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Multidisciplinary robust design optimization based on time-varying sensitivity analysis

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Abstract

The performance of complex mechanical systems often degrades over time primarily due to time-varying uncertainties. Improving the design of such systems entails addressing time-varying uncertainties through Multidisciplinary design optimization (MDO). In this study, a multidisciplinary robust design optimization method that is based on time-varying sensitivity analysis is proposed. First, the indices for the time-varying reliability sensitivity of limit state functions are calculated by combining sensitivity analysis and an empirical correction formula. The propagation effects of these time-varying uncertainties are qualified by combining the simplified implicit uncertainty propagation and sequential quadratic programming methods. Finally, the robust design method is integrated with MDO to reduce the effects of time-varying uncertainties. The feasibility and effectiveness of the proposed method are illustrated with a mathematical problem and an engineering example.

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References

  1. S. Sankararaman and S. Mahadevan, Likelihood-based approach to multidisciplinary analysis under uncertainty, ASME Journal of Mechanical Design, 134 (3) (2012) 031008.

    Article  Google Scholar 

  2. A. Chiralaksanakul and S. Mahadevan, Decoupled approach to multidisciplinary design optimization under uncertainty, Optimization and Engineering, 8 (1) (2007) 21–42.

    Article  MathSciNet  MATH  Google Scholar 

  3. W. Yao, X. Chen, W. Luo, M. Tooren and J. Guo, Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles, Progress in Aerospace Sciences, 47 (6) (2011) 450–479.

    Article  Google Scholar 

  4. X. Gu, J. E. Renaud, S. M. Batill, R. M. Brach and A. S. Budhiraja, Worst case propagated uncertainty of multidisciplinary systems in robust design optimization, Structural and Multidisciplinary Optimization, 20 (3) (2000) 190–213.

    Article  Google Scholar 

  5. X. Gu, J. E. Renaud and C. L. Penninger, Implicit uncertainty propagation for robust collaborative optimization, ASME Journal of Mechanical Design, 128 (4) (2006) 1001–1013.

    Article  Google Scholar 

  6. X. Du and W. Chen, Methodology for uncertainty propagation and management in simulation-based systems design, AIAA Journal, 38 (8) (2000) 1471–1478.

    Article  Google Scholar 

  7. X. Du and W. Chen, Efficient uncertainty analysis methods for multidisciplinary robust design, AIAA Journal, 40 (3) (2002) 545–552.

    Article  Google Scholar 

  8. Z. Jiang, W. Li, D. W. Apley and W. Chen, A spatialrandom-process based multidisciplinary system uncertainty propagation approach with model uncertainty, ASME Journal of Mechanical Design, 137 (10) (2015) 101402.

    Article  Google Scholar 

  9. L. Brevault, M. Balesdent, N. Bérend and R. Le Riche, Decoupled multidisciplinary design optimization formulation for interdisciplinary coupling satisfaction under uncertainty, AIAA Journal, 54 (1) (2016) 186–205.

    Article  Google Scholar 

  10. C. Liang and S. Mahadevan, Stochastic multidisciplinary analysis with high-dimensional coupling, AIAA Journal, 54 (2) (2016) 1209–1219.

    Article  Google Scholar 

  11. Y. K. Son, Reliability prediction of engineering systems with competing failure modes due to component degradation, Journal of Mechanical Science and Technology, 25 (7) (2011) 1717–1725.

    Article  Google Scholar 

  12. L. Xie and Z. Wang, Reliability degradation of mechanical components and systems, Handbook of performability engineering, Springer (2008) 413–429.

    Chapter  Google Scholar 

  13. P. Gao and L. Xie, Fuzzy dynamic reliability models of parallel mechanical systems considering strength degradation path dependence and failure dependence, Mathematical Problems in Engineering (2015) 1–9.

    Google Scholar 

  14. X. Zhang, L. Xiao and J. Kang, Degradation prediction model based on a neural network with dynamic windows, Sensors, 15 (3) (2015) 6996–7015.

