Technical Papers
Jun 10, 2020

Uncertainty-Based Design and Optimization Using First Order Saddle Point Approximation Method for Multidisciplinary Engineering Systems

Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 6, Issue 3

Abstract

The widely used First Order Reliability Method (FORM) is efficient for uncertainty quantification and safety assessment in Uncertainty-based Multidisciplinary Design Optimization (UBMDO). However, the Rosenblatt transformation is necessary for FORM. This transformation process can significantly increase the degree of nonlinearity of the computing process, especially in a multidisciplinary coupled computing environment. To deal with this case, the First Order Saddlepoint Approximation (FOSPA) strategy was utilized in this study. The method of UBMDO using FOSPA was proposed to enhance the accuracy of reliability evaluation in the calculation process. Moreover, the decoupling strategy of UBMDO was introduced here for higher computing efficiency. Two examples were utilized to illustrate the application of the proposed method.

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Data Availability Statement

All codes including reliability analysis and optimization generated or used during the study are available from the corresponding author by request.

Acknowledgments

The support from the National Natural Science Foundation of China (Grant Nos. 51605080 and 11672070), the Sichuan Science and Technology Program (Grant Nos. 2019YFG0350 and 2019YFG0348), the Fundamental Research Funds for the Central Universities of China (Grant No. ZYGX2019J035) and the Open Research Subject of Key Laboratory (Fluid Machinery and Engineering Research Base) of Sichuan Province (Grant No. szjj2019-030) are gratefully acknowledged.

