Hybrid IPSO-IAGA-BPNN algorithm-based rapid multi-objective optimization of a fully parameterized spaceborne primary mirror

Tao Qin; Tao Qin; Tao Qin; JunLi Guo; JunLi Guo; JunLi Guo; ZiJian Jing; ZiJian Jing; PeiXian Han; PeiXian Han; PeiXian Han; Bo Qi; Bo Qi

doi:10.1364/AO.419227

Applied Optics
Vol. 60,
Issue 11,
pp. 3031-3043
(2021)
•https://doi.org/10.1364/AO.419227

Hybrid IPSO-IAGA-BPNN algorithm-based rapid multi-objective optimization of a fully parameterized spaceborne primary mirror

Tao Qin, JunLi Guo, ZiJian Jing, PeiXian Han, and Bo Qi

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Tao Qin, JunLi Guo, ZiJian Jing, PeiXian Han, and Bo Qi, "Hybrid IPSO-IAGA-BPNN algorithm-based rapid multi-objective optimization of a fully parameterized spaceborne primary mirror," Appl. Opt. 60, 3031-3043 (2021)

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Abstract

The surface figure precision, weight, and dynamic performance of spaceborne primary mirrors depend on mirror structure parameters, which are usually optimized to improve the overall performance. To realize rapid multi-objective design optimization of a primary mirror with multiple apertures, a fully parameterized primary mirror structure is established. A surrogate model based on a hybrid of improved particle swarm optimization (IPSO), adaptive genetic algorithm (IAGA), and optimized back propagation neural network (IPSO-IAGA-BPNN) is developed to replace optomechanical simulation with its high computational cost. In this model, a self-adaptive inertia weight and a modified genetic operator are introduced into the particle swarm optimization (PSO) and adaptive genetic algorithm (AGA), respectively. The connection parameters of BPNN are optimized by the IPSO-IAGA algorithm for global searching capability. Further, the proposed IPSO-IAGA-BPNN, based on a rapid multi-objective optimization framework for a fully parameterized primary mirror structure, is established. Moreover, in addition to the proposed IPSO-IAGA-BPNN model, the Kriging, RSM, BPNN, GA-BPNN, PSO-BPNN, and PSO-GA-BPNN models are also analyzed as contrast models. The comparison results indicate that the predicted value obtained by IPSO-IAGA-BPNN is superior to the six other surrogate models since its mean absolute percentage error is less than 3% and its ${R^2}$ is more than 0.99. Finally, we present a Pareto-optimal primary mirror design and implement it through three optimization methods. The verification results show that the proposed method predicts mirror structural performance more accurately than existing surrogate-based methods, and promotes significantly superior computational efficiency compared to the conventional integration-based method.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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		Values (mm)
Name	Parameter	Lower	Upper
Diameter	$s_{d}$	500	800
Mirror surface thickness	$t_{f}$	$4 * α$	$6 * α$
Support hole wall thickness	$t_{h}$	$6 * α$	$12 * α$
Side surface thickness	$t_{s}$	2	10
1th group ribs thickness	$t_{r 1}$	2	10
2th group ribs thickness	$t_{r 2}$	2	10
3rd group rib thickness	$t_{r 3}$	2	10
The high node height	$h_{h}$	0	$30 * α$
The middle node height	$h_{m}$	$- 10 * α$	$10 * α$
The low node height	$h_{l}$	$- 100 * α$	$- 50 * α$
Support hole radius	$r_{h}$	$- 10 * α$	$- 30 * α$
$1 t h$ group ribs radius	$r_{r}$	$60 * α$	$100 * α$

$n h$	MSE	TS	MAE	MPE
8	8.34E-4	28	36.08	16.54
9	7.95E-4	32	22.41	14.78
10	6.98E-4	19	32.58	19.77
11	4.87E-4	30	19.31	14.0
12	3.55E-4	50	22.65	13.27
13	2.24E-4	70	18.52	12.59
14	2.88E-4	49	20.81	10.89
15	2.13E-4	46	18.00	11.25
16	1.27E-4	92	15.86	8.18
17	1.58E-4	72	22.12	11.04
18	1.57E-4	50	19.97	11.79

