An active learning method for structural reliability combining response surface model with Gaussian process of residual fitting and reliability-based sequential sampling design

Wei, Jianbao; Liu, Zhijie; Sun, Yuhang; Wang, Xiaobang

doi:10.17531/ein/193443

Artykuł - szczegóły

Tytuł artykułu

An active learning method for structural reliability combining response surface model with Gaussian process of residual fitting and reliability-based sequential sampling design

Autorzy

Wei Jianbao , Liu Zhijie , Sun Yuhang , Wang Xiaobang

Treść / Zawartość

Pełne teksty:

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Identyfikatory

DOI

10.17531/ein/193443

Warianty tytułu

Języki publikacji

Abstrakty

It is quite challenging to attain an accurate reliability estimation on complex structures with low computational burden. Therefore, an active learning method combining the response surface model with the Gaussian process (GP) of residual fitting and reliability-based sequential sampling design is proposed for structural reliability analysis. This method first utilizes a random quadrilateral grid to perturb the uniform design sampling and generates a small set of initial design of experiments (DoE) to establish a high-precision initial response surface model efficiently. Then, a GP model for residual prediction is constructed by using the residuals of the initial response surface model, which allows the response surface function to be closer to the limit state function (LSF). Further, a reliability-based expected improvement (REI) learning function, which inherits the property of the EI function and considers the probability of feasibility of the samples, is developed for the selection of the most feasible points to update the response surface model and the GP model. The importance sampling (IS) combined with the proposed method is employed to assess the rare failure probability of structures. Ultimately, five numerical examples are used to validate the accuracy and efficiency of the proposed method.

Słowa kluczowe

structural reliability analysis active learning sampling strategy surrogate model residual fitting

Wydawca

Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne

Czasopismo

Eksploatacja i Niezawodność

Rocznik

2025

Tom

Vol. 27, no. 1

Strony

art. no. 193443

Opis fizyczny

Bibliogr. 51 poz., rys., tab., wykr.

