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http://dx.doi.org/10.12989/sem.2022.82.3.271

A new structural reliability analysis method based on PC-Kriging and adaptive sampling region  

Yu, Zhenliang (School of Mechanical and Power Engineering, Yingkou Institute of Technology)
Sun, Zhili (School of Mechanical Engineering and Automation, Northeastern University)
Guo, Fanyi (School of Mechanical Engineering and Automation, Northeastern University)
Cao, Runan (School of Mechanical Engineering and Automation, Northeastern University)
Wang, Jian (School of Mechanical Engineering and Automation, Northeastern University)
Publication Information
Structural Engineering and Mechanics / v.82, no.3, 2022 , pp. 271-282 More about this Journal
Abstract
The active learning surrogate model based on adaptive sampling strategy is increasingly popular in reliability analysis. However, most of the existing sampling strategies adopt the trial and error method to determine the size of the Monte Carlo (MC) candidate sample pool which satisfies the requirement of variation coefficient of failure probability. It will lead to a reduction in the calculation efficiency of reliability analysis. To avoid this defect, a new method for determining the optimal size of the MC candidate sample pool is proposed, and a new structural reliability analysis method combining polynomial chaos-based Kriging model (PC-Kriging) with adaptive sampling region is also proposed (PCK-ASR). Firstly, based on the lower limit of the confidence interval, a new method for estimating the optimal size of the MC candidate sample pool is proposed. Secondly, based on the upper limit of the confidence interval, an adaptive sampling region strategy similar to the radial centralized sampling method is developed. Then, the k-means++ clustering technique and the learning function LIF are used to complete the adaptive design of experiments (DoE). Finally, the effectiveness and accuracy of the PCK-ASR method are verified by three numerical examples and one practical engineering example.
Keywords
adaptive sampling region; optimal number of Monte Carlo samples; PC-Kriging; real failure probability interval estimation; reliability analysis;
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1 Wang, J. and Sun, Z.L. (2018), "The stepwise accuracy-improvement strategy based on the kriging model for structural reliability analysis", Struct. Multidisc. Optim., 58(2), 595-612. https://doi.org/10.1007/s00158-018-1911-9   DOI
2 Jian, W., Zhili, S., Qiang, Y. and Rui, L. (2017) "Two accuracy measures of the kriging model for structural reliability analysis", Reliab. Eng. Syst. Saf., 167, 494-505. https://doi.org/10.1016/j.ress.2017.06.028.   DOI
3 Liu, Q., Fu, W., Qin, J., Zheng, W.X. and Gao, H. (2017), "Distributed k-means algorithm for sensor networks based on multi-agent consensus theory", IEEE Tran. Cybernet., 47(3), 772-783. http://doi.org/10.1109/TCYB.2016.2526683.   DOI
4 Lv, Z., Lu, Z. and Wang, P. (2015), "A new learning function for Kriging and its applications to solve reliability problems in engineering", Comput. Math. Appl., 70, 1182-1197. http://doi.org/10.1016/j.camwa.2015.07.004.   DOI
5 Arnold, T.W. (2011), "Uninformative parameters and model selection using akaike's information criterion", J. Wildlife Manage., 74(6), 1175-1178. http://doi.org/10.2193/2009-367.   DOI
6 Au, S.K. and Beck, J.L. (2001), "Estimation of small failure probabilities in high dimensions by subset simulation", Prob. Eng. Mech., 16(4), 263-277. https://doi.org/10.1016/S0266-8920(01)00019-4.   DOI
