Design Optimization Method for Composite Components Based on Moment Reliability-Sensitivity Criteria
-
Zhigang Sun
,
Changxi Wang
Abstract
In this paper, a Reliability-Sensitivity Based Design Optimization (RSBDO) methodology for the design of the ceramic matrix composites (CMCs) components has been proposed. A practical and efficient method for reliability analysis and sensitivity analysis of complex components with arbitrary distribution parameters are investigated by using the perturbation method, the respond surface method, the Edgeworth series and the sensitivity analysis approach. The RSBDO methodology is then established by incorporating sensitivity calculation model into RBDO methodology. Finally, the proposed RSBDO methodology is applied to the design of the CMCs components. By comparing with Monte Carlo simulation, the numerical results demonstrate that the proposed methodology provides an accurate, convergent and computationally efficient method for reliability-analysis based finite element modeling engineering practice.
Funding statement: Funding: Supports of this project provided by National Basic Research Program of China, National Natural Science Foundation of China (51575261), Aeronautical Science Foundation of China (2014ZB52024) and Fundamental Research Funds for the Central Universities (NS2014024).
Nomenclature
reliability
amendatory reliability
probability density function
limit state function (LSF)
vector of random variables
mean value of the random parameters
variance matrix
the third central moments of the random parameters
the fourth central moments of the random parameters
the first central moment of LSF
the second central moment of LSF
the third central moment of LSF
the fourth central moment of LSF
probability of occurrence
reliability index
standard normal probability density function
standard normal cumulative density function
Hermite polynomial
polynomial constants
approximate expression of LSF
lower bounds of design variables
upper bounds of design variables
allowable reliability of structure
sensitivity factor
reliability sensitivity of mean values
reliability sensitivity of variances
tensile modules of elasticity
shearing modules of elasticity
Poisson ratio
coefficient of thermal expansion
strength of material
thickness
pressure
max stress
References
1. Murthy PLN, Nemeth NN, Brewer DN, Mital S. Probabilistic analysis of a SiC/SiC ceramic matrix composite turbine vane. Composites Part B 2008;39:694–703.10.1016/j.compositesb.2007.05.006Search in Google Scholar
2. Awad ZK, Aravinthan T, Yan Z, Gonzalez F. A review of optimization techniques used in the design of fibre composite structures for civil engineering applications. Mater Des 2012;33:534–44.10.1016/j.matdes.2011.04.061Search in Google Scholar
3. Frangopol DM, Recek S. Reliability of fiber-reinforced composite laminate plates. Probab Eng Mech 2003;18:119–37.10.1016/S0266-8920(02)00054-1Search in Google Scholar
4. Lee DS, Morillo C, Bugeda G, Oller S, Onate E. Multilayered composite structure design optimisation using distributed/parallel multi-objective evolutionary algorithms. Compos Struct 2012;94:1087–96.10.1016/j.compstruct.2011.10.009Search in Google Scholar
5. Chiachio M, Chiachio J, Rus G. Reliability in composites - A selective review and survey of current development. Composites Part B 2012;43:902–13.10.1016/j.compositesb.2011.10.007Search in Google Scholar
6. Valdebenito MA, Schueller GI. A survey on approaches for reliability-based optimization. Struct Multidiscip Optim 2010;42:645–63.10.1007/s00158-010-0518-6Search in Google Scholar
7. Rahman S, Wei D. Design sensitivity and reliability-based structural optimization by univariate decomposition. Struct Multidiscip Optim 2008;35:245–61.10.1007/s00158-007-0133-3Search in Google Scholar
8. Hu Z, Du X, Kolekar NS, Banerjee A. Robust design with imprecise random variables and its application in hydrokinetic turbine optimization. Eng Optim 2014;46:393–419.10.1080/0305215X.2013.772603Search in Google Scholar
