Multidisciplinary reliability design optimization using an enhanced saddlepoint approximation in the framework of sequential optimization and reliability analysis
Restricted accessResearch articleFirst published online December, 2016
Multidisciplinary reliability design optimization using an enhanced saddlepoint approximation in the framework of sequential optimization and reliability analysis
For high reliability calculation efficiency and evaluation accuracy, saddlepoint approximation technology has been introduced into design and optimization under uncertainties. When using saddlepoint approximation, there are two prerequisites: all random information is tractable and saddlepoint equations are easy to be solved. However, the above requirements cannot always be met in complex multidisciplinary systems. Random variables sometimes are intractable, or saddlepoint equations are highly nonlinear. To tackle these problems, in this study, an efficient reliability-based multidisciplinary design optimization using the combination method of saddlepoint approximation and third-moment is given. A simplified alternative cumulant generating function can be constructed by saddlepoint approximation and third-moment with the first, second and third moments of a random variable effectively. Then, this cumulant generating function can be utilized to calculate the cumulative distribution function and the probability density function of this random variable approximately. Moreover, to obtain better efficiency, the framework of sequential optimization and reliability analysis is introduced in this study. The corresponding formula of the proposed reliability-based multidisciplinary design optimization is given in detail. Two test problems are solved to show the application of the proposed method.
SimpsonTWMartinsJRRA. Multidisciplinary design optimization for complex engineered systems: report from a national science foundation workshop. J Mech Design2011; 133(10): 101002–101012.
2.
MengDZhangXYangYJ. Interaction balance optimization in multidisciplinary design optimization problems. Concurrent Eng: Res A2016; 24(1): 48–57.
3.
ZhuSPHuangHZPengW. Probabilistic physics of failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty. Reliab Eng Syst Safe2016; 146: 1–12.
4.
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.
5.
YaoWChenXOuyangQ. A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory. Struct Multidiscip O2013; 48(2): 339–354.
6.
ChoTMLeeBC.Reliability-based design optimization using convex linearization and sequential optimization and reliability assessment method. Struct Saf2011; 33(1): 42–50.
7.
ZhangXHuangHZ.Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties. Struct Multidiscip O2010; 40: 165–175.
8.
LeeIChoiKKGorsichD.System reliability-based design optimization using the MPP-based dimension reduction method. Struct Multidiscip O2010; 41(6): 823–839.
9.
MengDZhangXHuangHZ. Interaction prediction optimization in multidisciplinary design optimization problems. Sci World J2014; 2014: 485–499.
10.
ZhuSPHuangHZLiYF. Probabilistic modeling of damage accumulation for time-dependent fatigue reliability analysis of railway axle steels. Proc IMechE, Part F: J Rail and Rapid Transit2015; 229(1): 23–33.
11.
HuangBDuX.Probabilistic uncertainty analysis by mean-value first order saddlepoint approximation. Reliab Eng Syst Safe2008; 93(2): 325–336.
12.
GuoS.An efficient third-moment saddlepoint approximation for probabilistic uncertainty analysis and reliability evaluation of structures. Appl Math Model2014; 38(1): 221–232.
13.
MengDLiYFHuangHZ. Reliability-based multidisciplinary design optimization using subset simulation analysis and its application in hydraulic transmission mechanism design. J Mech Design2015; 137(5): 051402-1–051402-9.
14.
PanRZhuangXSunQ.Product design optimization with simulation-based reliability analysis. In: Proceedings of the 2012 international conference on quality, reliability, risk, maintenance, and safety engineering (ICQR2MSE), Chengdu, China, 15–18 June 2012, pp.1028–1032. Chengdu, China: IEEE.
15.
HurtadoJE.Filtered importance sampling with support vector margin: a powerful method for structural reliability analysis. Struct Saf2007; 29(1): 2–15.
16.
LuZZSongSFYueZF. Reliability sensitivity method by line sampling. Struct Saf2008; 30(6): 517–532.
17.
ZhaoYGOnoT.Moment methods for structural reliability. Struct Saf2001; 23(1): 47–75.
18.
ZhaoYGAngAHS. System reliability assessment by method of moments. J Struct Eng: ASCE2003; 129(10): 1341–1349.
