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Mean-value first-order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty

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Abstract

Reliability-based multidisciplinary design optimization (RBMDO) has received increasing attention in engineering design for achieving high reliability and safety in complex and coupling systems (e.g., multidisciplinary systems). Mean-value first-order saddlepoint approximation (MVFOSA) is introduced in this paper and is combined with the collaborative optimization (CO) method for reliability analysis under aleatory uncertainty in RBMDO. Similar to the mean-value first-order second moment (MVFOSM) method, MVFOSA approximated the performance function with the first-order Taylor expansion at the mean values of random variables. MVFOSA uses saddlepoint approximation rather than the first two moments of the random variables to estimate the probability density and cumulative distribution functions. MVFOSA-based CO (MVFOSA-CO) is also formulated and proposed. Two examples are provided to show the accuracy and efficiency of the MVFOSA-CO method.

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References

  1. G. Apostolakis, The concept of probability in safety assessments of technological systems, Science, 250(4986) (1990) 1359–1364.

    Google Scholar 

  2. R. H. Sues, D. R. Oakley and G. S. Rhodes, Multidisciplinary stochastic optimization, Proceedings of the 10th conference on engineering mechanics, Boulder, USA (1995) 934–937.

    Google Scholar 

  3. R. H. Sues and M. A. Cesare, An innovative framework for reliability based MDO, Proceedings of the 41st AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Atlanta, USA (2000) 1–8.

    Google Scholar 

  4. P. K. Koch, B. Wujek and O. Golovidov, A multi-stage, parallel implementation of probabilistic design optimization in an MDO framework, Proceedings of the 8th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization, Long Beach, USA (2000) AIAA paper 4805.

    Google Scholar 

  5. D. Padmanabhan and S. M. Batill, Decomposition strategies for reliability based optimization in multidisciplinary system design, Proceedings of the 9th AIAA/USAF/NASA/ISSMO symposium in multidisciplinary analysis and optimization, Atlanta, USA (2002) 77–83.

    Google Scholar 

  6. D. Padmanabhan and S. M. Batill, Reliability based optimization using approximations with applications to multidisciplinary system design, Proceedings of the 40th AIAA sciences meeting & exhibit, Reno, USA (2002).

    Google Scholar 

  7. X. Du and W. Chen, Concurrent subsystem uncertainty analysis in multidisciplinary design, Proceedings of the 8th AIAA/NASA/USAF/ISSMO symposium on multidisciplinary analysis and optimization, Long Beach, USA (2000) AIAA 2000-4928.

    Google Scholar 

  8. H. Z. Huang, H. Yu, X. Zhang, S. Zeng and Z. Wang, Collaborative optimization with inverse reliability for multidisciplinary systems uncertainty analysis, Engineering Optimization, 42(8) (2010) 763–773.

    MathSciNet  Google Scholar 

  9. X. Du and W. Chen, Collaborative reliability analysis under the framework of multidisciplinary systems design, Optimization and Engineering, 6(1) (2005) 63–84.

    MathSciNet  MATH  Google Scholar 

  10. X. Du, J. Guo and H. Beeram, Sequential optimization and reliability assessment for multidisciplinary systems design, Structural and Multidisciplinary Optimization, 35(2) (2008) 117–130.

    MathSciNet  MATH  Google Scholar 

  11. H. Z. Huang, X. D. Zhang, Y. Liu, D. B. Meng and Z. L. Wang, Enhanced sequential optimization and reliability assessment for reliability-based design optimization, Journal of Mechanical Science and Technology, 26(7) (2012) 2039–2043.

    Google Scholar 

  12. X. D. Zhang, H. Z. Huang and H. W. Xu, Multidisciplinary design optimization with discrete and continuous variables of various uncertainties, Structural and Multidisciplinary Optimization, 42(4) (2010) 605–618.

    MathSciNet  MATH  Google Scholar 

  13. N. C. Xiao, H. Z. Huang, Z. L. Wang, Y. Liu and X. L. Zhang, Unified uncertainty analysis by the mean value first order saddlepoint approximation, Structural and Multidisciplinary Optimization, 46(6) (2012) 803–812.

    MATH  Google Scholar 

  14. A. Haldar and S. Mahadevan, Probability, reliability, and statistical methods in engineering design, John Wiley & Sons Inc. (2000).

    Google Scholar 

  15. B. Huang and X. Du, Probabilistic uncertainty analysis by mean-value first order Saddlepoint Approximation, Reliability Engineering and System Safety, 93(2) (2008) 325–336.