7 Basaga, H.B., Bayraktar, A. and Kaymaz, I. (2012), "An improved response surface method for reliability analysis of structures", Struct. Eng. Mech., 42(2), 175-189. https://doi.org/10.12989/sem.2012.42.2.175.   DOI
8 Beer, M. and Spanos, P.D. (2009), "A neural network approach for simulating stationary stochastic processes", Struct. Eng. Mech., 32(1), 71-94. https://doi.org/10.12989/sem.2009.32.1.071.   DOI
9 Bichon, B.J., Eldred, M.S., Swiler, L.P., Mahadevan, S. and McFarland, J.M. (2008), "Efficient global reliability analysis for nonlinear implicit performance functions", AIAA J., 46, 2459- 2468. http://doi.org/10.2514/1.34321.   DOI
10 Echard, B., Gayton, N. and Lemaire, M. (2011), "AK-MCS: An active learning reliability method combining kriging and monte carlo simulation", Struct. Saf., 33(2), 145-154. http://doi.org/10.1016/j.strusafe.2011.01.002.   DOI
11 Sun, Z., Wang, J., Li, R. and Tong, C. (2017), "LIF: A new kriging based learning function and its application to structural reliability analysis", Reliab. Eng. Syst. Saf., 157, 152-165. https://doi.org/10.1016/j.ress.2016.09.003.   DOI
12 Rackwitz, R. (2001), "Reliability analysis-a review and some perspectives", Struct. Saf., 23(4), 365-395. http://dx.doi.org/10.1016/S0167-4730(02)00009-7.   DOI
13 Rad, H.N., Hasanipanah, M., Rezaei, M. and Eghlim, A.L. (2018) "Developing a least squares support vector machine for estimating the blast-induced fly rock", Eng. Comput., 34(4), 709-717. https://doi.org/10.1007/s00366-017-0568-0.   DOI
14 Su, C.Q. and Zhang, Y.M. (2012), "Reliability sensitivity estimation of rotor system with oil whip and resonance", Adv. Mater. Res., 9(6), 110-114. https://doi.org/10.4028/www.scientific.net/AMR.544.110.   DOI
15 Echard, B., Gayton, N., Lemaire, M. and Relun, N. (2013), "A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models", Reliab. Eng. Syst. Saf., 111(2), 232-240. http://doi.org/10.1016/j.ress.2012.10.008.   DOI
16 Gaspar, B., Naess, A., Leira, B.J. and Soares, C.G. (2014), "System reliability analysis by Monte Carlo based method and finite element structural models", J. Offsh. Mech. Arct. Eng., 136(3), 031603. http://doi.org/10.1115/1.4025871.   DOI
17 Fang, Y. and Teea, K.F. (2017), "Structural reliability analysis using response surface method with improved genetic algorithm", Struct. Eng. Mech., 62(2), 139-142. https://doi.org/10.12989/sem.2017.62.2.139.   DOI
18 Fang, Y.F. and Teea, K.F. (2017), "Structural reliability analysis using response surface method with improved genetic algorithm", Struct. Eng. Mech., 62(2), 139-142. http://doi.org/10.12989/sem.2017.62.2.139.   DOI
19 Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004), "Least angle regression", Ann. Statist., 32(2), 407-451. https://doi.org/10.1214/009053604000000067.   DOI
20 Kaintura, A., Spina, D., Couckuyt, I., Knockaert, L., Bogaerts, W. and Dhaene, T. (2017), "A kriging and stochastic collocation ensemble for uncertainty quantification in engineering applications", Eng. Comput., 33(4), 935-949. http://doi.org/10.1007/s00366-017-0507-0.   DOI
21 Qiu, Y.S. and Bai, J.Q. (2015), "Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and kriging surrogate model", Chin. J. Aeronaut., 28(1), 44-56. http://doi.org/10.1016/j.cja.2014.12.017.   DOI
22 Schobi, R., Sudret, B. and Wiart, J. (2015), "Polynomial-chaos-based Kriging", Int. J. Uncert. Quantif., 5(2), 171-193. http://doi.org/10.1615/Int.J.UncertaintyQuantification.2015012467   DOI
23 Toal, D.J. (2016), "A study into the potential of GPUs for the efficient construction and evaluation of kriging models", Eng. Comput., 32(3), 377-404. http://doi.org/10.1007/s00366-015-0421-2.   DOI