References

Ai, Y., S. P. Zhu, D. Liao, J. A. F. O. Correia, A. M. De Jesus, and B. Keshtegar. 2019a. “Probabilistic modelling of notch fatigue and size effect of components using highly stressed volume approach.” Int. J. Fatigue 127 (Oct): 110–119. https://doi.org/10.1016/j.ijfatigue.2019.06.002.
Ai, Y., S. P. Zhu, D. Liao, J. A. F. O. Correia, C. Souto, A. M. P. De Jesus, and B. Keshtegar. 2019b. “Probabilistic modeling of fatigue life distribution and size effect of components with random defects.” Int. J. Fatigue 126 (Sep): 165–173. https://doi.org/10.1016/j.ijfatigue.2019.05.005.
Brevault, L., M. Balesdent, and A. Hebbal. 2020. “Multi-objective multidisciplinary design optimization approach for partially reusable launch vehicle design.” J. Spacecraft Rockets 57 (2): 1–17. https://doi.org/10.2514/1.A34601.
Du, X. 2008. “Saddlepoint approximation for sequential optimization and reliability analysis.” J. Mech. Design 130 (1): 011011. https://doi.org/10.1115/1.2717225.
Du, X., and A. Sudjianto. 2004. “The first order saddlepoint approximation for reliability analysis.” AIAA J. 42 (6): 1199–1207. https://doi.org/10.2514/1.3877.
Gao, S., and Y. Deng. 2019. “An evidential evaluation of nuclear safeguards.” Int. J. Distrib. Sens. Netw. 15 (12): 1550147719894550. https://doi.org/10.1177/1550147719894550.
Gong, Y., X. Su, H. Qian, and N. Yang. 2018. “Research on fault diagnosis methods for the reactor coolant system of nuclear power plant based on D-S evidence theory.” Ann. Nucl. Energy 112 (Feb): 395–399. https://doi.org/10.1016/j.anucene.2017.10.026.
Guo, J., and X. Du. 2009. “Reliability sensitivity analysis with random and interval variables.” Int. J. Numer. Methods Eng. 78 (13): 1585–1617. https://doi.org/10.1002/nme.2543.
He, P., C. A. Mader, J. R. R. A. Martins, and K. J. Maki. 2020. “DAfoam: An open-source adjoint framework for multidisciplinary design optimization with openFOAM.” AIAA J. 58 (Jan): 1–16. https://doi.org/10.2514/1.J058853.
Hu, X., X. Chen, G. T. Parks, and W. Yao. 2016. “Review of improved Monte Carlo methods in uncertainty-based design optimization for aerospace vehicles.” Prog. Aerosp. Sci. 86 (Oct): 20–27. https://doi.org/10.1016/j.paerosci.2016.07.004.
Huang, B., and X. Du. 2006. “Uncertainty analysis by dimension reduction integration and saddlepoint approximations.” J. Mech. Design 128 (1): 26–33. https://doi.org/10.1115/1.2118667.
Keshtegar, B., and S. Chakraborty. 2018. “A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis.” Appl. Math. Model. 53 (Jan): 319–332. https://doi.org/10.1016/j.apm.2017.09.017.
Keshtegar, B., and Z. Meng. 2017. “A hybrid relaxed first-order reliability method for efficient structural reliability analysis.” Struct. Saf. 66 (May): 84–93. https://doi.org/10.1016/j.strusafe.2017.02.005.
Kezirian, M. T., and S. L. Phoenix. 2017. “Natural gas hydrate as a storage mechanism for safe, sustainable and economical production from offshore petroleum reserves.” Energies 10 (6): 828. https://doi.org/10.3390/en10060828.
Li, L., H. Wan, W. Gao, F. Tong, and H. Li. 2019a. “Reliability based multidisciplinary design optimization of cooling turbine blade considering uncertainty data statistics.” Struct. Multidiscip. Optim. 59 (2): 659–673. https://doi.org/10.1007/s00158-018-2081-5.
Li, M., H. Xu, and Y. Deng. 2019b. “Evidential decision tree based on belief entropy.” Entropy-Switz. 21 (9): 897. https://doi.org/10.3390/e21090897.
Liu, B., and Y. Deng. 2019. “Risk evaluation in failure mode and effects analysis based on d numbers theory.” Int. J. Comput. Commun. 14 (5): 672–691. https://doi.org/10.15837/ijccc.2019.5.
Liu, X., Q. Fu, N. Ye, and L. Yin. 2019a. “The multi-objective reliability-based design optimization for structure based on probability and ellipsoidal convex hybrid model.” Struct. Saf. 77 (1): 48–56. https://doi.org/10.1016/j.strusafe.2018.11.004.
Liu, X., X. Wang, L. Sun, and Z. Zhou. 2019b. “An efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model.” Struct. Multidiscip. Optim. 59 (6): 2189–2203. https://doi.org/10.1007/s00158-018-2185-y.
Liu, X., X. Wang, J. Xie, and B. Li. 2019c. “Construction of probability box model based on maximum entropy principle and corresponding hybrid reliability analysis approach.” Struct. Multidiscip. Optim. 61 (2): 599–617. https://doi.org/10.1007/s00158-019-02382-9.
Meng, D., H. Huang, Z. Wang, N. Xiao, and X. Zhang. 2014. “Mean-value first-order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty.” J. Mech. Sci. Technol. 28 (10): 3925–3935. https://doi.org/10.1007/s12206-014-0903-y.
Meng, D., Y. Li, H. Huang, Z. Wang, and Y. Liu. 2015. “Reliability-based multidisciplinary design optimization using subset simulation analysis and its application in the hydraulic transmission mechanism design.” J. Mech. Des. 137 (5): 51402. https://doi.org/10.1115/1.4029756.
Meng, D., Y. Li, S. P. Zhu, Z. Hu, T. Xie, and Z. Fan. 2020. “Collaborative maritime design using sequential optimisation and reliability assessment.” Proc. Inst. Civ. Eng. Marit. Eng. 173 (1): 1–25. https://doi.org/10.1680/jmaen.2019.27.
Meng, D., H. Zhang, and T. Huang. 2016. “A concurrent reliability optimization procedure in the earlier design phases of complex engineering systems under epistemic uncertainties.” Adv. Mech. Eng. 8 (10): 168781401667397. https://doi.org/10.1177/1687814016673976.
Meng, Z., G. Li, D. Yang, and L. Zhan. 2017. “A new directional stability transformation method of chaos control for first order reliability analysis.” Struct. Multidiscip. Optim. 55 (2): 601–612. https://doi.org/10.1007/s00158-016-1525-z.
Papadimitriou, D., and Z. Mourelatos. 2017. “Mean-value second-order saddlepoint approximation for reliability analysis.” SAE Int. J. Commer. Veh. 10 (1): 73–80. https://doi.org/10.4271/2017-01-0207.
Papadimitriou, D. I., Z. P. Mourelatos, and Z. Hu. 2019. “Reliability analysis using second-order saddlepoint approximation and mixture distributions.” J. Mech. Des. 141 (2): 021401. https://doi.org/10.1115/1.4041370.
Su, X., L. Li, H. Qian, S. Mahadevan, and Y. Deng. 2019. “A new rule to combine dependent bodies of evidence.” Soft Comput. 23 (20): 9793–9799. https://doi.org/10.1007/s00500-019-03804-y.
Wei, X., and X. Du. 2020. “Robustness metric for robust design optimization under time- and space-dependent uncertainty through metamodeling.” J. Mech. Des. 142 (3): 031110. https://doi.org/10.1115/1.4045599.
Wen, T., and Y. Deng. 2020. “The vulnerability of communities in complex networks: An entropy approach.” Reliab. Eng. Syst. Saf. 196 (Apr): 106782. https://doi.org/10.1016/j.ress.2019.106782.
Yao, W., X. Chen, W. Luo, M. V. Tooren, and J. Guo. 2011. “Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicle.” Prog. Aerosp. Sci. 47 (6): 450–479. https://doi.org/10.1016/j.paerosci.2011.05.001.
Yao, W., X. Chen, Q. Ouyang, and M. V. Tooren. 2013. “A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory.” Struct. Multidiscip. Optim. 48 (2): 339–354. https://doi.org/10.1007/s00158-013-0901-1.
Youn, B. D., and K. K. Choi. 2004. “An investigation of nonlinearity of reliability-based design optimization approaches.” J. Mech. Des. 126 (3): 403–411. https://doi.org/10.1115/1.1701880.
Zhao, J., and Y. Deng. 2019. “Performer selection in human reliability analysis: D numbers approach.” Int. J. Comput. Commun. 14 (3): 437–452. https://doi.org/10.15837/ijccc.2019.3.3537.
Zhao, W., Y. Chen, and J. Liu. 2020. “An effective first order reliability method based on Barzilai–Borwein step.” Appl. Math. Model. 77 (Jan): 1545–1563. https://doi.org/10.1016/j.apm.2019.08.026.
Zhou, L., and F. Xiao. 2019. “A new matrix game with payoffs of generalized Dempster-Shafer structures.” Int. J. Intell. Syst. 34 (9): 2253–2268. https://doi.org/10.1002/int.22164.
Zhu, S. P., H. Z. Huang, Y. F. Li, Y. Liu, and Y. Yang. 2015. “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 229 (1): 23–33. https://doi.org/10.1177/0954409713496772.
Zhu, S. P., H. Z. Huang, W. Peng, H. K. Wang, and S. Mahadevan. 2016. “Probabilistic physics of failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty.” Reliab. Eng. Syst. Saf. 146 (Feb): 1–12. https://doi.org/10.1016/j.ress.2015.10.002.
Zhu, S. P., B. Keshtegar, N. T. Trung, Z. M. Yaseen, and D. T. Bui. 2019. “Reliability-based structural design optimization: Hybridized conjugate mean value approach.” Eng. Comput-Germany 1–14. https://doi.org/10.1007/s00366-019-00829-7.
Zhu, S. P., Q. Liu, W. Peng, and X. C. Zhang. 2018a. “Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks.” Int. J. Mech. Sci. 142 (Jul): 502–517. https://doi.org/10.1016/j.ijmecsci.2018.04.050.
Zhu, S. P., Q. Liu, J. Zhou, and Z. Y. Yu. 2018b. “Fatigue reliability assessment of turbine discs under multi-source uncertainties.” Fract. Eng. Mater. Struct. 41 (6): 1291–1305. https://doi.org/10.1111/ffe.12772.

