Multi-objective Approximate Optimization for the Boost-glide Morphing Flight Vehicle Trajectory Scheme

Yiyun ZHAI; Teng LONG; Zhenyu LIU; Renhe SHI; Nianhui YE

doi:10.19328/j.cnki.2096-8655.2024.03.012

AEROSPACE SHANGHAI, Volume. 41, Issue 3, 110(2024)

Multi-objective Approximate Optimization for the Boost-glide Morphing Flight Vehicle Trajectory Scheme

Yiyun ZHAI*... Teng LONG, Zhenyu LIU, Renhe SHI and Nianhui YE |Show fewer author(s)

Author Affiliations

School of Aerospace Engineering,Beijing Institute of Technology,Beijing100081,China

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Figures & Tables(16)

Fig. 1. Schematic diagram of the all-course trajectory for boost-glide morphing flight vehicles

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Fig. 2. Optimization framework of the boost-glide morphing flight vehicle trajectory scheme

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Fig. 3. Diagram of the nozzle profile

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Fig. 4. Flowchart of the Newton iteration method

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Fig. 5. Profile of the angle of attack

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Fig. 6. Flowchart of the MACO-DE

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Fig. 7. Pareto solution set of the boost-glide morphing flight vehicle trajectory scheme

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Table 1. Tab.1Segment time of the pitch program angle
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Table 1. Tab.1Segment time of the pitch program angle
参数 $t_{1}$ $t_{2}$ $t_{3}$ $t_{4}$ $t_{5}$
取值 5 25 110 122 160

Table 2. Tab.2Basic information of the numerical test examples
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Table 2. Tab.2Basic information of the numerical test examples
算例维度 $n_{v}$ 目标数 $m$ 约束数 $n_{c}$ 理论PF数 $|Y_{P F}^{*}|$
OSY 6 2 6 1 000
CF1 8 2 1 21
CF2 8 2 1 626
C2-CDTLZ2 6 2 1 1 014

Table 3. Tab.3<bold>Optimization results of the MACO-DE</bold>、<bold>MOEGO</bold>，<bold>and C-MOEA/D </bold>（<bold>IGD values</bold>）

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Table 3. Tab.3<bold>Optimization results of the MACO-DE</bold>、<bold>MOEGO</bold>，<bold>and C-MOEA/D </bold>（<bold>IGD values</bold>）

优化算法	IGD	OSY	CF1	CF2	C2-CDTLZ2
MACO-DE $N_{}^{m a x}$ =300	Best	10.556 9	0.127 4	0.227 6	0.005 3
	Mean	22.093 0	0.181 5	0.376 4	0.035 0
	Worst	49.798 3	0.209 3	0.545 8	0.079 1
	Std.	16.181 5	0.032 8	0.118 9	0.023 0
MOEGO $N_{}^{m a x}$ =300	Best	40.277 3	0.176 7	0.219 2	0.050 0
	Mean	97.865 4	0.230 8	0.374 0	0.064 1
	Worst	151.097 3	0.305 4	0.538 0	0.098 9
	Std.	36.315 1	0.043 6	0.105 5	0.013 8
C-MOEA/D $N_{}^{m a x}$ =1000	Best	24.999 5	0.211 3	0.283 9	0.058 9
	Mean	40.547 4	0.253 9	0.388 5	0.084 4
	Worst	73.854 0	0.278 8	0.542 0	0.140 6
	Std.	17.403 5	0.020 1	0.079 1	0.028 9

Table 4. Tab.4Launch parameters
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Table 4. Tab.4Launch parameters
参数 $λ$ /(°) $ϕ$ /(°) $h$ /km $v$ /( $m \cdot s^{- 1}$ ) $Θ$ /(°) $ψ$ /(°)
取值 100.00 40.00 0.05 0 90.00 90.00

Table 5. Tab.5Boundaries of the control parameters

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Table 5. Tab.5Boundaries of the control parameters

