An adaptive PC-Kriging method for time-variant structural reliability analysis

• Autorzy: Nan Hang , Li Hongshuang , Song Zhuocheng

Identyfikatory

DOI

10.17531/ein.2022.3.14

• Języki publikacji: EN

Abstrakty

EN

The practical application of time-variant reliability analysis is limited by its computationally expensive models which describe the structural system behavior. This paper presents a new adaptive PC-Kriging (APCK) approach to accurately and efficiently assess the time-variant reliabilities. Time interval is firstly discretized with a series of time instants and then the stochastic process is reconstructed by standard normal random variables and deterministic function of time. PC-Kriging (PCK) models are built at each time instant to predict the instantaneous responses of performance function. To improve the accuracy and efficiency, a new update strategy based on the integration of U- and H- learning functions is developed to refine the PCK models of instantaneous responses. One or two best samples are identified by the proposed learning criterion for updating the PCK models. Finally, Monte Carlo simulation (MCS) is used to estimate the time-variant reliability based on the updated PCK models. Four examples are used to validate the accuracy and efficiency of the proposed method.

Słowa kluczowe

EN

time-variant; reliability analysis; instantaneous response; adaptive PC-Kriging; learning; function

• Wydawca: Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne
• Czasopismo: Eksploatacja i Niezawodność
• Rocznik: 2022
• Tom: Vol. 24, no. 3
• Strony: 532--543
• Opis fizyczny: Bibliogr. 43 poz., rys., tab.

Twórcy

autor

Nan Hang

• Nanjing University of Aeronautics and Astronautics, College of Aerospace Engineering, Nanjing, 210016, China

• https://orcid.org/0000-0002-6683-6156

autor

Li Hongshuang

• Nanjing University of Aeronautics and Astronautics, College of Aerospace Engineering, Nanjing, 210016, China
• [e-mail]

• https://orcid.org/0000-0001-8106-5786

autor

Song Zhuocheng

• Nanjing University of Aeronautics and Astronautics, College of Aerospace Engineering, Nanjing, 210016, China

