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Adaptive hyperball Kriging method for efficient reliability analysis

Published online by Cambridge University Press:  08 November 2022

I-Tung Yang Open the ORCID record for I-Tung Yang [Opens in a new window]  and
Handy Prayogo Open the ORCID record for Handy Prayogo [Opens in a new window]
I-Tung Yang*
Affiliation:
Department of Civil and Construction Engineering, National Taiwan University of Science and Technology, No. 43 Section 4 Keelung Road, Taipei, Taiwan
Handy Prayogo
Affiliation:
Department of Civil and Construction Engineering, National Taiwan University of Science and Technology, No. 43 Section 4 Keelung Road, Taipei, Taiwan
*
Author for correspondence: I-Tung Yang, E-mail: [email protected]
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Abstract

Although an accurate reliability assessment is essential to build a resilient infrastructure, it usually requires time-consuming computation. To reduce the computational burden, machine learning-based surrogate models have been used extensively to predict the probability of failure for structural designs. Nevertheless, the surrogate model still needs to compute and assess a certain number of training samples to achieve sufficient prediction accuracy. This paper proposes a new surrogate method for reliability analysis called Adaptive Hyperball Kriging Reliability Analysis (AHKRA). The AHKRA method revolves around using a hyperball-based sampling region. The radius of the hyperball represents the precision of reliability analysis. It is iteratively adjusted based on the number of samples required to evaluate the probability of failure with a target coefficient of variation. AHKRA adopts samples in a hyperball instead of an n-sigma rule-based sampling region to avoid the curse of dimensionality. The application of AHKRA in ten mathematical and two practical cases verifies its accuracy, efficiency, and robustness as it outperforms previous Kriging-based methods.

Keywords

Active learningKrigingreliability analysisresilient infrastructuresoft computingstructural designsurrogate modeling
Type
Research Article
Information
AI EDAM , Volume 36 , 2022 , e34
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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References