    Article  Google Scholar 

  15. Ø. Hagen and L. Tvedt, Vector process out-crossing as parallel system sensitivity measure, Journal of Engineering Mechanics, 117 (10) (1991) 2201–2220.

    Article  Google Scholar 

  16. O. Ditlevsen and H. O. Madsen, Structural reliability methods, New York: John Wiley & Sons (2005).

    Google Scholar 

  17. B. Sudret and A. Der Kiureghian, Stochastic finite element methods and reliability, a state-of-the-art report, Report UCB/SEMM-2000/08, University of California, Berkeley, CA (2000).

    Google Scholar 

  18. J. Zhang and X. Du, Time-dependent reliability analysis for function generator mechanisms, ASME Journal of Mechanical Design, 133 (3) (2011) 031005.

    Article  Google Scholar 

  19. J. D. Sorensen, Notes in structural reliability theory and risk analysis, Aalborg (2004).

    Google Scholar 

  20. G. J. Savage and Y. K. Son, Dependability-based design optimization of degrading engineering systems, ASME Journal of Mechanical Design, 131 (1) (2009) 011002.

    Article  Google Scholar 

  21. A. Singh and Z. P. Mourelatos, On the time-dependent reliability of non-monotonic, non-repairable systems, SAE International Journal of Materials and Manufacturing, 3 (2010-01-0696) (2010) 425–444.

    Google Scholar 

  22. J. O. Royset, A. Der Kiureghian and E. Polak, Optimal design with probabilistic objectives and constraints, Journal of Engineering Mechanics, 132 (1) (2006) 107–118.

    Article  Google Scholar 

  23. J. Li and Z. P. Mourelatos, Reliability estimation for time dependent problems using a niching genetic algorithm, Proceeding of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, American Society of Mechanical Engineers (2007).

    Google Scholar 

  24. B. Sudret, Analytical derivation of the outcrossing rate in time variant reliability problems, Structures and Infrastructure Engineering, 4 (5) (2008) 353–362.

    Article  Google Scholar 

  25. C. Andrieu-Renaud, B. Sudret and M. Lemaire, The PHI2 method: A way to compute time variant reliability, Reliability Engineering and System Safety, 84 (1) (2004) 75–86.

    Article  Google Scholar 

  26. N. Kuschel and R. Rackwitz, Optimal design under timevariant reliability constraints, Structural Safety, 22 (2) (2000) 113–127.

    Article  MATH  Google Scholar 

  27. Z. Wang and P. Wang, A nested extreme response surface approach for time-dependent reliability-based design optimization, ASME Journal of Mechanical Design, 134 (12) (2012) 121007.

    Article  Google Scholar 

  28. X. Du and W. Chen, Sequential optimization and reliability assessment method for efficient probabilistic design, ASME Journal of Mechanical Design, 126 (2) (2004) 225–233.

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  30. H. Liu, W. Chen, M. Kokkolaras, P. Y. Papalambros and H. M. Kim, Probabilistic analytical target cascading—a moment matching formulation for multilevel optimization under uncertainty, ASME Journal of Mechanical Design, 128 (4) (2006) 991–1000.

    Article  Google Scholar 

  31. M. Toyoda and N. Kogiso, Robust multiobjective optimization method using satisficing trade-off method, Journal of Mechanical Science and Technology, 29 (4) (2015) 1361–1367.

    Article  Google Scholar 

  32. T. P. Dao and S. C. Huang, Robust design for a flexible bearing with 1-DOF translation using the Taguchi method and the utility concept, Journal of Mechanical Science and Technology, 29 (8) (2015) 3309–3320.

    Article  Google Scholar 

  33. W. Wu and S. S. Rao, Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis, Reliability Engineering and System Safety, 92 (1) (2007) 54–64.

    Article  Google Scholar 

  34. S. Ferson and L. R. Ginzburg, Different methods are needed to propagate ignorance and variability, Reliability Engineering and System Safety, 54 (2–3) (1996) 133–144.

    Article  Google Scholar 

  35. M. Li and S. Azarm, Multi-objective collaborative robust optimization with interval uncertainty and interdisciplinary uncertainty propagation, ASME Journal of Mechanical Design, 130 (8) (2008) 081402.