Twórcy

autor

Wei Jianbao

wjb2022@dlmu.edu.cn

Dalian Maritime University, China

autor

Liu Zhijie

liuzj@dlmu.edu.cn

Dalian Maritime University, China

autor

Sun Yuhang

syh-2021@dlmu.edu.cn

Dalian Maritime University, China

autor

Wang Xiaobang

wxb@dlmu.edu.cn

Dalian Maritime University, China

Bibliografia

1. Zhou S, Zhang JG, You LF, Zhang QY. Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties. Eksploatacja i Niezawodnoś ć – Maintenance and Reliability 2021; 23(2): 231-241. https://doi.org/10.17531/ein.2021.2.3.
2. Peng CL, Chen C, Guo T, Xu WJ. AK-SEUR: An adaptive Kriging-based learning function for structural reliability analysis through sample-based expected uncertainty reduction. Structural Safety 2024; 106: 102384. https://doi.org/10.1016/j.strusafe.2023.102384.
3. Zhao YG, Ono T. A general procedure for first/second-order reliability method (FORM/SORM). Structural Safety 1999; 21: 95-112. https://doi.org/10.1016/s0167-4730(99)00008-9.
4. Lu ZH, Hu DZ, Zhao YG. Second-order Fourth-Moment Method for Structural Reliability. Journal of Engineering Mechanics 2017; 143: 06016010. https://doi.org/10.1061/(asce)em.1943-7889.0001199.
5. Meng Z, Wan HP, Sheng ZL, Li G. A novel study of structural reliability analysis and optimization for super parametric convex model. International Journal for Numerical Methods in Engineering 2020; 121: 4208-4229. http:/dx.doi.org/10.1002/nme.6437.
6. Luo CQ, Keshtegar B, Zhu SP, Taylan Osmanet, Liu XP. Hybrid enhanced Monte Carlo simulation coupled with advanced machine learning approach for accurate and efficient structural reliability analysis. Computer Methods in Applied Mechanics and Engineering 2022; 388: 114218. https://doi.org/10.1016/J.CMA.2021.114218
7. Zhang JH, Xiao M, Gao L, Chu S. Combined projection-outline-based active learning Kriging and adaptive importance sampling method for hybrid reliability analysis with small failure probabilities. Computer Methods in Applied Mechanics and Engineering 2019; 344: 13-33. http://dx.doi.org/10.1016/j.cma.2018.10.003.
8. Xie JY, Tian ZR, Zhi PP, Zhao YD. Reliability analysis method of coupling optimal importance sampling density and multi-fidelity Kriging model. Eksploatacja i Niezawodnoś ć – Maintenance and Reliability 2023; 25(2): 161893. https://doi.org/10.17531/ein/161893.
9. Nguyen T-T, Dang V-H, Nguyen H-X. Efficient framework for structural reliability analysis based on adaptive ensemble learning paired with subset simulation. Structures 2022; 45: 1738-1750. https://doi.org/10.1016/j.istruc.2022.09.072.
10. Morio J, Balesdent M, Jacquemart D, Vergé C. A survey of rare event simulation methods for static input-output models. Simulation Modelling Practice and Theory 2014; 49: 287-304. https://doi.org/10.1016/j.simpat.2014.10.007.
11. Grooteman F. An adaptive directional importance sampling method for structural reliability. Probabilistic Engineering Mechanics 2011; 26: 134-141. http://dx.doi.org/10.1016/j.probengmech.2010.11.002.
12. Keshtegar B. Chaotic conjugate stability transformation method for structural reliability analysis. Computer Methods in Applied Mechanics and Engineering 2016; 310: 866-885. http://dx.doi.org/10.1016/j.cma.2016.07.046.
13. Gao SZ, Zhao YK, Zhao XD, Zhang YM. Application of response surface method based on new strategy in structural reliability analysis. Structures 2023; 57: 105202. https://doi.org/10.1016/j.istruc.2023.105202.
14. Alibrandi U. A response surface method for stochastic dynamic analysis. Reliability Engineering and System Safety 2014; 126: 44-53. https://doi.org/10.1016/j.ress.2014.01.003.
15. Sajad AS, Fatemeh E, Xu XY, Liang XH. Machine learning-based methods in structural reliability analysis: A review. Reliability Engineering and System Safety 2022; 219: 108223. https://doi.org/10.1016/j.ress.2021.108223.
16. Zhang YM, Ma J, Du WY. A new radial basis function active learning method based on distance constraint for structural reliability analysis. International Journal of Mechanics and Materials in Design 2023; 19(3): 567-581. https://doi.org/10.1007/S10999-023-09644-X.