Allaix, DL and Carbone, VI (2011) An improvement of the response surface method. Structural Safety 33, 165–172. doi:10.1016/j.strusafe.2011.02.001CrossRefGoogle Scholar
Au, S-K and Beck, JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics 16, 263–277. doi:10.1016/S0266-8920(01)00019-4CrossRefGoogle Scholar
Bichon, BJ, Eldred, MS, Swiler, LP, Mahadevan, S and McFarland, JM (2008) Efficient global reliability analysis for non-linear implicit performance functions. AIAA Journal 46, 2459–2468. doi:10.2514/1.34321CrossRefGoogle Scholar
Bjerager, P (1988) Probability integration by directional simulation. Journal of Engineering Mechanics 114, 1285–1302. doi:10.1061/(ASCE)0733-9399(1988)114:8(1285)CrossRefGoogle Scholar
Bourinet, JM, Deheeger, F and Lemaire, M (2011) Assessing small failure probabilities by combined subset simulation and support vector machines. Structural Safety 33, 343–353. doi:10.1016/j.strusafe.2011.06.001CrossRefGoogle Scholar
Cadini, F, Santos, F and Zio, E (2014) An improved adaptive Kriging-based importance technique for sampling multiple failure regions of low probability. Reliability Engineering & System Safety 131, 109–117. doi:10.1016/j.ress.2014.06.023CrossRefGoogle Scholar
Chen, Z, Wu, Z, Li, X, Chen, G, Chen, G, Gao, L and Qiu, H (2018) An accuracy analysis method for first-order reliability method. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, 095440621881338. doi:10.1177/0954406218813389Google Scholar
Chen, W, Xu, C, Shi, Y, Ma, J and Lu, S (2019) A hybrid Kriging-based reliability method for small failure probabilities. Reliability Engineering & System Safety 189, 31–41. doi:10.1016/j.ress.2019.04.003CrossRefGoogle Scholar
Echard, B, Gayton, N and Lemaire, M (2011) AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety 33, 145–154. doi:10.1016/j.strusafe.2011.01.002CrossRefGoogle Scholar
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. Reliability Engineering & System Safety 111, 232–240. doi:10.1016/j.ress.2012.10.008CrossRefGoogle Scholar
Goswami, S, Ghosh, S and Cahkraborty, S (2016) Reliability analysis of structures by iterative improved response surface method. Structural Safety 60, 56–66. doi:10.1016/j.strusafe.2016.02.002CrossRefGoogle Scholar
Guo, X, Dias, D, Carvajal, C, Peyras, L and Breul, P (2018) Reliability analysis of embankment dam sliding stability using the sparse polynomial chaos expansion. Engineering Structures 174, 295–307. doi:10.1016/j.engstruct.2018.07.053CrossRefGoogle Scholar
Guo, Q, Liu, Y, Chen, B and Zhao, Y (2020) An active learning Kriging model combined with directional importance sampling method for efficient reliability analysis. Probabilistic Engineering Mechanics 60, 103054. doi:10.1016/j.probengmech.2020.103054CrossRefGoogle Scholar
Hasofer, AM and Lind, N (1974) Exact and invariant second-moment code format. Journal of Engineering Mechanics-ASCE 100, 111–121.Google Scholar
Hawchar, L, El Soueidy, C-P and Schoefs, F (2017) Principal component analysis and polynomial chaos expansion for time-variant reliability problems. Reliability Engineering & System Safety 167, 406–416. doi:10.1016/j.ress.2017.06.024CrossRefGoogle Scholar
Hu, C and Youn, BD (2011) Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems. Structural and Multidisciplinary Optimization 43, 419–442. doi:10.1007/s00158-010-0568-9CrossRefGoogle Scholar
Huang, X, Chen, J and Zhu, H (2016) Assessing small failure probabilities by AK–SS: an active learning method combining Kriging and subset simulation. Structural Safety 59, 86–95. doi:10.1016/j.strusafe.2015.12.003CrossRefGoogle Scholar
Jones, D, Schonlau, M and Welch, W (1998) Efficient global optimization of expensive black-box functions. Journal of Global Optimization 13, 455–492. doi:10.1023/A:1008306431147CrossRefGoogle Scholar
Ju, BH and Lee, BC (2008) Reliability-based design optimization using a moment method and a Kriging metamodel. Engineering Optimization 40, 421–438. doi:10.1080/03052150701743795Google Scholar
Kang, S-C, Koh, H-M and Choo, JF (2010) An efficient response surface method using moving least squares approximation for structural reliability analysis. Probabilistic Engineering Mechanics 25, 365–371. doi:10.1016/j.probengmech.2010.04.002CrossRefGoogle Scholar
Kaymaz, I (2005) Application of Kriging method to structural reliability problems. Structural Safety 27, 133–151. doi:10.1016/j.strusafe.2004.09.001CrossRefGoogle Scholar
Kim, J and Song, J (2020) Probability-adaptive Kriging in n-Ball (PAK-Bn) for reliability analysis. Structural Safety 85, 101924. doi:10.1016/j.strusafe.2020.101924CrossRefGoogle Scholar
Kiureghian, A (1989) Measures of structural safety under imperfect states of knowledge. Journal of Structural Engineering-ASCE 115, 1119–1140.CrossRefGoogle Scholar
Kiureghian, AD, Lin, HZ and Hwang, SJ (1987) Second order reliability approximations. Journal of Engineering Mechanics 113, 1208–1225. doi:10.1061/(ASCE)0733-9399(1987)113:8(1208)CrossRefGoogle Scholar
Lophaven, SN, Nielsen, HB and Søndergaard, J (2002) DACE - a Matlab Kriging toolbox, Version 2.0 [Report].Google Scholar
Lv, Z, Lu, Z and Wang, P (2015) A new learning function for Kriging and its applications to solve reliability problems in engineering. Computers & Mathematics with Applications 70, 1182–1197. doi:10.1016/j.camwa.2015.07.004CrossRefGoogle Scholar