    Google Scholar 

  16. B. D. Youn and K. K. Choi, Selecting probabilistic approaches for reliability-based design optimization, AIAA Journal, 42(1) (2004) 124–131.

    Google Scholar 

  17. H. Z. Huang, Y. Tao and Y. Liu, Multidisciplinary collaborative optimization using fuzzy satisfaction degree and fuzzy sufficiency degree model, Soft Computing, 12(10) (2008) 995–1005.

    Google Scholar 

  18. X. Du and W. Chen, Towards a better understanding of modeling feasibility robustness in engineering design, Journal of Mechanical Design, 122(4) (2000) 385–394.

    Google Scholar 

  19. K. Ding, Z. Zhou and C. Liu, Latin hypercube sampling used in the calculation of the fracture probability, Reliability Engineering & System Safety, 59(2) (1998) 239–242.

    Google Scholar 

  20. J. C. Helton and F. J. Davis, Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Reliability Engineering & System Safety, 81(1) (2003) 23–69.

    Google Scholar 

  21. M. R. Moarefzadeh and R. E. Melchers, Directional importance sampling for ill-proportioned spaces, Structural Safety, 21(1) (1999) 1–22.

    Google Scholar 

  22. A. Dey and S. Mahadevan, Ductile structural system reliability analysis using adaptive importance sampling, Structural Safety, 20(2) (1998) 137–154.

    Google Scholar 

  23. R. Pan, X. Zhuang and Q. Sun, Product design optimization with simulation-based reliability analysis, Proceedings of the 2012 International conference on quality, reliability, risk, maintenance, and safety engineering (ICQR2MSE), Chengdu, China (2012) 1028–1032.

    Google Scholar 

  24. A. M. Hasofer and N. C. Lind, Exact and invariant secondmoment code format, ASCE Journal of Engineering Mechanics Division, 100(1) (1974) 111–121.

    Google Scholar 

  25. Y. G. Zhao and A. H. Ang, System reliability assessment by method of moments, ASCE Journal of Structural Engineering, 129(10) (2003) 1341–1349.

    Google Scholar 

  26. L. Wang, D. Beeson and G. Wiggs, Efficient and accurate point estimate method for moments and probability distribution estimation, Proceedings of the 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, Albany, USA (2004).

    Google Scholar 

  27. K. Breitung, Asymptotic approximations for multinomial integrals, Journal of Engineering Mechanics, 110(3) (1984) 357–367.

    Google Scholar 

  28. M. Hohenbichler, S. Gollwitzer, Kruse W. and R. Rackwitz, New light on first- and second-order reliability methods, Structural Safety, 4(4) (1987) 267–284.

    Google Scholar 

  29. M. Murray, Remarks on a multivariate transformation, The Annals of Mathematical Statistics, 23(3) (1952) 470–472.

    MathSciNet  MATH  Google Scholar 

  30. B. D. Youn and K. K. Choi, An investigation of nonlinearity of reliability based design optimization approaches, Journal of Mechanical Design, 126(3) (2004) 403–411.

    Google Scholar 

  31. X. Du and A. Sudjianto, First-order saddlepoint approximation for reliability analysis, AIAA Journal, 42(6) (2004) 1199–1207.

    Google Scholar 

  32. Y. F. Zhang, Y. L. Zhang and Y. M. Zhang, Reliability sensitivity based on first-order reliability method, Journal of Mechanical Engineering Science, 255(9) (2011) 2189–2197.

    Google Scholar 

  33. S. F. Song and Z. Z. Lu, Saddlepoint approximation based structural reliability analysis with non-normal random variables, Science China Technological Sciences, 53(2) (2010) 566–576.

    MATH  Google Scholar 

  34. X. Du, Saddlepoint approximation for sequential optimization and reliability analysis, Journal of Mechanical Design, 130(1) (2008) 011011-1–011011-11.

    Google Scholar 

  35. H. E. Daniels, Saddlepoint approximations in statistics, The Annals of Mathematical Statistics, 25(4) (1954) 631–650.

    MathSciNet  MATH  Google Scholar 

  36. R. Lugannani and S. Rice, Saddle point approximation for the distribution of the sum of independent random variables, Advances in Applied Probability, 12(2) (1980) 475–490.

    MathSciNet  MATH  Google Scholar 

  37. O. E. Barndorff-Nielsen, Inference on full or partial parameters based on the standardized signed log likelihood ratio, Biometrika, 73(2) (1986) 307–322.

    MathSciNet  MATH  Google Scholar 

  38. R. D. Braun, Collaborative optimization: an architecture for large-scale distributed design, Doctoral Dissertation, Stanford University (1996).