参数	$α_{m, m i n}$ /(°)	$\begin{array}{l} {\dot{φ}}_{c, m i n} / \\ [(°) / s] \end{array}$	$\begin{array}{l} {\dot{χ}}_{1, m i n} / \\ [(°) / s] \end{array}$	$\begin{array}{l} {\dot{\bar{χ}}}_{2, m i n} / \\ (s^{- 1}) \end{array}$	$\begin{array}{l} {\dot{W}}_{m i n} / \\ (m / s) \end{array}$
取值	0	-1	-0.135	-0.005	-0.002 05
参数	$α_{m, m a x}$ /(°)	$\begin{array}{l} {\dot{φ}}_{c, m a x} / \\ [(°) / s] \end{array}$	$\begin{array}{l} {\dot{χ}}_{1, m a x} / \\ [(°) / s] \end{array}$	$\begin{array}{l} {\dot{\bar{χ}}}_{2, m a x} / \\ (s^{- 1}) \end{array}$	$\begin{array}{l} {\dot{W}}_{m a x} / \\ (m / s) \end{array}$
取值	25	3	0.135	0.005	0.002 05

Table 6. Tab.6Parameters of the MACO-DE
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Table 6. Tab.6Parameters of the MACO-DE
参数 $N_{I n i t}$ $N_{g l o b a l}$ $N_{l o c a l}$ $N_{f e}$ $F$ $C_{R}$
取值 120 4 2 400 0.8 0.8

Table 7. Tab.7Comparison of the initial and optimized objectives
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Table 7. Tab.7Comparison of the initial and optimized objectives
参数初始方案优化方案A 优化方案B
起飞质量 $m_{t o t a l}$ /kg 48 930.66 47 066.90 48 869.13
射程 $R_{t o t a l}$ /km 6 039.09 6 063.24 6 438.94

Table 8. Tab.8Comparison of the initial and optimized design variables

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Table 8. Tab.8Comparison of the initial and optimized design variables

参数	取值范围	初始方案	优化方案A	优化方案B
一级装药量 $m_{g r 1}$ /kg	[22 000,24 000]	23 000	22 090.52	23 014.45
二级装药量 $m_{g r 2}$ /kg	[11 000,13 000]	12 000	11 173.81	12 798.56
三级装药量 $m_{g r 3}$ /kg	[4 500,6 000]	5 500	5 503.61	4 632.45
高度 $h_{1}^{E}$ /km	[55,65]	60	55.23	60.65
当地速度倾角 $Θ_{1}^{E}$ /（°）	[0,5]	3	4.21	2.77
剖面参数 $v_{g α 1}$ /（m·s^-1）	[4 000,4 500]	4 500	4 012.71	4 237.48
剖面参数 $v_{g α 2}$ /（m·s^-1）	[3 200,3 700]	3 500	3 403.05	3 460.65
剖面参数 $α_{g 1}$ /（°）	[16,19]	18	16.35	16.03
剖面参数 $α_{g 2}$ /（°）	[11,15]	12	12.24	11.67

Table 9. Tab.9Comparison of the initial and optimized constraints

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Table 9. Tab.9Comparison of the initial and optimized constraints

参数	范围	初始方案	优化方案A	优化方案B
射程 $R_{t o t a l}$ /km	≥6 000	6 039.09	6 063.24	6 438.94
最大高度 $h_{m a x}$ /km	≤70	67.24	64.47	64.44
攻角动压积 $\|α_{b} \cdot q_{b}\|$ / [kPa $\cdot$ (°)]	≤150	96.63	96.74	98.84
滑翔段动压 $q_{g}$ /kPa	≤50	46.60	44.67	35.20
滑翔段热流 $Q_{g}$ /kW	≤1 500	1 228.63	1 289.36	1 271.98
滑翔段过载 $n_{g}$ /g	≤3	1.93	2.17	1.94

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Yiyun ZHAI, Teng LONG, Zhenyu LIU, Renhe SHI, Nianhui YE. Multi-objective Approximate Optimization for the Boost-glide Morphing Flight Vehicle Trajectory Scheme[J]. AEROSPACE SHANGHAI, 2024, 41(3): 110

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