Matheron, G (1973) The intrinsic random functions and their applications. Advances in Applied Probability 5, 439–468. doi:10.2307/1425829CrossRefGoogle Scholar
Melchers, RE (1990) Radial importance sampling for structural reliability. Journal of Engineering Mechanics 116, 189–203. doi:10.1061/(ASCE)0733-9399(1990)116:1(189)CrossRefGoogle Scholar
Moustapha, M and Sudret, B (2019) Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework. Structural and Multidisciplinary Optimization 60, 2157–2176. doi:10.1007/s00158-019-02290-yCrossRefGoogle Scholar
Muller, ME (1959) A note on a method for generating points uniformly on n-dimensional spheres. Communications of the ACM 2, 19–20. doi:10.1145/377939.377946CrossRefGoogle Scholar
Pan, Q and Dias, D (2017) An efficient reliability method combining adaptive support vector machine and Monte Carlo simulation. Structural Safety 67. doi:10.1016/j.strusafe.2017.04.006CrossRefGoogle Scholar
Papadopoulos, V, Giovanis, DG, Lagaros, ND and Papadrakakis, M (2012) Accelerated subset simulation with neural networks for reliability analysis. Computer Methods in Applied Mechanics and Engineering 223-224, 70–80. doi:10.1016/j.cma.2012.02.013CrossRefGoogle Scholar
Pedroni, N and Zio, E (2017) An adaptive metamodel-based subset importance sampling approach for the assessment of the functional failure probability of a thermal-hydraulic passive system. Applied Mathematical Modelling 48, 269–288. doi:10.1016/j.apm.2017.04.003CrossRefGoogle Scholar
Peijuan, Z, Ming, WC, Zhouhong, Z and Liqi, W (2017) A new active learning method based on the learning function U of the AK-MCS reliability analysis method. Engineering Structures 148, 185–194. doi:10.1016/j.engstruct.2017.06.038CrossRefGoogle Scholar
Sen, D and Chatterjee, A (2013) Subset simulation with Markov chain Monte Carlo: a review. Journal of Structural Engineering (India) 40, 142–149.Google Scholar
Shayanfar, MA, Barkhordari, MA, Barkhori, M and Barkhori, M (2018) An adaptive directional importance sampling method for structural reliability analysis. Structural Safety 70, 14–20. doi:10.1016/j.strusafe.2017.07.006CrossRefGoogle Scholar
Song, K, Zhang, Y, Zhuang, X, Yu, X and Song, B (2021) An adaptive failure boundary approximation method for reliability analysis and its applications. Engineering with Computers 37, 2457–2472. doi:10.1007/s00366-020-01011-0CrossRefGoogle Scholar
Teixeira, R, Nogal, M, O'Connor, A and Martinez-Pastor, B (2020) Reliability assessment with density scanned adaptive Kriging. Reliability Engineering & System Safety 199, 106908. doi:10.1016/j.ress.2020.106908CrossRefGoogle Scholar
Thedy, J and Liao, K-W (2021) Multisphere-based importance sampling for structural reliability. Structural Safety 91, 102099. doi:10.1016/j.strusafe.2021.102099CrossRefGoogle Scholar
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. Journal of Mechanical Science and Technology 29, 3183–3193. doi:10.1007/s12206-015-0717-6CrossRefGoogle Scholar
Vazirizade, SM, Nozhati, S and Zadeh, MA (2017) Seismic reliability assessment of structures using artificial neural network. Journal of Building Engineering 11, 230–235. doi:10.1016/j.jobe.2017.04.001CrossRefGoogle Scholar
Wen, Z, Pei, H, Liu, H and Yue, Z (2016) A sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability. Reliability Engineering & System Safety 153, 170–179. doi:10.1016/j.ress.2016.05.002CrossRefGoogle Scholar
Yang, IT and Hsieh, Y-H (2013) Reliability-based design optimization with cooperation between support vector machine and particle swarm optimization. Engineering with Computers 29. doi:10.1007/s00366-011-0251-9CrossRefGoogle Scholar
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. Structural and Multidisciplinary Optimization 51, 1003–1016. doi:10.1007/s00158-014-1189-5CrossRefGoogle Scholar
Zhang, J, Xiao, M and Gao, L (2019 a) An active learning reliability method combining Kriging constructed with exploration and exploitation of failure region and subset simulation. Reliability Engineering & System Safety 188, 90–102. doi:10.1016/j.ress.2019.03.002CrossRefGoogle Scholar
Zhang, X, Wang, L and Sørensen, JD (2019 b) REIF: a novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis. Reliability Engineering & System Safety 185, 440–454. doi:10.1016/j.ress.2019.01.014CrossRefGoogle Scholar
Zhang, X, Wang, L and Sørensen, JD (2020) AKOIS: an adaptive Kriging oriented importance sampling method for structural system reliability analysis. Structural Safety 82, 101876. doi:10.1016/j.strusafe.2019.101876CrossRefGoogle Scholar
Zhong, C, Wang, M, Dang, C, Ke, W and Guo, S (2020) First-order reliability method based on Harris Hawks optimization for high-dimensional reliability analysis. Structural and Multidisciplinary Optimization 62, 1951–1968. doi:10.1007/s00158-020-02587-3CrossRefGoogle Scholar
Zhou, C, Lu, Z and Yuan, X (2013) Use of relevance vector machine in structural reliability analysis. Journal of Aircraft 50, 1726–1733. doi:10.2514/1.C031950CrossRefGoogle Scholar
Zhu, Z and Du, X (2016) Reliability analysis with Monte Carlo simulation and dependent Kriging predictions. Journal of Mechanical Design 138. doi:10.1115/1.4034219CrossRefGoogle Scholar