• https://orcid.org/0000-0002-7091-089X

Bibliografia

• 1. Andrieu-Renaud C, Sudret B, Lemaire M. The PHI2 method: a way to compute time-variant reliability. Reliability Engineering & System Safety 2004; 84(1): 75–86, https://doi.org/10.1016/j.ress.2003.10.005.
• 2. Breitung K. Asymptotic approximations for probability integrals. Probabilistic Engineering Mechanics 1989; 4(4): 187–190, https://doi.org/10.1016/0266-8920(89)90024-6.
• 3. Breitung K. Asymptotic crossing rates for stationary Gaussian vector processes. Stochastic Processes and their Applications 1988; 29(2): 195–207, https://doi.org/10.1016/0304-4149(88)90037-3.
• 4. Cai C-H, Lu Z-H, Leng Y et al. Time-Dependent Structural Reliability Assessment for Nonstationary Non-Gaussian Performance Functions. Journal of Engineering Mechanics 2021; 147(2): 04020145, https://doi.org/10.1061/(ASCE)EM.1943-7889.0001883.
• 5. Chakraborty S, Tesfamariam S. Subset simulation based approach for space-time-dependent system reliability analysis of corroding pipelines. Structural Safety 2021; 90: 102073, https://doi.org/10.1016/j.strusafe.2020.102073.
• 6. Chen J-B, Li J. The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters. Structural Safety 2007; 29(2): 77–93, https://doi.org/10.1016/j.strusafe.2006.02.002.
• 7. Ebrahimian M, Pirouzmand A, Rabiee A. Developing a method for time-variant reliability assessment of passive heat removal systems in nuclear power plants. Annals of Nuclear Energy 2021; 160: 108365, https://doi.org/10.1016/j.anucene.2021.108365.
• 8. Echard B, Gayton N, Lemaire M. AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation. Structural Safety 2011; 33(2): 145–154, https://doi.org/10.1016/j.strusafe.2011.01.002.
• 9. Hu Y, Lu Z, Wei N, Zhou C. A single-loop Kriging surrogate model method by considering the first failure instant for time-dependent reliability analysis and safety lifetime analysis. Mechanical Systems and Signal Processing 2020; 145: 106963, https://doi.org/10.1016/j.ymssp.2020.106963.
• 10. Hu Z, Du X. A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis. Journal of Mechanical Design 2013; 135(7): 071003, https://doi.org/10.1115/1.4023925.
• 11. Hu Z, Du X. Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis. Journal of Mechanical Design 2015; 137(5): 051401, https://doi.org/10.1115/1.4029520.
• 12. Hu Z, Mahadevan S. A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis. Journal of Mechanical Design 2016; 138(6): 061406, https://doi.org/10.1115/1.4033428.
• 13. Huang S P, Quek S T, Phoon K K. Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes. International Journal for Numerical Methods in Engineering 2001; 52(9): 1029–1043, https://doi.org/10.1002/nme.255.
• 14. Kanjilal O, Manohar C S. Time variant reliability estimation of randomly excited uncertain dynamical systems by combined Markov chain splitting and Girsanov’s transformation. Archive of Applied Mechanics 2020; 90(11): 2363–2377, https://doi.org/10.1007/s00419-020-01726-y.
• 15. Kersaudy P, Sudret B, Varsier N et al. A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry. Journal of Computational Physics 2015; 286: 103–117, https://doi.org/10.1016/j.jcp.2015.01.034.
• 16. Lelièvre N, Beaurepaire P, Mattrand C, Gayton N. AK-MCSi: A Kriging-based method to deal with small failure probabilities and timeconsuming models. Structural Safety 2018; 73: 1–11, https://doi.org/10.1016/j.strusafe.2018.01.002.
• 17. Li C, Der Kiureghian A. Optimal Discretization of Random Fields. Journal of Engineering Mechanics 1993; 119(6): 1136–1154, https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1136).
• 18. Li H-S, Wang T, Yuan J-Y, Zhang H. A sampling-based method for high-dimensional time-variant reliability analysis. Mechanical Systems and Signal Processing 2019; 126: 505–520, https://doi.org/10.1016/j.ymssp.2019.02.050.
• 19. Li J, Chen J, Chen Z. Developing an improved composite limit state method for time-dependent reliability analysis. Quality Engineering 2020; 32(3): 298–311, https://doi.org/10.1080/08982112.2020.1735004.
• 20. Li J, Chen J, Wei J et al. Developing an Instantaneous Response Surface Method t-IRS for Time-Dependent Reliability Analysis. Acta Mechanica Solida Sinica 2019; 32(4): 446–462, https://doi.org/10.1007/s10338-019-00096-5.
• 21. Linxiong H, Huacong L, Kai P, Hongliang X. A novel kriging based active learning method for structural reliability analysis. Journal of Mechanical Science and Technology 2020; 34(4): 1545–1556, https://doi.org/10.1007/s12206-020-0317-y.
• 22. Lv Z, Lu Z, Wang P. A new learning function for Kriging and its applications to solve reliability problems in engineering. Computers & Mathematics with Applications 2015; 70(5): 1182–1197, https://doi.org/10.1016/j.camwa.2015.07.004.
