_{cx3}$($^\circ$/s)	-0.40	0.00	-0.20	-0.400
	-	-	-	-	-

Constraint function	Pre-optimization	Post-optimization
$g_2$	-1.00	-0.005
$g_7$	-1.00	0
$g_{12}$	-1.00	-0.018
$g_{19}$	-0.02	-0.012
$g_{20}$	-0.06	-0.074
$g_{21}$	-0.06	-0.049
$g_{26}$	-0.02	-1.57e3
$g_{27}$	-0.21	-6.46e-3
$g_{28}$	-1.53	-8.16e2
$g_{30}$	-8.95	-0.074
$g_{31}$	-354.44	-1.94e3
$g_{32}$	-16.98	-3.83e3

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