An active learning Kriging-based multipoint sampling strategy for structural reliability analysis
Zongrui Tian
Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou, China
Anyang Key Laboratory of Advanced Aeronautical Materials and Processing Technology, Anyang Institute of Technology, Anyang, China
Search for more papers by this authorCorresponding Author
Pengpeng Zhi
Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou, China
Anyang Key Laboratory of Advanced Aeronautical Materials and Processing Technology, Anyang Institute of Technology, Anyang, China
Sichuan Province Engineering Technology Research Center of General Aircraft Maintenance, Civil Aviation Flight University of China, Guanghan, China
Correspondence
Pengpeng Zhi, Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Building B1, Science and Technology Innovation Complex, No. 819, Xisaishan Road, Huzhou, Zhejiang 313000, China.
Email: [email protected]
Search for more papers by this authorYi Guan
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, China
Search for more papers by this authorXinghua He
Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou, China
Search for more papers by this authorZongrui Tian
Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou, China
Anyang Key Laboratory of Advanced Aeronautical Materials and Processing Technology, Anyang Institute of Technology, Anyang, China
Search for more papers by this authorCorresponding Author
Pengpeng Zhi
Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou, China
Anyang Key Laboratory of Advanced Aeronautical Materials and Processing Technology, Anyang Institute of Technology, Anyang, China
Sichuan Province Engineering Technology Research Center of General Aircraft Maintenance, Civil Aviation Flight University of China, Guanghan, China
Correspondence
Pengpeng Zhi, Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Building B1, Science and Technology Innovation Complex, No. 819, Xisaishan Road, Huzhou, Zhejiang 313000, China.
Email: [email protected]
Search for more papers by this authorYi Guan
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, China
Search for more papers by this authorXinghua He
Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou, China
Search for more papers by this authorAbstract
In order to effectively and accurately assess the failure probability of mechanical structures, this paper proposes a multi-point sampling active learning reliability analysis method called AKMP. First, a GA-Halton sequence is introduced to make the initial samples well dispersed and homogeneous in the design space. Second, a new learning function FELF is constructed to efficiently update the Kriging model, which takes into account the relationship between the location of the sampling points and the performance fun. Then, a combination of NCC criterion and multipoint sampling strategy is proposed to further improve the convergence efficiency, which can effectively terminate the active learning process. Finally, numerical and engineering cases are tested to verify the application performance of the proposed AKMP. The results show that the method has superior performance in terms of both accuracy and failure probability efficiency, and can reduce the computational resources of the active learning process.
Open Research
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to their containing information that could compromise the privacy of the patient.
REFERENCES
- 1Chen WM, Gong CQ, Wang ZQ, et al. Application of first-order reliability method with orthogonal plane sampling for high-dimensional series system reliability analysis. Eng Struct. 2023; 282:115778. doi:10.1016/j.engstruct.2023.115778
- 2Huang XZ, Li YX, Zhang YM, et al. A new direct second-order reliability analysis method. Appl Math Model. 2018; 55: 68-80. doi:10.1016/j.apm.2017.10.026
- 3Mansour R, Olsson M. A closed-form second-order reliability method using noncentral chi-squared distributions. J Mech Design. 2014; 136(10):101402. doi:10.1115/1.4027982