9. Youn BD, Xi Z, Wells LJ, Gorsich DJ. Sensitivity-free approach for Reliability-Based Robust Design Optimization. ASME International Design Engineering Technical Conferences/Computers and Information in Engineering Conference, Vol. 6: American Society of Mechanical Engineers, 2007, pp. 1309–20.10.1115/DETC2007-35619Search in Google Scholar
10. Zhu S, Huang H, Peng W, Wang H, Probabilistic MS. Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty. Reliab Eng Syst Saf 2016;146:1–12.10.1016/j.ress.2015.10.002Search in Google Scholar
11. Zhu S, Huang H, Li Y, Liu Y, Yang Y. Probabilistic modeling of damage accumulation for time-dependent fatigue reliability analysis of railway axle steels. Proc Inst Mech Eng Part F J Rail Rapid Transit 2015;229:23–33.10.1177/0954409713496772Search in Google Scholar
12. Nguyen XS, Sellier A, Duprat F, Pons G. Adaptive response surface method based on a double weighted regression technique. Probab Eng Mech 2009;24:135–43.10.1016/j.probengmech.2008.04.001Search in Google Scholar
13. Der Kiureghian A, Dakessian T. Multiple design points in first and second-order reliability. Struct Saf 1998;20:37–49.10.1016/S0167-4730(97)00026-XSearch in Google Scholar
14. Zhao YG, Ono T. New approximations for SORM: Part I. J Eng Mech 1999;125:79–85.10.1061/(ASCE)0733-9399(1999)125:1(79)Search in Google Scholar
15. Zhao YG, New OT. Approximations for SORM: Part II. J Eng Mech 1999;125:86–93.10.1061/(ASCE)0733-9399(1999)125:1(86)Search in Google Scholar
16. Kiureghian AD, Lin H, Hwang S. Second‐Order Reliability Approximations. J Eng Mech 1987;113:1208–25.10.1061/(ASCE)0733-9399(1987)113:8(1208)Search in Google Scholar
17. Au SK, Beck JL. A new adaptive importance sampling scheme for reliability calculations. Struct Saf 1999;21:135–58.10.1016/S0167-4730(99)00014-4Search in Google Scholar
18. Zhao YG, Ono T. Moment methods for structural reliability. Struct Saf 2001;23:47–75.10.1016/S0167-4730(00)00027-8Search in Google Scholar
19. Zhao Y, Lu Z. Fourth-moment standardization for structural reliability assessment. J Struct Eng ASCE 2007;133:916–24.10.1061/(ASCE)0733-9445(2007)133:7(916)Search in Google Scholar
20. Zhao Y, Lu Z, Ono TA. Simple third-moment method for structural reliability. J Asian Archit Build Eng 2006;5:129–36.10.3130/jaabe.5.129Search in Google Scholar
21. Zhao YG, Ono T, Kato M. Second-order third-moment reliability method. J Struct Eng ASCE 2002;128:1087–90.10.1061/(ASCE)0733-9445(2002)128:8(1087)Search in Google Scholar
22. Sun Z, Kong C, Niu X, Song Y, Wang X. Optimization and reliability analysis of 2.5D C/SiC composites turbine stator vane. Appl Compos Mater 2014;21:789–803.10.1007/s10443-013-9374-zSearch in Google Scholar
23. Lu Z, Song J, Song S, Yue Z, Wang J. Reliability sensitivity by method of moments. Appl Math Model 2010;34:2860–71.10.1016/j.apm.2009.12.020Search in Google Scholar
24. Zhang YM, He XD, Liu QL, Wen BC, Zheng JX. Reliability sensitivity of automobile components with arbitrary distribution parameters. Proc Inst Mech Eng Part D J Automobile Eng 2005;219:165–82.10.1243/095440705X5894Search in Google Scholar
25. Zhang YM, Wen BC, Liu QL. Reliability sensitivity for rotor-stator systems with rubbing. J Sound Vib 2003;259:1095–107.10.1006/jsvi.2002.5117Search in Google Scholar
26. Zhang YM, Yang Z. Reliability-based sensitivity analysis of vehicle components with non-normal distribution parameters. Int J Automot Technol 2009;10:181–94.10.1007/s12239-009-0022-4Search in Google Scholar
27. Zhang YM, He XD, Liu QL, Wen BC. Robust reliability design of banjo flange with arbitrary distribution parameters. J Pressure Vessel Technol Trans ASME 2005;127:408–13.10.1115/1.2042478Search in Google Scholar
28. Zhang YM, Wen BC, Liu QL. First passage of uncertain single degree-of-freedom nonlinear oscillators. Comput Methods Appl Mech Eng 1998;165:223–31.10.1016/S0045-7825(98)00042-5Search in Google Scholar