17. Liu H, Xiao CN. Global non-probabilistic reliability sensitivity analysis based on surrogate model. Eksploatacja i Niezawodnoś ć – Maintenance and Reliability 2022; 24(4): 612-616. https://doi.org/10.17531/ein.2022.4.2.
18. Chen PY, Zhao CB, Yao H, Zhao SN. An adaptive method based on PC-Kriging for system reliability analysis of truss structures. Eksploatacja i Niezawodnoś ć – Maintenance and Reliability 2023; 25(3): 169497. https://doi.org/10.17531/ein/169497.
19. Alibrandi U, Alani AM, Ricciardi G. A new sampling strategy for SVM-based response surface for structural reliability analysis. Probabilistic Engineering Mechanics 2015; 41: 1-12. https://doi.org/10.1016/j.probengmech.2015.04.001.
20. Atin R, Subrata C. Support vector machine in structural reliability analysis: A review. Reliability Engineering and System Safety 2023; 233: 109126. https://doi.org/10.1016/j.ress.2023.109126.
21. Li K, Tang KJ, Li JL, et al. A hierarchical neural hybrid method for failure probability estimation. IEEE Access 2019; 7: 112087-112096. https://doi.org/10.1109/ACCESS.2019.2934980
22. Chao R, Younes A, Didier L, et al. Ensemble of surrogates combining Kriging and Artificial Neural Networks for reliability analysis with local goodness measurement. Structural Safety 2022; 96: 102186. https://doi.org/10.1016/j.strusafe.2022.102186.
23. David W, Carmine G. Gaussian process regression for fatigue reliability analysis of offshore wind turbines. Structural Safety 2021; 88: 102020. https://doi.org/10.1016/j.strusafe.2020.102020.
24. Liu D, Wang SP, Zhang C, Tomovic M. Bayesian model averaging based reliability analysis method for monotonic degradation dataset based on inverse Gaussian process and Gamma process. Reliability Engineering and System Safety 2018; 180: 25-38. https://doi.org/10.1016/j.ress.2018.06.019.
25. Xia Y, Wang YM. Improved Hybrid Response Surface Method Based on Double Weighted Regression and Vector Projection. Mathematical Problems in Engineering 2022; 2022: 5104027. https://doi.org/10.1155/2022/5104027.
26. Zhou D, Pan E, Zhang YM. Fractional polynomial function in stochastic response surface method for reliability analysis. Journal of Mechanical Science and Technology 2021; 35(1): 121-131. https://doi.org/10.1007/S12206-020-1211-3.
27. Xia Y, Kong WZ, Yu YY, Hu YY, Li JY. Improved Response Surface Method Based on Linear Gradient Iterative Criterion. Advances in Civil Engineering 2023; 023: 6360796. https://doi.org/10.1155/2023/6360796.
28. Roussouly N, Petitjean F, Salaun M. A new adaptive response surface method for reliability analysis. Probabilistic Engineering Mechanics 2013; 32: 103-115. https://doi.org/10.1016/j.probengmech.2012.10.001.
29. Li P, Hu SX, Li HY, Yang SQ, Wen HX. An improved quasi-sparse response surface model using the weighting method for low-dimensional simulation. Applied Soft Computing Journal 2019; 85: 105883-105883. https://doi.org/10.1016/j.asoc.2019.105883.
30. Romero VJ, Swiler LP, Giunta AA. Construction of response surfaces based on progressive-lattice-sampling experimental designs with application to uncertainty propagation. Structural Safety 2004; 26(2): 201-209. https://doi.org/10.1016/j.strusafe.2003.03.001.
31. Rathi KA, Sharma SVP, Chakraborty A. Sequential Stochastic Response Surface Method Using Moving Least Squares-Based Sparse Grid Scheme for Efficient Reliability Analysis. International Journal of Computational Methods 2019; 16(5): 38. https://doi.org/10.1142/S0219876218400170.
32. Myridis NE. Stochastic processes: theory for applications, by Robert G. Gallager. Contemporary Physics 2016; 57(2): 264-265. https://doi.org/10.1080/00107514.2015.1133711.
33. Chen C, Liao Q. ANOVA Gaussian process modeling for high-dimensional stochastic computational models. Journal of Computational Physics 2020; 416: 109519. https://doi.org/0.1016/j.jcp.2020.109519.