    Google Scholar 

  39. R. D. Braun and I. M. Kroo, Development and application of the collaborative optimization architecture in a multidisciplinary design environment, Multidisciplinary Design Optimization: State of the Art (1997) 98–116.

    Google Scholar 

  40. R. D. Braun, A. A. Moore and I. M. Kroo, Collaborative approach to launch vehicle design, Journal of Spacecraft and Rockets, 34(4) (1997) 478–486.

    Google Scholar 

  41. I. Kroo, MDO for large-scale design, Multidisciplinary Design Optimization: State of the Art (1997) 22–44.

    Google Scholar 

  42. I. Sobieski and I. Kroo, Aircraft design using collaborative optimization, Proceedings of the 34th AIAA aerospace sciences meeting and exhibit, Reno, USA (1996).

    Google Scholar 

  43. N. M. Alexandrov and R. M. Lewis, Analytical and Computational Aspects of Collaborative Optimization, The NASA STIP Program Office, NASA/TM-2000-210104 (2000).

    Google Scholar 

  44. R. D. Braun, R. W. Powell, R. A. Lepsch, D. O. Stanley and I. M. Kroo, Comparison of two multidisciplinary optimization strategies for launch-vehicle design, Journal of Spacecraft and Rockets, 32(3) (1995) 404–410.

    Google Scholar 

  45. X. Gu, J. E. Renaud and Ashe L. M., Decision-based collaborative optimization, Journal of Mechanical Design, 124(1) (2002) 1–13.

    Google Scholar 

  46. R. Balling and M. R. Rawlings, Collaborative optimization with disciplinary conceptual design, Structural and Multidisciplinary Optimization, 20(3) (2000) 232–241.

    Google Scholar 

  47. S. Kodiyalam, Evaluation of methods for multidisciplinary design optimization (MDO), Phase I, The NASA STIP Program Office, NASA/CR-1998-208716 (1998).

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical, Electronic, and Industrial Engineering, University of Electronic Science and Technology of China, No. 2006, Xiyuan Avenue, West Hi-Tech Zone, Chengdu, Sichuan, 611731, China

    Debiao Meng, Hong-Zhong Huang, Zhonglai Wang, Ning-Cong Xiao & Xiao-Ling Zhang

Authors
  1. Debiao Meng
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  2. Hong-Zhong Huang
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  3. Zhonglai Wang
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  4. Ning-Cong Xiao
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  5. Xiao-Ling Zhang
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Corresponding author

Correspondence to Hong-Zhong Huang.

Additional information

Debiao Meng is a Ph.D. student at the University of Electronic Science and Technology of China. He received his B.S. degree in Mechanical Engineering from Northwest A&F University. His main research interests include reliability-based design and optimization and reliability-based multidisciplinary design and optimization.

Hong-Zhong Huang is the Dean of the School of Mechanical, Electronic, and Industrial Engineering at the University of Electronic Science and Technology of China. He received his Ph.D. in Reliability Engineering from Shanghai Jiaotong University, China. He has published 150 journal papers and 5 books on reliability engineering. He has held visiting appointments at several universities in the United States, Canada, and Asia. He received the Golomski Award from the Institute of Industrial Engineers in 2006. His current research interests include system reliability analysis, warranty, maintenance planning and optimization, and computational intelligence in product design.

Zhonglai Wang received his Ph.D. in Mechatronics Engineering from the University of Electronic Science and Technology of China, where he is currently an associate professor. He was a visiting scholar in the Department of Mechanical and Aerospace Engineering of Missouri University of Science and Technology from 2007 to 2008. His research interests include reliability-based design and robust design.

Ning-Cong Xiao received his Ph.D. in Mechatronics Engineering from the University of Electronic Science and Technology of China, where he is currently a lecturer. He was a visiting scholar in the Department of Industrial and Systems Engineering of Rutgers University from 2011 to 2012. His research interests include reliability-based design and robust design.

Xiao-Ling Zhang received her Ph.D. in Mechatronics Engineering from the University of Electronic Science and Technology of China, where she is currently a lecturer. She was a visiting scholar in the Department of Mechanical and Aerospace Engineering of Rutgers University from 2009 to 2011. Her research interests include reliability-based multidisciplinary design and optimization.

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Meng, D., Huang, HZ., Wang, Z. et al. Mean-value first-order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty. J MECH SCI TECHNOL 28, 3925–3935 (2014). https://doi.org/10.1007/s12206-014-0903-y

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  • DOI: https://doi.org/10.1007/s12206-014-0903-y

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