24 Wang, C. and Matthies, H.G. (2020), "A comparative study of two interval-random models for hybrid uncertainty propagation analysis", Mech. Syst. Signal Pr., 136(1), 106531. https://doi.org/10.1016/j.ymssp.2019.106531.   DOI
25 Wen, Z., Pei, H., Liu, H. and Yue, Z. (2016), "A sequential kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability", Reliab. Eng. Syst. Saf., 153, 170-179. http://doi.org/10.1016/j.ress.2016.05.002.   DOI
26 Zhang, Y., Sun, Z., Yan, Y., Yu, Z. and Wang, J. (2019), "An efficient adaptive reliability analysis method based on kriging and weighted average misclassification rate improvement", IEEE Access, 7, 94954-94965. http://doi.org/10.1109/ACCESS.2019.2928332.   DOI
27 Zhao, Y.G. and Ono, T. (1999), "A general procedure for first/second-order reliability method (FORM/SORM)", Struct. Saf., 21(2), 95-112. https://doi.org/10.1016/S0167-4730(99)00008-9.   DOI
28 Tong, C., Sun, Z., Zhao, Q., Wang, Q. and Wang, S. (2015), "A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling", J. Mech. Sci. Technol., 29(8), 3183-3193. http://doi.org/10.1007/s12206-015-0717-6.   DOI
29 Vahedi, J., Ghasemi, M.R. and Miri, M. (2018), "Structural reliability assessment using an enhanced adaptive kriging method", Struct. Eng. Mech., 66(6), 677-691. https://doi.org/10.12989/sem.2018.66.6.677.   DOI
30 Wang, C., Qiu, Z., Xu, M. and Li, Y. (2017), "Novel reliability-based optimization method for thermal structure with hybrid random, interval and fuzzy parameters", Appl. Math. Model., 47(7), 573-586. https://doi.org/10.1016/j.apm.2017.03.053.   DOI
31 Yang, X., Mi, C., Deng, D. and Liu, Y. (2019), "A system reliability analysis method combining active learning kriging model with adaptive size of candidate points", Struct. Multidisc. Optim., 60(1), 137-150. https://doi.org/10.1007/s00158-019-02205-x.   DOI
32 Wang, Z. and Shafieezadeh, A. (2019), "REAK: Reliability analysis through error rate-based adaptive kriging", Reliab. Eng. Syst Saf., 182, 33-45. https://doi.org/10.1016/j.ress.2018.10.004.   DOI
33 Cheng, J., Cai, C. and Xiao, R.C. (2007), "Application of artificial neural networks to the response prediction of geometrically nonlinear truss structures", Struct. Eng. Mech., 26(3), 251-262. https://doi.org/10.12989/sem.2007.26.3.251.   DOI
34 Yang, X., Liu, Y., Gao, Y., Zhang, Y. and Gao, Z. (2015), "An active learning Kriging model for hybrid reliability analysis with both random and interval variables", Struct. Multidisc. Optim., 51, 1003-1016. http://doi.org/10.1007/s00158-014-1189-5.   DOI
35 Zhao, H., Yue, Z., Liu, Y., Gao, Z. and Zhang, Y. (2015), "An efficient reliability method combining adaptive importance sampling and kriging metamodel", Appl. Math. Model., 39(7), 1853-1866. http://doi.org/10.1016/j.apm.2014.10.015   DOI
36 Zhao, W.T., Shi, X.Y. and Tang, K. (2016), "A response surface method based on sub-region of interest for structural reliability analysis", Struct. Eng. Mech., 57(4), 587-602. https://doi.org/10.12989/sem.2016.57.4.587.   DOI
37 Wang, H., Wang, S.P. and Milete, M.T. (2010), "Modified sequential kriging optimization for multidisciplinary complex product simulation chinese", J. Aeronaut., 23(5), 616-622. http://doi.org/10.1016/S1000-9361(09)60262-4.   DOI
38 Hong, Y.L. (2013), "On computing the distribution function for the poisson binomial distribution", Comput. Stat. Data Anal., 59, 41-51. https://doi.org/10.1016/j.csda.2012.10.006.   DOI
39 Wang, C. and Matthies, H.G. (2019), "Epistemic uncertainty-based reliability analysis for engineering system with hybrid evidence and fuzzy variables", Comput. Meth. Appl Mech. Eng., 355, 438-455. https://doi.org/10.1016/j.cma.2019.06.036.   DOI