面向引力波探测航天器多物理场噪声抑制的组件布局优化

doi:10.7527/S1000-6893.2025.31817

Abstract

Abstract:

The space-based gravitational wave detection mission places extremely high demands on the cleanliness of the core environment within spacecraft. To meet these demands， a Bilevel Sequential Optimization Approach （BSOA） is proposed to solve the Spacecraft Component Layout Design （SCLD） problem， aiming to effectively suppress electromagnetic forces and self-gravity noise. SCLD is a typical mixed-integer programming problem， and the BSOA method is further formulated as a bilevel optimization problem for solution. The upper-level optimization is defined as an integer nonlinear programming problem to determine the orientation and region of components， while the lower-level optimization is defined as a real-valued nonlinear programming problem to optimize the placement of components within the selected region. By introducing a feedback iterative mechanism， the results of the lower-level optimization influence upper-level decisions， enabling progressive optimization of the layout scheme. Within the bilevel sequential optimization framework， an elite genetic algorithm is employed for global optimization of the upper-level problem using， while the lower-level problem is locally searched using a differential evolution algorithm. To address various technical challenges in the optimization process， a hybrid encoding strategy is proposed to meet the coding requirements of evolutionary algorithms， a regional division strategy is introduced to discretize installation positions， and a collision detection approach is implemented to identify violations of geometric constraints among components. Experimental results demonstrate that the proposed approach efficiently solves layout design problems under complex multi-constraint conditions， generates layout schemes that meet scientific mission requirements， and significantly outperforms traditional single-stage and two-stage optimization methods in terms of performance indicators such as mean and standard deviation. This approach exhibits significant application potential and extensibility， laying a technical foundation for future gravitational wave detection missions.

Key words: gravitational wave detection, layout design, mixed-integer programming, nonlinear programming, bilevel optimization

CLC Number:

Ziruo FANG, Ningbiao TANG, Ye LIU, Zhiming CAI, Wen CHEN, Zhencai ZHU, Xingjian SHI. Component layout design optimization for multi-physical field noise suppression in gravitational wave detection spacecraft[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(18): 231817.

Figures/Tables 26

Fig.1

Fig.2

Table 1

Definition of design variables

变量	描述	单位	类型	取值集合/范围
$f i$	组件的安装面		离散	$S' ⊆ 0,1, 2,3, 4,5$
$θ i$	组件的旋转角度	rad	离散	$S' ⊆ - π / 2,0, π / 2, π$
$s i$	组件在卫星平台的安装面		离散	$S' ⊆ 0,1, 2,3, 4,5, 6$
$x i$	组件在 $s i$ 面上 $x$ 轴方向位置	mm	连续	$R = x m i n, x m a x$
$y i$	组件在 $s i$ 面上 $y$ 轴方向位置	mm	连续	$R = y m i n, y m a x$
$p i$	组件在 $s i$ 面上的安装区域		离散	$S' ⊆ 0,1, …, N r - 1$
$x p i$	相对 $p i$ 区域中心点 $x$ 轴方向偏移	mm	连续	$R = x p i x p i - C p i, x 2 + y p i - C p i, y 2 ≤ r p$
$y p i$	相对 $p i$ 区域中心点 $y$ 轴方向偏移	mm	连续	$R = y p i x p i - C p i, x 2 + y p i - C p i, y 2 ≤ r p$

Table 1

Table 2

Definition of variable decision types

类型	变量	关联性
方向选择	$f i, θ i, s i$
区域选择	$p i$	$s i → p i$
位置选择	$x p i, y p i$	$p i → x p i, y p i$

Table 2

Fig.3

Fig.4

Fig.5

Table 3

Scientific mission objective metrics

指标	指标含义	目标值	单位
$B$	TM处磁感应强度	$1 × 10 - 5$	$T$
$∇ B$	TM处磁感应强度梯度	$5 × 10 - 6$	$T / m$
$F$	TM处自引力偏置	$1 × 10 - 10$	$m / s 2$
$K$	TM处自引力刚度	$1 × 10 - 8$	$1 / s 2$

Table 3

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 4

Component properties

组件	尺寸/mm	质量/kg	磁矩/（ $m A · m 2$ ）
A1/A2	［480，350，150］	24	［70，70，70］
B1/B2	［450，400，200］	15	［50，50，0］
C1/C2	［320，300，250］	20	［70，70，70］
D1/D2	［300，300，200］	10	［12，6，0］
E1/E2	［250，150，150］	2.2	［30，0，0］
F1/F2	［240，200，150］	4	［70，70，70］
G1/G2	［220，200，150］	5.25	［0，20，50］
H1/H2	［160，135，30］	5	［30，0，20］
I1	［150，130，100］	5	［26，353，344］
J1	［420，250，250］	16	［41，95，95］
K1	［380，255，150］	12	［4，32，32］
L1	［350，240，210］	8	［70，70，70］
M1	［320，270，40］	15	［70，70，70］
N1	［300，300，200］	8	［12，50，30］
O1	［240，170，90］	20	［50，50，50］