34. Gao HF, Fei CW, Bai GC, Ding BL. Reliability-based low-cycle fatigue damage analysis for turbine blade with thermo-structural interaction. Aerospace Science and Technology 2016; 49: 289-300. https://doi.org/10.1016/j.ast.2015.12.017.
35. Song ZZ, Liu Z, Zhang HY, Zhu P. An improved sufficient dimension reduction-based Kriging modeling method for high-dimensional evaluation-expensive problems. Computer Methods in Applied Mechanics and Engineering 2024; 418: 116544. https://doi.org/10.1016/j.cma.2023.116544.
36. Li YT, Luo YJ, Zhong Z. An active sparse polynomial chaos expansion approach based on sequential relevance vector machine, Computer Methods in Applied Mechanics and Engineering 2024; 418: 116554. https://doi.org/10.1016/j.cma.2023.116554.
37. Gao Y, Wang X. An effective warpage optimization method in injection molding based on the Kriging model. The International Journal of Advanced Manufacturing Technology 2008; 37: 953-960. https://doi.org/10.1007/s00170-007-1044-6.
38. Ranjan P, Haynes R, Karsten R. A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data. Technometrics 2011; 53(4): 366-378. https://doi.org/10.1198/TECH.2011.09141.
39. Jones RD, Schonlau M, Welch JW. Efficient Global Optimization of Expensive Black-Box Functions. Journal of Global Optimization 1998; 13(4): 455-492. https://doi.org/10.1023/A:1008306431147
40. Zhi PP, Wang ZL, Li YH, Tian ZR. RMQGS-APS-Kriging-based Active Learning Structural Reliability Analysis Method. Journal of Mechanical Engineering (Chinese) 2022; 58(16): 420-429. https://doi.org/10.3901/JME.2022.16.420
41. Meng Z, Zhang ZH, Li G, Zhang DQ. An active weight learning method for efficient reliability assessment with small failure probability. Structural and Multidisciplinary Optimization 2020; 61(3): 1157-1170. https://doi.org/10.1007/s00158-019-02419-z.
42. Xiao NC, Zuo MJ, Guo W. Efficient reliability analysis based on adaptive sequential sampling design and cross-validation. Applied Mathematical Modelling 2018; 58: 404-420. https://doi.org/10.1016/j.apm.2018.02.012.
43. Zheng PJ, Wang CM, Zong ZH, Wang LQ. A new active learning method based on the learning function U of the AK-MCS reliability analysis method. Engineering Structures 2017; 148: 185-194. https://doi.org/10.1016/j.engstruct.2017.06.038.
44. Zhang LG, Lu ZZ, Wang P. Efficient structural reliability analysis method based on advanced Kriging model. Applied Mathematical Modelling 2015; 39(2): 781-793. https://doi.org/10.1016/j.apm.2014.07.008.
45. Wang JS, Xu GJ, Li YL, Ahsan K. AKSE: A novel adaptive Kriging method combining sampling region scheme and error-based stopping criterion for structural reliability analysis. Reliability Engineering and System Safety 2022; 219: 108214. https://doi.org/10.1016/J.RESS.2021.108214.
46. Xu CL, Chen WD, Ma JX, Shi YQ, Lu SZ. AK-MSS: An adaptation of the AK-MCS method for small failure probabilities. Structural Safety 2020; 86: 101971. https://doi.org/10.1016/j.strusafe.2020.101971.
47. Meng Z, Zhang ZH, Li G, Zhang DQ. An active weight learning method for efficient reliability assessment with small failure probability. Structural and Multidisciplinary Optimization 2020; 61(3): 1157-1170. https://doi.org/10.1007/s00158-019-02419-z.
48. Yun WY, Lu ZZ, Jiang X, Zhang LG, He PF. AK-ARBIS: An improved AK-MCS based on the adaptive radial-based importance sampling for small failure probability. Structural Safety 2020; 82: 101891. https://doi.org/10.1016/j.strusafe.2019.101891.
49. Wen ZX ,Pei HQ ,Liu H , et al. A Sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability. Reliability Engineering and System Safety, 2016; 153: 170-179. https://doi.org/10.1016/j.ress.2016.05.002.
50. Au SK, Beck JL. Estimation of small failure probabilities in high dimension by subset simulation. Probabilistic Engineering Mechanics 2001; 16(4): 263-277. https://doi.org/10.1016/S0266-8920(01)00019-4.
51. Zhou CC, Lu ZZ, Yuan LX. Use of Relevance Vector Machine in Structural Reliability Analysis. Journal of aircraft 2013; 50(6): 1726-1733. https://doi.org/10.2514/1.C031950.

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