    Article  Google Scholar 

  36. M. Li, Robust optimization and sensitivity analysis with multi-objective genetic algorithms: Single-and multidisciplinary applications, Ph.D. Thesis, University of Maryland, College Park (2007).

    Google Scholar 

  37. P. Bjerager and S. Krenk, Parametric sensitivity in first order reliability theory, Journal of Engineering Mechanics, 115 (7) (1989) 1577–1582.

    Article  Google Scholar 

  38. A. Karamchandani and C. A. Cornell, Senitivity estimation within first and second order reliability methods, Structure Safety, 11 (2) (1992) 95–107.

    Article  Google Scholar 

  39. R. E. Melchers and M. Ahammed, A fast approximate method for parameter sensitivity estimation in Monte Carlo structural reliability, Computer Structure, 82 (1) (2004) 55–61.

    Article  Google Scholar 

  40. X. Wang, Y. Zhang and B. Wang, Dynamic reliabilitybased robust optimization design for a torsion bar, Journal of Mechanical Engineering Science, 223 (2) (2009) 483–490.

    Article  MathSciNet  Google Scholar 

  41. X. Huang and Y. Zhang, Reliability-sensitivity analysis using dimension reduction methods and saddlepoint approximations, International Journal for Numerical Methods in Engineering, 93 (8) (2013) 857–886.

    MathSciNet  MATH  Google Scholar 

  42. N. Xiao, H. Huang, Z. 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.

    Article  MATH  Google Scholar 

  43. Z. Yang, Y. M. Zhang, X. F. Zhang and X. Z. Huang, Reliability-based sensitivity design of gear pairs with non-Gaussian random parameters, Applied Mechanics and Materials, 121–126 (2012) 3411–3418.

    Google Scholar 

  44. H. Li, M. Ma and Y. Jing, A new method based on LPP and NSGA-II for multi-objective robust collaborative optimization, Journal of Mechanical Science and Technology, 25 (5) (2011) 1071–1079.

    Article  Google Scholar 

  45. L. Chan, Evaluation of two concurrent design approaches in multidisciplinary design optimization, NRC report LMA-077, Canadian Aeronautics and Space Institute, January (2001).

    Google Scholar 

  46. P. Meng, Y. Li, Z. Jiang, W. Yin and J. Li, Structure optimal design of four-high rolling mill stand based on improved collaborative optimization algorithm, International Journal of Advancements in Computing Technology, 5 (8) (2013) 843–851.

    Article  Google Scholar 

Download references

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Correspondence to Huanwei Xu.

Additional information

Recommended by Associate Editor Byeng Dong Youn

Huanwei Xu is currently an Associate Professor at the School of Mechatronics Engineering of the University of Electronic Science and Technology of China in Chengdu, Sichuan, China. He received his Ph.D. in Mechanical Engineering from the Dalian University of Technology in Dalian, China. He has published 20 journal papers, and his research interests include multidisciplinary design optimization and robust and reliability designs.

Wei Li is currently studying at the School of Mechatronics Engineering of the University of Electronic Science and Technology of China as a graduate student. His main research interests include uncertainty analysis, sensitivity analysis, and MDO.

Mufeng Li is studying at the University of Electronic Science and Technology of China as a graduate student. His main research interest is robust design.

Cong Hu is currently studying at the University of Electronic Science and Technology of China as a graduate student under the guidance of Professor Huanwei Xu. His main research interests include time-dependent multidisciplinary optimization design.

Suichuan Zhang is studying at the University of Electronic Science and Technology of China as a graduate student. His main research direction is structural strength optimization, life prediction, and multidisciplinary design optimization.

Xin Wang is currently studying at the University of Electronic Science and Technology of China as a graduate student. His main research interests are engineering design and optimization.

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Xu, H., Li, W., Li, M. et al. Multidisciplinary robust design optimization based on time-varying sensitivity analysis. J Mech Sci Technol 32, 1195–1207 (2018). https://doi.org/10.1007/s12206-018-0223-8

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  • DOI: https://doi.org/10.1007/s12206-018-0223-8

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