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Go to ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 6Issue 3September 2020

History

Received: Feb 17, 2020
Accepted: Mar 23, 2020
Published online: Jun 10, 2020
Published in print: Sep 1, 2020
Discussion open until: Nov 10, 2020

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Authors

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Associate Professor, School of Mechanical and Electrical Engineering, Univ. of Electronic Science and Technology of China, Chengdu 611731, China; Researcher, Key Laboratory (Fluid Machinery and Engineering Research Base) of Sichuan Province, Xihua Univ., Chengdu 610039, China (corresponding author). ORCID: https://orcid.org/0000-0002-8306-0046. Email: [email protected]
Tianwen Xie [email protected]
Researcher, School of Mechanical and Electrical Engineering, Univ. of Electronic Science and Technology of China, Chengdu 611731, China. Email: [email protected]
Researcher, School of Mechanical and Electrical Engineering, Univ. of Electronic Science and Technology of China, Chengdu 611731, China. Email: [email protected]
Shun-Peng Zhu [email protected]
Professor, Center for System Reliability and Safety, School of Mechanical and Electrical Engineering, Univ. of Electronic Science and Technology of China, Chengdu 611731, China. Email: [email protected]
Zhengguo Hu [email protected]
Researcher, School of Mechanical and Electrical Engineering, Univ. of Electronic Science and Technology of China, Chengdu 611731, China. Email: [email protected]
Researcher, School of Mechanical and Electrical Engineering, Univ. of Electronic Science and Technology of China, Chengdu 611731, China. Email: [email protected]

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