19.
LeeSHKwakBM.Response surface augmented moment method for efficient reliability analysis. Struct Saf2006; 28(3): 261–272.
ZhuSPHuangHZSmithR. Bayesian framework for probabilistic low cycle fatigue life prediction and uncertainty modeling of aircraft turbine disk alloys. Probabilist Eng Mech2013; 34: 114–122.
22.
LimJLeeBLeeI.Second-order reliability method-based inverse reliability analysis using Hessian update for accurate and efficient reliability-based design optimization. Int J Numer Meth Eng2014; 100(10): 773–792.
23.
MahadevanSShiP.Multiple linearization method for nonlinear reliability analysis. J Eng Mech: ASCE2001; 127(11): 1165–1173.
24.
RackwitzR.Reliability analysis—a review and some perspectives. Struct Saf2001; 23(4): 365–395.
25.
ZhaoYGOnoT.A general procedure for first/second-order reliability method (FORM/SORM). Struct Saf1999; 21(2): 95–112.
26.
ZhuSPHuangHZOntiverosV. Probabilistic low cycle fatigue life prediction using an energy-based damage parameter and accounting for model uncertainty. Int J Damage Mech2012; 21(8): 1128–1153.
27.
SuXMahadevanSXuP.Dependence assessment in human reliability analysis using evidence theory and AHP. Risk Anal2015; 35(7): 1296–1316.
28.
DuXSudjiantoA.First-order saddlepoint approximation for reliability analysis. AIAA J2004; 42(6): 1199–1207.
29.
DuX.Saddlepoint approximation for sequential optimization and reliability analysis. J Mech Design2008; 130(1): 011011-1–011011-11.
30.
MengDHuangHZWangZ. Mean-value first-order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty. J Mech Sci Technol2014; 28(10): 3925–3935.
31.
XiongJWongASalopekD.Saddlepoint approximations to option price in a general equilibrium model. Stat Probabil Lett2005; 71(4): 361–369.
32.
SudjiantoADuXChenW.Probabilistic sensitivity analysis in engineering design using uniform sampling and saddlepoint approximation. In: Proceedings of the SAE 2005 transactions journal of passenger cars: mechanical systems, Detroit, MI, 11–14 April 2005, pp.267–276, http://ideal.mech.northwestern.edu/pdf/SAE05.pdf
33.
HuzurbazarS.Practical saddlepoint approximations. Am Stat1999; 53(3): 225–232.
34.
DuXSudjiantoA. A saddlepoint approximation method for uncertainty analysis. In: Proceedings of the 2004 ASME international design engineering technical conferences and the computers and information in engineering conference, Salt Lake City, UT, 28 September–2 October, paper no. DETC2004–57269. New York: ASME.
35.
HuangBDuX.Uncertainty analysis by dimension reduction integration and saddlepoint approximations. J Mech Design2005; 127(6): 1068–1076.
36.
DanielsHE.Saddlepoint approximations in statistics. Ann Math Stat1954; 25(4): 631–650.
37.
LugannaniRRiceSO.Saddlepoint approximation for the distribution of the sum of independent random variables. Adv Appl Probab1980; 12: 475–490.
38.
Barndorff-NielsenOE.Inference on full or partial parameters based on the standardized signed log likelihood ratio. Biometrika1986; 73: 307–322.
39.
DuXChenW.Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Design2004; 126(2): 225–234.
40.
DuXGuoJBeeramH.Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidiscip O2008; 35(2): 117–130.
41.
HuangHZZhangXDLiuY. Enhanced sequential optimization and reliability assessment for reliability-based design optimization. J Mech Sci Technol2012; 26(7): 2039–2043.
42.
YounBDChoiKKDuL. Integration of reliability and possibility-based design optimizations using performance measure approach. In: Proceedings of the 2005 SAE world congress, Detroit, MI, 11–14 April 2005, paper no. 2005-01-0342. Detroit: SAE International.
43.
DuLChoiKK.An inverse analysis method for design optimization with both statistical and fuzzy uncertainties. Struct Multidiscip O2008; 37(2): 107–119.
