Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (2): 308318.doi: 10.21629/JSEE.2019.02.10
• Systems Engineering • Previous Articles Next Articles
Liangqi WAN(), Hongzhuan CHEN(), Linhan OUYANG*()
Received:
20180315
Online:
20190401
Published:
20190428
Contact:
Linhan OUYANG
Email: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 reliabilitybased design optimization and robust design optimization. Email:Supported by:
Liangqi WAN, Hongzhuan CHEN, Linhan OUYANG. Response surface methodologybased hybrid robust design optimization for complex product under mixed uncertainties[J]. Journal of Systems Engineering and Electronics, 2019, 30(2): 308318.
Table 2
Experimental results with 4 design variables and 2 responses"
Runs  
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 
Table 4
Random variables and interval variable"
Random variable  Interval variable  
Variable  Mean  Standard deviation  Distribution  Variable  Interval  
Normal  
Normal  
Normal 
Table 5
Comparison of the robustness assessment"
Design variable  Optimal solution  
Deterministic approach  Proposed approach  Deterministic solution  Robust solution  
0.475 2  0.470 1  
14.788 5  14.776 0  
5.172 9  5.182 7  
2.388 3  2.399 7  
13.424 3  14.897 4  
0.181 1  0.180 7  
0.004 6  0.003 4 
1  HOWELL L L, MAGLEBY S P, OLSEN B M. Handbook of compliant mechanisms. New York: Wiley, 2013. 
2 
ZHAO Q H, CHEN X K, MA Z D, et al. A comparison of deterministic, reliabilitybased topology optimization under uncertainties. Acta Mechanica Solida Sinica, 2016, 29 (1): 31 45.
doi: 10.1016/S08949166(16)600058 
3  WANG X J, GENG X Y, WANG L, et al. Motion error based robust topology optimization for compliant mechanisms under material dispersion and uncertain forces. Structural & Multidisciplinary Optimization, 2017, 547 (6): 2161 2175. 
4 
LI G J, LU Z Z, LI L Y, et al. Aleatory and epistemic uncertainties analysis based on nonprobabilistic reliability and its kriging solution. Applied Mathematical Modelling, 2016, 40 (910): 5703 5716.
doi: 10.1016/j.apm.2016.01.017 
5  WANG X J, GENG X Y, WANG L, et al. Motion error based robust topology optimization for compliant mechanisms under material dispersion and uncertain forces. Structural & Multidisciplinary Optimization, 2018, 57, 2161 2175. 
6  WITTWER J W, BAKER M S, HOWELL L L. Robust design and model validation of nonlinear compliant micromechanisms. Journal of Microelectromechanical Systems, 2005, 15 (1): 33 41. 
7 
LAZAROV B S, SCHEVENELS M, SIGMUND O. Robust design of largedisplacement compliant mechanisms. Mechanical Sciences, 2011, 2 (2): 175 182.
doi: 10.5194/ms21752011 
8  GARCIALOPEZ N P, SANCHEZSILVA M, MEDAGLIA A L, et al. An improved robust topology optimization approach using multiobjective evolutionary algorithms. Computers & Structures, 2013, 125, 1 10. 
9 
DAO T P, HUANG S C, CHAU N L. Robust parameter design for a compliant microgripper based on hybrid Taguchidifferential evolution algorithm. Microsystem Technologies, 2018, 24, 1461 1477.
doi: 10.1007/s0054201735342 
10  OUYANG L H, MA Y Z, CHEN J X, et al. Robust optimisation of ND:YLF laser beam microdrilling process using Bayesian probabilistic approach. International Journal of Production Research, 2016, 54 (2): 1 16. 
11  YOUN B D, CHOI K K, YANG R J, et al. Reliabilitybased design optimization for crashworthiness of vehicle side impact. Structural & Multidisciplinary Optimization, 2004, 26 (34): 272 283. 