Table 4

Table 5

Table 6

Initial values of strength indicators at TM

r 0

B 0

F 0

r T M 1

［-7.82×10^-6，4.44×10^-6，

4.59×10^-7］

［8.31×10^-10，

3.45×10^-10，0］

r T M 2

［-7.82×10^-6，-4.44×10^-6，

4.59×10^-7］

［8.31×10^-10，

-3.45×10^-10，0］

Table 6

Table 7

Initial settings of experimental parameters

参数	初值
$ω$	［0.5，0.5，0.5，0.5，0.5，0.5，0.5，0.5］
$ω c$	［1，1，1］
$a$ /mm	200
$r p$ /mm	200
$ε$ /mm	175
$N P$	100
$I$	300
R	3
$P E G A c$	0.7
$P E G A m$	BG-0.01， RI-0.5， P-0.5
$P D E c$	0.5
$P D E m$	0.5

Table 7

Table 8

Orthogonal experiment result

编号	$a / m m$	$r p / m m$	$R$	Best	Worst	Avg	Std
1	200	200	1	-1.25	2	-0.30	1.15
2	200	300	2	-1.25	2	-0.44	1.06
3	200	400	3	-1.25	1	-0.60	0.90
4	250	200	2	-1.26	1	-0.85	0.83
5	250	300	3	-1.24	1	-0.40	0.95
6	250	400	1	-1.25	2	-0.71	0.96
7	300	200	3	-1.27	2	-0.26	1.12
8	300	300	1	-1.26	1	-0.50	1.05
9	300	400	2	-1.25	1	-0.69	0.93

Table 8

Table 9

Results of comparative experiment Ⅰ

算法	$I s$	Best	Worst	Avg	Std
OSOA	300	0.29	4.32	2.65	1.01
TSOA	150	1	3	1.57	0.67
BSOA	75	-1.26	1	-0.85	0.83

Table 9

Fig.11

Table 10

Results of comparative experiment Ⅱ

$I s$	OSOA				TSOA				BSOA
$I s$	Best	Worst	Avg	Std	Best	Worst	Avg	Std	Best	Worst	Avg	Std
75	2.83	6.67	4.52	1.21	-1.14	3	1.05	1.44	-1.26	1	-0.85	0.83
150	2.15	5.07	3.54	0.97	-1.27	2	0.68	1.30	-1.28	1	-1.03	0.71
300	1.75	4.10	2.54	0.81	-1.26	3	0.94	1.51	-1.28	1	-0.81	0.95

Table 10

Table 11

Optimal solution

组件	$f$	$θ$	$s$	$p$	$x / m m$	$y / m m$
A1	1	1	4	3	-150.26	-0.74
B1	1	2	5	2	-83.57	200.00
C1	4	1	2	4	-200.00	5.29
D1	4	3	4	0	-8.65	150.38
E1	1	1	1	4	-136.92	2.96
F1	2	2	4	4	-109.18	-84.28
G1	4	1	0	0	-144.83	166.11
H1	4	3	2	0	200.00	-52.95
A2	3	1	3	1	-71.08	76.77
B2	4	2	3	4	-54.26	-65.89
C2	4	1	3	3	-5.58	200.00
D2	2	0	6	4	-9.99	-200.00
E2	3	1	5	0	-72.32	174.10
F2	1	2	6	2	-159.30	35.99
G2	2	3	2	2	173.80	179.65
H2	2	1	6	3	-88.46	109.31
I1	1	1	3	0	200.00	9.38
J1	4	3	1	0	-123.61	192.07
K1	3	3	5	3	-144.72	55.51
L1	3	0	0	3	36.35	-9.04
M1	0	1	1	1	83.83	-148.28
N1	3	1	5	1	-68.53	14.18
O1	2	1	1	3	-133.50	195.60

Table 11

Fig.12

Table 12

Calculated values of various indicators for optimal solution

$r 0$	$B 0$ /（10^-6 T）	$∇ B 0$ /（10^-6 T·m^-1）	$F 0$ /（10^-11 m·s^-2）	$K 0$ /（10^-8 s^-2）
$r T M 1$	8.76	4.65	1.36	9.07
$r T M 2$	8.95	4.64	1.00	9.14