- 4Peherstorfer B, Willcox K, Gunzburger M. Optimal model management for multifidelity Monte Carlo estimation. SIAM J Sci Comput. 2016; 38(5): A3163-A3194. doi:10.1137/15M1046472
- 5Di Maio F, Pettorossi C, Zio E. Entropy-driven Monte Carlo simulation method for approximating the survival signature of complex infrastructures. Reliab Eng Syst Saf. 2023; 231:108982. doi:10.1016/j.ress.2022.108982
- 6Wang ZQ, Broccardo M, Song JH. Hamiltonian Monte Carlo methods for subset simulation in reliability analysis. Struct Saf. 2019; 76: 51-67. doi:10.1016/j.strusafe.2018.05.005
- 7Wang ZY, Shafieezadeh A. Bayesian updating with adaptive, uncertainty-informed subset simulations: high-fidelity updating with multiple observations. Reliab Eng Syst Saf. 2023; 230:108901. doi:10.1016/j.ress.2022.108901
- 8Dai HZ, Zhang H, Rasmussen KJR, et al. Wavelet density-based adaptive importance sampling method. Struct Saf. 2015; 52: 161-169. doi:10.1016/j.strusafe.2014.02.003
- 9Yun WY, Lu ZZ, Wang L, et al. Error-based stopping criterion for the combined adaptive Kriging and importance sampling method for reliability analysis. Probabilist Eng Mech. 2021; 65:103131. doi:10.1016/j.probengmech.2021.103131
- 10Shayanfar MA, Barkhordari MA, Barkhori M, et al. An adaptive directional importance sampling method for structural reliability analysis. Struct Saf. 2018; 70: 14-20. doi:10.1016/j.strusafe.2017.07.006
- 11Cheng K, Papaioannou I, Lu ZZ, et al. Rare event estimation with sequential directional importance sampling. Struct Saf. 2023; 100:102291. doi:10.1016/j.strusafe.2022.102291
- 12Cheng K, Lu ZZ. Structural reliability analysis based on ensemble learning of surrogate models. Struct Saf. 2020; 83:101905. doi:10.1016/j.strusafe.2019.101905
- 13Moustapha M, Bourinet JM, Guillaume B, et al. Comparative study of Kriging and support vector regression for structural engineering applications. ASCE-ASME J Risk U A. 2018; 4(2):04018005. doi:10.1061/AJRUA6.0000950
- 14Meng DB, Yang SY, de JAMP, et al. A novel Kriging-model-assisted reliability-based multidisciplinary design optimization strategy and its application in the offshore wind turbine tower. Renew Energ. 2023; 203: 407-420. doi:10.1016/j.renene.2022.12.062
- 15Xiao NC, Yuan K, Zhan HY. System reliability analysis based on dependent Kriging predictions and parallel learning strategy. Reliab Eng Syst Saf. 2022; 218:108083. doi:10.1016/j.ress.2021.108083
- 16Chojaczyk AA, Teixeira AP, Neves LC, et al. Review and application of Artificial Neural Networks models in reliability analysis of steel structures. Struct Saf. 2015; 52: 78-89. doi:10.1016/j.strusafe.2014.09.002
- 17Lu CJ, Li SH, Lu ZJ. Building energy prediction using artificial neural networks: a literature survey. Energ Buildings. 2022; 262:111718. doi:10.1016/j.enbuild.2021.111718
- 18Bucher C. Metamodels of optimal quality for stochastic structural optimization. Probabilist Eng Mech. 2018; 54: 131-137. doi:10.1016/j.probengmech.2017.09.003
- 19Li ZW, Zhou YL, Liu XZ, et al. Service reliability assessment of ballastless track in high speed railway via improved response surface method. Reliab Eng Syst Saf. 2023; 234:109180. doi:10.1016/j.ress.2023.109180
- 20Roy A, Chakraborty S. Support vector regression based metamodel by sequential adaptive sampling for reliability analysis of structures. Reliab Eng Syst Saf. 2020; 200:106948. doi:10.1016/j.ress.2020.106948
- 21Roy A, Chakraborty S. Support vector machine in structural reliability analysis: a review. Reliab Eng Syst Saf. 2023; 233:109126. doi:10.1016/j.ress.2023.109126
- 22Bichon BJ, Eldred MS, Swiler LP, et al. Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J. 2008; 46(10): 2459-2468. doi:10.2514/1.34321
10.2514/1.34321 Google Scholar
- 23Echard B, Gayton N, Lemaire M. AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Struct Saf. 2011; 33(2): 145-154. doi:10.1016/j.strusafe.2011.01.002
- 24Lv ZY, Lu ZZ, Wang P. A new learning function for Kriging and its applications to solve reliability problems in engineering. Comput Math Appl. 2015; 70(5): 1182-1197. doi:10.1016/j.camwa.2015.07.004