	Predicted ${Freq}_{1}$			Predicted ${RMS}_{L}$			Predicted ${RMS}_{A}$			Predicted $Mass$
Surrogate Model	$R^{2}$	MAPE	MAE	$R^{2}$	MAPE	MAE	$R^{2}$	MAPE	MAE	$R^{2}$	MAPE	MAE
Kriging	0.699	10.97	108.9	0.591	23.65	0.873	0.654	25.95	2.447	0.724	22.79	2.322
RSM	0.919	5.79	59.56	0.844	14.75	0.620	0.782	22.3	2.167	0.971	7.33	0.721
BPNN	0.987	2.50	23.45	0.938	9.74	0.371	0.958	8.24	0.988	0.988	3.01	0.367
GA-BPNN	0.983	2.86	27.25	0.947	8.67	0.366	0.966	7.86	0.825	0.994	3.11	0.394
PSO-BPNN	0.985	2.76	25.94	0.949	8.06	0.354	0.961	9.59	0.967	0.993	2.76	0.383
PSO-GA-BPNN	0.986	2.59	22.53	0.977	4.98	0.231	0.985	4.44	0.534	0.998	1.60	0.216
IPSO-IAGA-BPNN	0.991	1.72	17.28	0.994	2.17	0.104	0.993	2.92	0.379	0.999	0.67	0.088

$S_{d} / m m$	Index	NSGA-II	MOEA/D	MOPSO
500	Runtime/s	149	328	154
500	HV	0.74	0.71	0.72
600	Runtime/s	128	315	176
600	HV	0.80	0.76	0.79
700	Runtime/s	132	302	116
700	HV	0.71	0.67	0.68
800	Runtime/s	119	275	118
800	HV	0.58	0.53	0.56

	500 mm		600 mm		700 mm		800 mm
Name	$x^{(1)}$	$x^{(2)}$	$x^{(3)}$	$x^{(4)}$	$x^{(5)}$	$x^{(6)}$	$x^{(7)}$	$x^{(8)}$
$t_{f}$	2.5	2.5	3.0	3.1	3.5	3.5	4.0	4.0
$t_{h}$	3.77	3.8	4.6	4.5	5.3	5.2	6.1	6.0
$t_{s}$	2.0	2.0	2.0	2.0	2.1	2.0	2.0	2.0
$t_{r} 1$	2.9	3.1	2.4	2.0	2.9	2.6	2.4	2.0
$t_{r} 2$	2.0	2.0	2.0	2.0	2.0	2.0	2.0	2.0
$t_{r} 3$	2.0	2.0	2.0	2.0	2.0	2.0	2.0	2.0
$h_{h}$	18.5	18.7	22.5	22.4	25.2	26.3	29.9	30
$h_{m}$	−6.2	−6.3	−7.5	−7.4	−8.2	−8.6	−8.9	−9.9
$h_{l}$	−62.1	−62.5	−75.0	−74.6	−87.4	−87.5	−100	−100
$r_{h}$	15.1	14.4	10.5	11.2	14.1	17.9	26.0	29.7
$r_{r}$	42.7	44.8	74.9	74.8	83.4	84.1	60.4	60.1
$F_{1} / k g$	3.32	3.37	5.15	4.96	8.17	7.98	11.13	10.89
$F_{2} / n m$	3.34	3.28	4.97	5.40	6.57	6.79	9.50	9.98

Design	Objective	$x^{(1)}$	$x^{(2)}$	$x^{(3)}$	$x^{(4)}$	$x^{(5)}$	$x^{(6)}$	$x^{(7)}$	$x^{(8)}$
Simulation results	$F_{1}$	3.30	3.38	5.22	5.02	8.22	7.97	11.07	10.81
Simulation results	$F_{2}$	3.347	3.25	5.19	5.62	6.76	6.95	9.87	10.52
Predicted results I	$F_{1}$	3.74	3.86	5.66	5.57	8.52	8.36	11.32	14.52
Predicted results I	$F_{2}$	3.43	3.23	5.61	6.03	6.61	6.61	7.42	5.17
Predicted results II	$F_{1}$	3.32	3.37	5.15	4.96	8.17	7.98	11.13	10.89
Predicted results II	$F_{2}$	3.34	3.28	4.97	5.40	6.57	6.79	9.50	9.98
AEP I(%)	$F_{1}$	18.04	14.33	8.30	11.13	3.69	4.80	2.27	3.01
AEP I(%)	$F_{2}$	3.33	0.42	7.89	7.26	1.87	4.96	24.83	25.25
AEP II(%)	$F_{1}$	0.51	0.11	1.50	1.12	0.64	0.02	0.58	0.78
AEP II(%)	$F_{2}$	2.27	0.80	4.44	3.952	2.715	2.266	3.758	5.08

		CPU Time/h
Optimization Methods	D/mm	Total	Relative (%)
Method I	500	198.56	100%
	600
	700
	800
Method II	500	0.15	0.20%
	600
	700
	800
Proposed method	500	0.13	0.19%
	600
	700
	800

Abstract

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Applied Optics