Table 12

Fig.13

Fig.14

References 24

[1]	BAILES M， BERGER B K， BRADY P R， et al. Gravitational-wave physics and astronomy in the 2020 s and 2030 s［J］. Nature Reviews Physics， 2021， 3（5）： 344-366.
[2]	LUO Z R， GUO Z K， JIN G， et al. A brief analysis to Taiji： Science and technology［J］. Results in Physics， 2020， 16： 102918.
[3]	Arranz C J， Marchese V， Léger J M， et al. Magnetic cleanliness on NanoMagSat， a CubeSats’constellation science mission［C］∥2023 International Symposium on Electromagnetic Compatibility-EMC Europe. Piscataway： IEEE Press， 2023： 1-6.
[4]	TENG H F， SUN S L， LIU D Q， et al. Layout optimization for the objects located within a rotating vessel： A three-dimensional packing problem with behavioral constraints［J］. Computers & Operations Research， 2001， 28（6）： 521-535.
[5]	XU Y C， XIAO R B， AMOS M. A novel genetic algorithm for the layout optimization problem［C］∥2007 IEEE Congress on Evolutionary Computation. Piscataway： IEEE Press， 2007： 3938-3943.
[6]	FAKOOR M， GHOREISHI S M N， SABAGHZADEH H. Spacecraft Component Adaptive Layout Environment （SCALE）： An efficient optimization tool［J］. Advances in Space Research， 2016， 58（9）： 1654-1670.
[7]	QIN Z， LIANG Y G. Multiobjective methodology for satellite cabin layout optimization considering space debris impact risk［J］. Journal of Spacecraft and Rockets， 2017， 55（1）： 232-235.
[8]	CUI F Z， XU Z Z， WANG X K， et al. A dual-system cooperative co-evolutionary algorithm for satellite equipment layout optimization［J］. Proceedings of the Institution of Mechanical Engineers， Part G： Journal of Aerospace Engineering， 2018， 232（13）： 2432-2457.
[9]	FENG Y B， WU X D， CHEN W D， et al. Optimal design of space assembly microsatellite structure based on sequential quadratic programming［J］. Aircraft Engineering and Aerospace Technology， 2023， 95（1）： 145-154.
[10]	CHEN X Q， LIU S C， SHENG T， et al. The satellite layout optimization design approach for minimizing the residual magnetic flux density of micro-and nano-satellites［J］. Acta Astronautica， 2019， 163： 299-306.
[11]	CHEN X Q， CHEN X Q， XIA Y F， et al. An ILP-assisted two-stage layout optimization method for satellite payload placement［J］. Space： Science and Technology， 2022， 2022： 9765260.
[12]	FAKOOR M， TAGHINEZHAD M. Layout and configuration design for a satellite with variable mass using hybrid optimization method［J］. Proceedings of the Institution of Mechanical Engineers， Part G： Journal of Aerospace Engineering， 2016， 230（2）： 360-377.
[13]	CHEN X Q， YAO W， ZHAO Y， et al. A practical satellite layout optimization design approach based on enhanced finite-circle method［J］. Structural and Multidisciplinary Optimization， 2018， 58（6）： 2635-2653.
[14]	BELLO W B， PEDDADA S R T， BHATTACHARYYA A， et al. Multi-physics three-dimensional component placement and routing optimization using geometric projection［J］. Journal of Mechanical Design， 2024， 146（8）： 081702.
[15]	Teschner M， Kimmerle S， Heidelberger B， et al. Collision detection for deformable objects［C］∥Computer Graphics Forum. 2005， 24（1）： 61-81.
[16]	CHEN S J， SUN S Y， DI M C. Real-time collision detection algorithm optimization in game physics engines［C］∥2024 IEEE 6th International Conference on Civil Aviation Safety and Information Technology （ICCASIT）. Piscataway： IEEE Press， 2024： 1317-1320.
[17]	ZHAO G， THIENMONGKOL R， NIMNOI R， et al. Adaptive cauchy mutation integrated particle swarm optimization for random collision detection in virtual museum［C］∥2024 International Conference on Data Science and Network Security （ICDSNS）. 2024： 1-5.
[18]	SUN Z G， TENG H F. Optimal layout design of a satellite module［J］. Engineering Optimization， 2003， 35（5）： 513-529.
[19]	ZHANG B， TENG H F， SHI Y J. Layout optimization of satellite module using soft computing techniques［J］. Applied Soft Computing， 2008， 8（1）： 507-521.
[20]	HEKMATFAR M， ALIHA M R M， PISHVAEE M S， et al. A robust flexible optimization model for 3D-layout of interior equipment in a multi-floor satellite［J］. Mathematics， 2023， 11（24）： 4932.
[21]	MEJÍA-DE-DIOS J A， RODRÍGUEZ-MOLINA A， MEZURA-MONTES E. Multiobjective bilevel optimization： A survey of the state-of-the-art［J］. IEEE Transactions on Systems， Man， and Cybernetics： Systems， 2023， 53（9）： 5478-5490.
[22]	ZHANG D Q， LIU Z Q， LIANG Y， et al. Bilevel optimization of non-uniform offshore wind farm layout and cable routing for the refined LCOE using an enhanced PSO［J］. Ocean Engineering， 2024， 299： 117244.
[23]	LUO Y L， GAO Y. Real-time pricing strategy considering carbon emissions and time coupling in smart grid： A binary integer bilevel optimization model with decision-making［J］. Engineering Applications of Artificial Intelligence， 2025， 141： 109858.
[24]	CHEN J W， WANG F R， CHEN Y G， et al. A generalized bilevel optimization model for large-scale task scheduling in multiple agile earth observation satellites［J］. Knowledge-Based Systems， 2025， 309： 112809.