• 23. Majcher M, Mourelatos Z, Tsianika V. Time-Dependent Reliability Analysis Using a Modified Composite Limit State Approach. SAE International Journal of Commercial Vehicles 2017; 10(1): 66–72, https://doi.org/10.4271/2017-01-0206.
• 24. Marelli S, Sudret B. UQLab: A Framework for Uncertainty Quantification in Matlab. Vulnerability, Uncertainty, and Risk, Liverpool, UK, American Society of Civil Engineers: 2014: 2554–2563, https://doi.org/10.1061/9780784413609.257.
• 25. Ping M H, Han X, Jiang C, Xiao X Y. A time-variant extreme-value event evolution method for time-variant reliability analysis. Mechanical Systems and Signal Processing 2019; 130: 333–348, https://doi.org/10.1016/j.ymssp.2019.05.009.
• 26. Qian H-M, Huang H-Z, Li Y-F. A novel single-loop procedure for time-variant reliability analysis based on Kriging model. Applied Mathematical Modelling 2019; 75: 735–748, https://doi.org/10.1016/j.apm.2019.07.006.
• 27. Qian H-M, Huang T, Huang H-Z. A single-loop strategy for time-variant system reliability analysis under multiple failure modes. Mechanical Systems and Signal Processing 2021; 148: 107159, https://doi.org/10.1016/j.ymssp.2020.107159.
• 28. Quezada del Villar A V, Rodríguez-Picón L A, JC Pérez-Olguín I, Méndez-González L C. Stochastic modelling of the temperature increase in metal stampings with multiple stress variables and random effects for reliability assessment. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2019; 21(4): 654–661, https://doi.org/10.17531/ein.2019.4.15.
• 29. Rice S O. Mathematical Analysis of Random Noise. Bell System Technical Journal 1945; 24(1): 46–156, https://doi.org/10.1002/j.1538-7305.1945.tb00453.x.
• 30. Schöbi R, Sudret B, Marelli S. Rare Event Estimation Using Polynomial-Chaos Kriging. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 2017; 3(2): D4016002, https://doi.org/10.1061/AJRUA6.0000870.
• 31. Schobi R, Sudret B, Wiart J. Polynomial-chaos-based Kriging. International Journal for Uncertainty Quantification 2015; 5(2): 171–193, https://doi.org/10.1615/Int.J.UncertaintyQuantification.2015012467.
• 32. Straub D, Schneider R, Bismut E, Kim H-J. Reliability analysis of deteriorating structural systems. Structural Safety 2020; 82: 101877, https://doi.org/10.1016/j.strusafe.2019.101877.
• 33. Sudret B. Analytical derivation of the outcrossing rate in time-variant reliability problems. Structure and Infrastructure Engineering 2008; 4(5): 353–362, https://doi.org/10.1080/15732470701270058.
• 34. Wang W, Wang J, Fu J, Lu G. A moment-matching based method for the analysis of manipulator’s repeatability of positioning with arbitrarily distributed joint clearances. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2018; 21(1): 10–20, https://doi.org/10.17531/ein.2019.1.2.
• 35. Wang Z, Chen W. Confidence-based adaptive extreme response surface for time-variant reliability analysis under random excitation. Structural Safety 2017; 64: 76–86, https://doi.org/10.1016/j.strusafe.2016.10.001.
• 36. Wang Z, Wang P. A new approach for reliability analysis with time-variant performance characteristics. Reliability Engineering & System Safety 2013; 115: 70–81, https://doi.org/10.1016/j.ress.2013.02.017.
• 37. Xu J. A new method for reliability assessment of structural dynamic systems with random parameters. Structural Safety 2016; 60: 130–143, https://doi.org/10.1016/j.strusafe.2016.02.005.
• 38. Yang M, Zhang D, Han X. New efficient and robust method for structural reliability analysis and its application in reliability-based design optimization. Computer Methods in Applied Mechanics and Engineering 2020; 366: 113018, https://doi.org/10.1016/j.cma.2020.113018.
• 39. Yang M, Zhang D, Wang F, Han X. Efficient local adaptive Kriging approximation method with single-loop strategy for reliability-based design optimization. Computer Methods in Applied Mechanics and Engineering 2022; 390: 114462, https://doi.org/10.1016/j.cma.2021.114462.
• 40. Yu Z, Sun Z, Cao R et al. RCA-PCK: A new structural reliability analysis method based on PC-Kriging and radial centralized adaptive sampling strategy. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2021; 235(17): 3424–3438, https://doi.org/10.1177/0954406220957711.
• 41. Zhang D, Han X, Jiang C et al. Time-Dependent Reliability Analysis Through Response Surface Method. Journal of Mechanical Design 2017; 139(4): 041404, https://doi.org/10.1115/1.4035860.
• 42. Zhang D, Zhou P, Jiang C et al. A stochastic process discretization method combing active learning Kriging model for efficient timevariant reliability analysis. Computer Methods in Applied Mechanics and Engineering 2021; 384: 113990, https://doi.org/10.1016/j.cma.2021.113990.
• 43. Zhang X-Y, Lu Z-H, Zhao Y-G, Li C-Q. The GLO method: An efficient algorithm for time-dependent reliability analysis based on outcrossing rate. Structural Safety 2022; 97: 102204, https://doi.org/10.1016/j.strusafe.2022.102204.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).