12  DU X P, CHEN W. Sequential optimization and reliability assessment method for efficient probabilistic design. Journal of Mechanical Design, 2003, 126 (2): 871 880. 
13  STEFANOU G. The stochastic finite element method:past, present and future. Computer Methods in Applied Mechanics & Engineering, 2009, 198 (9): 1031 1051. 
14 
KANG R, ZHANG Q Y, ZENG Z G, et al. Measuring reliability under epistemic uncertainty:review on nonprobabilistic reliability metrics. Chinese Journal of Aeronautics, 2016, 29 (3): 571 579.
doi: 10.1016/j.cja.2016.04.004 
15 
ZHANG H, MULLEN R L, MUHANNA R L. Interval Monte Carlo methods for structural reliability. Structural Safety, 2010, 32 (3): 183 190.
doi: 10.1016/j.strusafe.2010.01.001 
16 
FUJITA K, TAKEWAKI I. An efficient methodology for robustness evaluation by advanced interval analysis using updated secondorder Taylor series expansion. Engineering Structures, 2011, 33 (12): 3299 3310.
doi: 10.1016/j.engstruct.2011.08.029 
17  BECK A T, GOMES W J S, BAZAN F A V. On the robustness of structural risk optimization with respect to epistemic uncertainties. Mecnica Computacional, 2012, 2 (1): 1 19. 
18  BOX G E P, HUNTER W G, HUNTER J S. Statistics for experimenters:an introduction to design, data analysis and model building. New York: Wiley, 1978. 
19  KIM K J, LIN D K J. Optimization of multiple responses considering both location and dispersion effects. European Journal of Operational Research, 2006, 169 (1): 133 145. 
20 
HE Z, ZHU P F, PARK S H. A robust desirability function method for multiresponse surface optimization considering model uncertainty. European Journal of Operational Research, 2012, 221 (1): 241 247.
doi: 10.1016/j.ejor.2012.03.009 
21  CHO B R, PARK C. Robust design modeling and optimization with unbalanced data. Computers & Industrial Engineering, 2005, 48 (2): 173 180. 
22  OUYANG L H, MA Y Z, BYUN J H, et al. A prediction regionbased approach to model uncertainty for multiresponse optimization. Quality & Reliability Engineering International, 2016, 32 (3): 783 794. 
23  JIN R C, CHEN W, SIMPSON T W. Comparative studies of metamodelling techniques under multiple modelling criteria. Structural & Multidisciplinary Optimization, 2001, 23 (1): 1 13. 
24  OUYANG L H, ZHOU D Q, MA Y Z, et al. Ensemble modeling based on 01 programming in micromanufacturing process. Computers & Industrial Engineering, 2018, 123, 242 253. 
25 
WU W D, RAO S S. Interval approach for the modeling of tolerances and clearances in mechanism analysis. Journal of Mechanical Design, 2004, 126 (4): 581 592.
doi: 10.1115/1.1760775 
26  HUANG B Q, DU X P. Analytical robustness assessment for robust design. Structural & Multidisciplinary Optimization, 2007, 34 (2): 123 137. 
27  DU X P, VENIGELLA P K, LIU D S. Robust mechanism synthesis with random and interval variables. Mechanism & Machine Theory, 2009, 44 (7): 1321 1337. 
28  KOCH P N, YANG R J, GU L. Design for six Sigma through robust optimization. Structural & Multidisciplinary Optimization, 2004, 26 (34): 235 248. 
29  DU X P, VENIGELLA P K, LIU D S. Robust mechanism synthesis with random and interval variables. Mechanism & Machine Theory, 2009, 44 (7): 1321 1337. 
30 
WU H, ZHANG X M, GAN J Q, et al. Highprecision displacement measurement method for three degrees of freedomcompliant mechanisms based on computer microvision. Applied Optics, 2016, 55 (10): 2594 2600.
doi: 10.1364/AO.55.002594 
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