- 25Zhang XF, Wang L, Sørensen JD. REIF: a novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis. Reliab Eng Syst Saf. 2019; 185: 440-454. doi:10.1016/j.ress.2019.01.014
- 26Sun ZL, Wang J, Li R, et al. LIF: a new Kriging based learning function and its application to structural reliability analysis. Reliab Eng Syst Saf. 2017; 157: 152-165. doi:10.1016/j.ress.2016.09.003
- 27Shi Y, Lu ZZ, He RY, et al. A novel learning function based on Kriging for reliability analysis. Reliab Eng Syst Saf. 2020; 198:106857. doi:10.1016/j.ress.2020.106857
- 28Meng Z, Zhang ZH, Li G, et al. An active weight learning method for efficient reliability assessment with small failure probability. Struct Multidiscip Optimiz. 2020; 61: 1157-1170. doi:10.1007/s00158-019-02419-z
- 29Yi JX, Zhou Q, Cheng YS, et al. Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion. Struct Multidiscip Optim. 2020; 62(5): 2517-2536. doi:10.1007/s00158-020-02622-3
- 30Chai XD, Sun ZL, Wang J, et al. A new Kriging-based learning function for reliability analysis and its application to fatigue crack reliability. IEEE Access. 2019; 7: 122811-122819. doi:10.1109/ACCESS.2019.2936530
- 31Wang JS, Xu GJ, Li YL, et al. AKSE: a novel adaptive Kriging method combining sampling region scheme and error-based stopping criterion for structural reliability analysis. Reliab Eng Syst Saf. 2022; 219:108214. doi:10.1016/j.ress.2021.108214
- 32Wang ZY, Shafieezadeh A. ESC: an efficient error-based stopping criterion for Kriging-based reliability analysis methods. Struct Multidiscip Optim. 2019; 59: 1621-1637. doi:10.1007/s00158-018-2150-9
- 33Echard B, Gayton N, Lemaire M, et al. A combined importance sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models. Reliab Eng Syst Saf. 2013; 111: 232-240. doi:10.1016/j.ress.2012.10.008
- 34Xu CL, Chen WD, Ma JX, et al. AK-MSS: an adaptation of the AK-MCS method for small failure probabilities. Struct Saf. 2020; 86:101971. doi:10.1016/j.strusafe.2020.101971
- 35Su MJ, Xue GF, Wang DY, et al. A novel active learning reliability method combining adaptive Kriging and spherical decomposition-MCS (AK-SDMCS) for small failure probabilities. Struct Multidiscip Optim. 2020; 62: 3165-3187. doi:10.1007/s00158-020-02661-w
- 36Lv ZY, Lu ZZ, Wang P. A new learning function for Kriging and its applications to solve reliability problems in engineering. Comput Math Appl. 2015; 70(5): 1182-1197. doi:10.1016/j.camwa.2015.07.004
- 37Tong C, Sun ZL, Zhao QL, et al. A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling. J Mech Sci Technol. 2015; 29: 3183-3193. doi:10.1007/s12206-015-0717-6
- 38Lelièvre N, Beaurepaire P, Mattrand C, et al. AK-MCSi: a Kriging-based method to deal with small failure probabilities and time-consuming models. Struct Saf. 2018; 73: 1-11. doi:10.1016/j.strusafe.2018.01.002
- 39Zhang XB, Lu ZZ, Cheng K. AK-DS: an adaptive Kriging-based directional sampling method for reliability analysis. Mech Syst Signal Pr. 2021; 156:107610. doi:10.1016/j.ymssp.2021.107610
- 40Yun WY, Lu ZZ, Jiang X, et al. AK-ARBIS: an improved AK-MCS based on the adaptive radial-based importance sampling for small failure probability. Struct Saf. 2020; 82:101891. doi:10.1016/j.strusafe.2019.101891
- 41Morris MD, Mitchell TJ. Exploratory designs for computational experiments. J Stat Plan Infer. 1995; 43(3): 381-402. doi:10.1016/0378-3758(94)00035-T
- 42Katoch S, Chauhan SS, Kumar V. A review on genetic algorithm: past, present, and future. Multimed Tools Appl. 2021; 80: 8091-8126. doi:10.1007/s11042-020-10139-6
- 43Jones DR, Schonlau M, Welch WJ. Efficient global optimization of expensive black-box functions. J Global Optim. 1998; 13(4): 455. doi:10.1023/A:1008306431147
- 44You XX, Zhang MY, Tang DY, et al. An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis. P I Mech Eng O-J Ris. 2022; 236(1): 160-172. doi:10.1177/1748006x211016148
10.1177/1748006x211016148 Google Scholar