29. Zhang Y, He X, Yang Z, Liu Q, Wen B. Reliability-based sensitivity of mechanical components with arbitrary distribution parameters. J Mech Sci Technol 2010;24:1187–93.10.1007/s12206-010-0334-3Search in Google Scholar
30. Lee SH, Kwak BM. Response surface augmented moment method for efficient reliability analysis. Struct Saf 2006;28:261–72.10.1016/j.strusafe.2005.08.003Search in Google Scholar
31. Sun W, Dong R, Xu H. A novel non-probabilistic approach using interval analysis for robust design optimization. J Mech Sci Technol 2009;23:3199–208.10.1007/s12206-009-0921-3Search in Google Scholar
32. Melchers RE, Ahammed M. A fast approximate method for parameter sensitivity estimation in Monte Carlo structural reliability. Comput Struct 2004;82:55–61.10.1016/j.compstruc.2003.08.003Search in Google Scholar
33. Bjerager P, Krenk S. Parametric sensitivity in first order reliability theory. J Eng Mech 1989;115:1577–82.10.1061/(ASCE)0733-9399(1989)115:7(1577)Search in Google Scholar
34. Lu Z, Song S, Yue Z, Wang J. Reliability sensitivity method by line sampling. Struct Saf 2008;30:517–32.10.1016/j.strusafe.2007.10.001Search in Google Scholar
35. Sues RH, Cesare MA. System reliability and sensitivity factors via the MPPSS method. Probab Eng Mech 2005;20:148–57.10.1016/j.probengmech.2005.02.001Search in Google Scholar
36. Johnson N, Kotz S, Balakrishnan N. Continuous univariate distributions. New York: Wiley, 1995.Search in Google Scholar
37. Bucher CG, Bourgund U. A fast and efficient response surface approach for structural reliability problems. Struct Saf 1990;7:57–66.10.1016/0167-4730(90)90012-ESearch in Google Scholar
38. Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 2002;6:182–97.10.1109/4235.996017Search in Google Scholar
39. Dong WF, Xiao J, Li Y. Finite element analysis of the tensile properties of 2.5D braided composites. Mater Sci Eng A 2007;457:199–204.10.1016/j.msea.2006.12.032Search in Google Scholar
40. Yanjun C, Guiqiong J, Bo W, Wei L. Elastic behavior analysis of 3D angle-interlock woven ceramic composites. Acta Mech Solida Sin 2006;19:152–9.10.1007/s10338-006-0618-4Search in Google Scholar
41. Sun SJ. Integrated Design Optimization of Structure and Material of Braided Composites. Nanjing: Nanjing University of Aeronautics and Astronautics, 2010.Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Effects of Cavity Configurations on Flameholding and Performances of Kerosene Fueled Scramjet Combustor
- Metaheuristic and Machine Learning Models for TFE-731-2, PW4056, and JT8D-9 Cruise Thrust
- Design Optimization Method for Composite Components Based on Moment Reliability-Sensitivity Criteria
- Use Deflected Trailing Edge to Improve the Aerodynamic Performance and Develop Low Solidity LPT Cascade
- A Co-modeling Method Based on Component Features for Mechatronic Devices in Aero-engines
- Evaluation and Analysis of Curvature-Corrected Filter-based Turbulent Model
- Aircraft Engine Thrust Estimator Design Based on GSA-LSSVM
- Effect of Inner Nozzle Lip Thickness on Co-flow Jet Characteristics
- Comparisons of Two Non-probabilistic Structural Reliability Analysis Methods for Aero-engine Turbine Disk
Articles in the same Issue
- Frontmatter
- Effects of Cavity Configurations on Flameholding and Performances of Kerosene Fueled Scramjet Combustor
- Metaheuristic and Machine Learning Models for TFE-731-2, PW4056, and JT8D-9 Cruise Thrust
- Design Optimization Method for Composite Components Based on Moment Reliability-Sensitivity Criteria
- Use Deflected Trailing Edge to Improve the Aerodynamic Performance and Develop Low Solidity LPT Cascade
- A Co-modeling Method Based on Component Features for Mechatronic Devices in Aero-engines
- Evaluation and Analysis of Curvature-Corrected Filter-based Turbulent Model
- Aircraft Engine Thrust Estimator Design Based on GSA-LSSVM
- Effect of Inner Nozzle Lip Thickness on Co-flow Jet Characteristics
- Comparisons of Two Non-probabilistic Structural Reliability Analysis Methods for Aero-engine Turbine Disk
