Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties

doi:10.21629/JSEE.2019.02.10

Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (2): 308-318.doi: 10.21629/JSEE.2019.02.10

• Systems Engineering • Previous Articles Next Articles

Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties

Liangqi WAN(), Hongzhuan CHEN(), Linhan OUYANG*()

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Received:2018-03-15 Online:2019-04-01 Published:2019-04-28
Contact: Linhan OUYANG E-mail:wanliangqi@nuaa.edu.cn;hongzhuanchen@nuaa.edu.cn;ouyang@nuaa.edu.cn
About author:WAN Liangqi was born in 1991. He received his M.S. degree from Jiangxi University of Science and Technology in 2016. Now, he is a Ph.D. student at College of Economics and Management, Nanjing University of Aeronautics and Astronautics. He is also a joint Ph.D. student (2018.09- 2019.09) in the Reliability Research Laboratory, University of Alberta. His research interests are reliability-based design optimization and robust design optimization. E-mail:wanliangqi@nuaa.edu.cn|CHEN Hongzhuan was born in 1977. She received her M.S. degree from Shandong University of Science and Technology in 2002 and her Ph.D. degree from Hohai University in 2005. Now, she is a professor at College of Economics and Management, Nanjing University of Aeronautics and Astronautics. Her research interests are quality management and quality engineering. E-mail:hongzhuanchen@nuaa.edu.cn|OUYANG Linhan was born in 1987. He received his Ph.D. degree from Nanjing University of Science and Technology in 2016. Now, he is an assistant professor at College of Economics and Management, Nanjing University of Aeronautics and Astronautics. His research interests are quality engineering, modeling process, and engineering optimization. E-mail:ouyang@nuaa.edu.cn
Supported by:
the National Natural Science Foundation of China(71702072);the National Natural Science Foundation of China(71811540414);the National Natural Science Foundation of China(71573115);the Natural Science Foundation for Jiangsu Institutions(BK20170810);the Ministry of Education of Humanities and Social Science Planning Fund(18YJA630008);This work was supported by the National Natural Science Foundation of China (71702072; 71811540414; 71573115), the Natural Science Foundation for Jiangsu Institutions (BK20170810), and the Ministry of Education of Humanities and Social Science Planning Fund (18YJA630008)

Abstract

Abstract:

Minimizing the impact of the mixed uncertainties (i.e., the aleatory uncertainty and the epistemic uncertainty) for a complex product of compliant mechanism (CPCM) quality improvement signifies a fascinating research topic to enhance the robustness. However, most of the existing works in the CPCM robust design optimization neglect the mixed uncertainties, which might result in an unstable design or even an infeasible design. To solve this issue, a response surface methodology-based hybrid robust design optimization (RSM-based HRDO) approach is proposed to improve the robustness of the quality characteristic for the CPCM via considering the mixed uncertainties in the robust design optimization. A bridge-type amplification mechanism is used to manifest the effectiveness of the proposed approach. The comparison results prove that the proposed approach can not only keep its superiority in the robustness, but also provide a robust scheme for optimizing the design parameters.

Key words: response surface methodology (RSM), hybrid robust design optimization (HRDO), uncertainty, complex product of compliant mechanism (CPCM)

Liangqi WAN, Hongzhuan CHEN, Linhan OUYANG. Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties[J]. Journal of Systems Engineering and Electronics, 2019, 30(2): 308-318.

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References 30

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Variable	Represent	Unit	Low level	High level
$x_1 $	Flexible hinge thickness	mm	0.48	0.52
$x_2 $	Rigid beam length	mm	14.8	15.2
$x_3 $	Hinge distance	mm	1.8	2.2
$x_4 $	Flexible hinge length	mm	4.8	5.2

Runs	$x_1 $	$x_2 $	$x_3 $	$x_4 $	$y_{{{{\rm{RSM}}}}}^A$	$g_{{{{\rm{RSM}}}}}^{\sigma _{\max } }$
1	1	1	-1	-1	16.182 1	6.598 1
2	-1	-1	-1	1	16.329 9	6.661 9
3	1	-1	1	-1	13.891 3	4.334 1
4	0	0	0	0	15.394 5	4.905 3
5	-1	1	-1	1	16.630 0	6.748 0
6	-1	1	1	1	14.759 3	4.040 9
7	1	1	1	-1	14.159 0	4.387 4
8	1	-1	-1	-1	15.809 9	7.350 3
9	0	0	0	0	15.394 5	4.905 3
10	1	-1	1	1	14.214 6	3.959 7
11	-1	1	-1	-1	16.331 0	7.363 4
12	0	0	0	0	15.394 5	4.905 3
13	-1	-1	1	-1	14.155 9	4.516 3
14	1	-1	-1	1	16.178 1	6.278 0
15	-1	1	1	-1	14.442 1	4.479 9
16	1	1	1	1	14.484 3	4.059 0
17	1	1	-1	1	16.492 1	6.291 4
18	-1	-1	-1	-1	15.965 1	7.749 0
19	0	0	0	0	15.394 5	4.905 3
20	-1	-1	1	1	14.474 9	4.077 2
21	0	0	0	-2	15.052 2	6.177 4
22	-2	0	0	0	15.603 2	5.316 3
23	0	0	0	2	15.685 3	4.756 8
24	0	2	0	0	15.692 3	5.254 0
25	0	0	0	0	15.394 5	4.905 3
26	0	0	-2	0	16.826 8	8.856 7
27	0	0	2	0	13.238 9	3.829 4
28	0	-2	0	0	15.086 8	5.207 7
29	0	0	0	0	15.394 5	4.905 3
30	2	0	0	0	15.164 9	4.738 9

Items	$MSE$	$AAE$	$MAE$
$y_{{{{\rm{RSM}}}}}^A $	0.001 5	0.026 1	0.096 5
$g_{{{{\rm{RSM}}}}}^{\sigma _{\max } } $	0.005 9	0.062 9	0.130 2
Allowable value	${\leqslant} 0.2$	${\leqslant} 0.2$	${\leqslant} 0.2$

Random variable				Interval variable
Variable	Mean	Standard deviation	Distribution	Variable	Interval
$x_1 $	$\mu _{x_1 } $	$\sigma _{x_1 } = 0.01\mu _{x_1 } $	Normal
$x_2 $	$\mu _{x_2}$	$\sigma _{x_2} = 0.01\mu _{x_2} $	Normal	$x_3 $	$(x_3-0.025x_3, x_3+0.025x_3)$
$x_4 $	$\mu _{x_4 } $	$\sigma _{x_4 } = 0.01\mu _{x_4 } $	Normal

Design variable		Optimal solution
Deterministic approach	Proposed approach	Deterministic solution	Robust solution
$x_1 $	$\mu _{x_1 } $	0.475 2	0.470 1
$x_2 $	$\mu _{x_2 } $	14.788 5	14.776 0
$x_3 $	$x_3 $	5.172 9	5.182 7
$x_4 $	$\mu _{x_4 } $	2.388 3	2.399 7
$y_{{{{\rm{RSM}}}}}^A $	$y_{{{{\rm{RSM}}}}}^A $	13.424 3	14.897 4
$\overline {\sigma }_{y_{{{{\rm{RSM}}}}}^A } $	$\overline {\sigma}_{y_{{{{\rm{RSM}}}}}^A } $	0.181 1	0.180 7
$\delta \sigma _{y_{{{{\rm{RSM}}}}}^A } $	$\delta \sigma _{y_{{{{\rm{RSM}}}}}^A } $	0.004 6	0.003 4

Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties

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