名称	尺寸/mm	位置/mm	方向/（°）
TM1	［46，46，46］	［0，200，600］	［0，0，-30］
TM2	［46，46，46］	［0，-200，600］	［0，0，30］

Component layout design optimization for multi-physical field noise suppression in gravitational wave detection spacecraft

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 26

References 24

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Shufan WU, Xiaoyun Sun, Qianyun ZHANG, Qiang SHEN, Yu XIANG. Research progress in test mass dynamics and control of space inertial sensor [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(17): 331781-331781.
[2]	Xiaoyun SUN, Shufan WU, Qiang SHEN. LMI-based output tracking robust drag-free control with model reference adaptive scheme [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 727654-727654.
[3]	ZHOU Zhenyao, LYU Fei, ZHOU Bin, YANG Zhao. Verification method for natural laminar flow drag reduction and layout design of test section [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(11): 526751-526751.
[4]	YUAN Jisen, SUN Jue, LI Lingyu, YU Shenghao, NIE Han, GAO Liangjie, HAN Zhonghua, QIAN Zhansen. Progress of supersonic aircraft laminar flow layout design and evaluation technologies [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(11): 526316-526316.
[5]	ZHANG Liming, XING Jianjun, CHEN Ziang, WANG Yi, YU Yang. Effect of Dryden atmospheric turbulence on minimum-energy trajectory of stratospheric airships [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(1): 120180-120180.
[6]	LIU Gang, LI Chuanjiang, MA Guangfu. Station-keeping of Tethered Satellite System Around a Halo Orbit Using Nonlinear Model Predictive Control [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(9): 2605-2614.
[7]	WANG Pidong, ZHANG Jianguo, MA Zhiyi, SUN Jing, GAO Peng. Pulse Transiently Chaotic Neural Network for the Analysis Method of Reliability [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(2): 469-477.
[8]	WEI Wenshu, JING Wuxing, GAO Changsheng. Research Automatic Stability Technology of Spacecraft Assembly with Captured Non-cooperative Targets on Orbit [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013, 34(7): 1520-1530.
[9]	MENG Wanli, CHEN Renliang. Trajectory Optimization of Helicopter Autorotation Landing After One Engine Failure [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(9): 1599-1607.
[10]	WANG Lei, WANG Lixin, JIA Zhongren. Control Allocation Method for Combat Flying Wing with Multiple Control Surfaces [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(4): 571-579.
[11]	Zhong Rui;Xu Shijie. Orbit-transfer Control for TSS Using Direct Collocation Method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2010, 31(3): 572-578.
[12]	Kang Bingnan;Tang Shuo. Trajectory Design and Optimization of Powered Common Aero Vehicles [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2009, 30(4): 738-743.
[13]	Liu Lili;Wen Hao;Jin Dongping;Hu Haiyan. Optimal Control of Orbit Transfer for a Tethered Subsatellite System [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2009, 30(2): 332-336.
[14]	Tong Kewei;Zhou Jianping;He Linshu. Legendre-Gauss Pseudospectral Method for Solving Optimal Control Problem [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2008, 30(6): 1531-1537.
[15]	Liu Tongren. A CALCULATION OF OPTIMAL FLIGHT TRAJECTORY USING THE PARAMETERIZED OPTIMIZATION METHOD [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1994, 15(11): 1298-1305.