This article presents a procedure for reliability-based multidisciplinary design optimization with both random and interval variables. The sign of performance functions is predicted by the Kriging model which is constructed by the so-called learning function in the region of interest. The Monte Carlo simulation with the Kriging model is performed to evaluate the failure probability. The sample methods for the random variables, interval variables, and design variables are discussed in detail. The multidisciplinary feasible and collaborative optimization architectures are provided with the proposed method. The method is demonstrated with three examples.
McAllisterCDSimpsonTW. Multidisciplinary robust design optimization of an internal combustion engine. J Mech Des: T ASME2003; 125(1): 124–130.
4.
KodiyalamSYangRGuLet al. Multidisciplinary design optimization of a vehicle system in a scalable, high performance computing environment. Struct Multidiscip O2004; 26(3–4): 256–263.
5.
YangRGuLThoC-Het al. Multidisciplinary design optimization of a full vehicle with high performance computing. In: Proceedings of the 19th AIAA applied aerodynamics conference, fluid dynamics and co-located conferences, Anaheim, CA, 11–14 June 2001, paper no. AIAA paper 2001-1273. Reston, VA: AIAA.
6.
AgarwalHRenaudJEPrestonELet al. Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliab Eng Syst Safe2004; 85(1): 281–294.
7.
YounBDChoiKYangR-Jet al. Reliability-based design optimization for crashworthiness of vehicle side impact. Struct Multidiscip O2004; 26(3–4): 272–283.
8.
AhnJKwonJ. An efficient strategy for reliability-based multidisciplinary design optimization using BLISS. Struct Multidiscip O2006; 31(5): 363–372.
SuesRHCesareMA. An innovative framework for reliability-based MDO. In: Proceedings of the 41st structures, structural dynamics, and materials conference and exhibit, Atlanta, GA, 3–6 April 2000. Reston, VA: AIAA.
11.
PadmanabhanDBatillSM (eds). Decomposition strategies for reliability based optimization in multidisciplinary system design. In: Proceedings of the 9th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta, GA, 4–6 September 2002. Reston, VA: AIAA.
12.
AgarwalHRenaudJEMackJDet al. A decomposition approach for reliability-based multidisciplinary design optimization. In: Proceedings of the 44th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Norfolk, VA, 7–10 April 2003. Reston, VA: AIAA.
13.
MousaviSRomliFI. A strategy for reliability-based multidisciplinary design optimization of wind turbine using BLISS and PMA. Int J Innovat Manag2014; 5(1): 71–77.
14.
YounBDChoiKK. An investigation of nonlinearity of reliability-based design optimization approaches. J Mech Des: T ASME2004; 126(3): 403–411.
15.
Ting LinPChang GeaH. Reliability-based multidisciplinary design optimization using probabilistic gradient-based transformation method. J Mech Des: T ASME2012; 135(2): 021001.
16.
MavrisDNBandteODeLaurentisDA. Robust design simulation: a probabilistic approach to multidisciplinary design. J Aircraft1999; 36(1): 298–307.
17.
YaoWChenXLuoWet al. Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles. Prog Aerosp Sci2011; 47(6): 450–479.
18.
FengZZhenzhouLLijieCet al. Reliability sensitivity algorithm based on stratified importance sampling method for multiple failure modes systems. Chinese J Aeronaut2010; 23(6): 660–669.
19.
ZhangFDengWNanHet al. Reliability analysis of bleed air anti-icing system based on subset simulation method. Appl Therm Eng2017; 115: 17–21.
20.
DuXGuoJBeeramH. Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidiscip O2008; 35(2): 117–130.
21.
LiLLiuJHLiuS. An efficient strategy for multidisciplinary reliability design and optimization based on CSSO and PMA in SORA framework. Struct Multidiscip O2014; 49(2): 239–252.
22.
JiangCHanXLuGYet al. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique. Comput Method Appl M2011; 200(33): 2528–2546.
23.
SongJLuZWeiPet al. Global sensitivity analysis for model with random inputs characterized by probability-box. Proc IMechE, Part O: J Risk and Reliability2015; 229(3): 237–253.
24.
KarankiDRKushwahaHSVermaAKet al. Uncertainty analysis based on probability bounds (P-Box) approach in probabilistic safety assessment. Risk Anal2009; 29(5): 662–675.
25.
BaeH-RGrandhiRVCanfieldRA. An approximation approach for uncertainty quantification using evidence theory. Reliab Eng Syst Safe2004; 86(3): 215–225.
26.
RaviVReddyPZimmermannH-J. Fuzzy global optimization of complex system reliability. IEEE T Fuzzy Syst2000; 8(3): 241–248.
27.
DjapanMJTadicDPMacuzicIDet al. A new fuzzy model for determining risk level on the workplaces in manufacturing small and medium enterprises. Proc IMechE, Part O: J Risk and Reliability2015; 229(5): 456–468.
28.
SoltaniRSadjadiSJ. Reliability optimization through robust redundancy allocation models with choice of component type under fuzziness. Proc IMechE, Part O: J Risk and Reliability2014; 228(5): 449–459.
29.
HuangZLJiangCZhangZet al. A decoupling approach for evidence-theory-based reliability design optimization. Struct Multidiscip O2017; 56: 647–661.
30.
MengDLiY-FHuangH-Zet al. Reliability-based multidisciplinary design optimization using subset simulation analysis and its application in the hydraulic transmission mechanism design. J Mech Des: T ASME2015; 137(5): 051402.
31.
YuanRMengDLiH. Multidisciplinary reliability design optimization using an enhanced saddlepoint approximation in the framework of sequential optimization and reliability analysis. Proc IMechE, Part O: J Risk and Reliability2016; 230(6): 570–578.
32.
HuZDuX. A random field approach to reliability analysis with random and interval variables. J Risk Uncertainty Eng Syst B: Mech Eng2015; 1(4): 041005.
33.
HuangZJiangCZhouYet al. Reliability-based design optimization for problems with interval distribution parameters. Struct Multidiscip O2017; 55: 513–528.
34.
DuXSudjiantoAHuangB. Reliability-based design with the mixture of random and interval variables. J Mech Des: T ASME2005; 127(6): 1068–1076.
35.
YaoWChenXOuyangQet al. A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory. Struct Multidiscip O2013; 48(2): 339–354.
36.
ZamanKMahadevanS. Reliability-based design optimization of multidisciplinary system under aleatory and epistemic uncertainty. Struct Multidiscip O2017; 55(2): 681–699.
37.
CramerEJDennisJJohnEet al. Problem formulation for multidisciplinary optimization. SIAM J Optimiz1994; 4(4): 754–776.
38.
AllisonJKokkolarasMPapalambrosPet al. On the impact of coupling strength on complex system optimization for single-level formulations. In: Proceedings of the ASME design engineering technical conferences (DETC’05), Long Beach, CA, 24–28 September 2005. New York: ASME.
39.
BraunRD. Collaborative optimization: an architecture for large-scale distributed design. Doctoral Dissertation, Stanford University, Stanford, CA, 1996.
40.
AlexandrovNMLewisRM. Analytical and computational aspects of collaborative optimization for multidisciplinary design. AIAA J2002; 40(2): 301–309.
41.
JeungG-WKimD-WSungY-Het al. Reliability-based design optimization of a superconducting magnetic energy storage system (SMES) utilizing reliability index approach. J Magn2012; 17(1): 46–50.
BichonBJEldredMSSwilerLPet al. Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J2008; 46(10): 2459–2468.
50.
BraunRDKrooIM. Development and application of the collaborative optimization architecture in a multidisciplinary design environment. Washington, DC: NASA, 1995.
