Abstract
Simulation based structural reliability analysis suffers from a heavy computational burden, as each sample needs to be evaluated on the performance function, where structural analysis is performed. To alleviate the computational burden, related research focuses mainly on reduction of samples and application of surrogate model, which substitutes the performance function. However, the reduction of samples is achieved commonly at the expense of loss of robustness, and the construction of surrogate model is computationally expensive. In view of this, this paper presents a robust and efficient method in the same direction. The present method uses radial-based importance sampling (RBIS) to reduce samples without loss of robustness. Importantly, Kriging is fully used to efficiently implement RBIS. It not only serves as a surrogate to classify samples as we all know, but also guides the procedure to determine the optimal radius, with which RBIS would reduce samples to the highest degree. When used as a surrogate, Kriging is established through active learning, where the previously evaluated points to determine the optimal radius are reused. The robustness and efficiency of the present method are validated by five representative examples, where the present method is compared mainly with two fundamental reliability methods based on active learning Kriging.
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References
Wu Z, Deng J, Su C, et al. Performance of the micro-texture selflubricating and pulsating heat pipe self-cooling tools in dry cutting process. Int J Refract Met H, 2014, 45: 238–248
Schueller G I. Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis—Recent advances. Struct Eng Mech, 2009, 32: 1–20
Melchers R E. Importance sampling in structural systems. Struct Saf, 1989, 6: 3–10
Harbitz A. An efficient sampling method for probability of failure calculation. Struct Saf, 1986, 3: 109–115
Grooteman F. Adaptive radial-based importance sampling method for structural reliability. Struct Saf, 2008, 30: 533–542
Zhou G, Duan L B, Zhao W Z, et al. An enhanced hybrid and adaptive meta-model based global optimization algorithm for engineering optimization problems. Sci China Tech Sci, 2016, 59: 1147–1155
Bucher C G, Bourgund U. A fast and efficient response surface approach for structural reliability problems. Struct Saf, 1990, 7: 57–66
Han X, Jiang C, Liu L X, et al. Response-surface-based structural reliability analysis with random and interval mixed uncertainties. Sci China Tech Sci, 2014, 57: 1322–1334
Papadrakakis M, Papadopoulos V, Lagaros N D. Structural reliability analyis of elastic-plastic structures using neural networks and Monte Carlo simulation. Comp Methods Appl Mech Eng, 1996, 136: 145–163
Hurtado J E, Alvarez D A. Classification approach for reliability analysis with stochastic finite-element modeling. J Struct Eng, 2003, 129: 1141–1149
Dai H, Zhang B, Wang W. A multiwavelet support vector regression method for efficient reliability assessment. Reliab Eng Syst Safe, 2015, 136: 132–139
Kaymaz I. Application of Kriging method to structural reliability problems. Struct Saf, 2005, 27: 133–151
Dubourg V, Sudret B, Deheeger F. Metamodel-based importance sampling for structural reliability analysis. Probabilist Eng Mech, 2013, 33: 47–57
Jones D R, Schonlau M, Welch W J. Efficient global optimization of expensive black-box functions. J Glob Optim, 1998, 13: 455–492
Echard B, Gayton N, Lemaire M. AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation. Struct Saf, 2011, 33: 145–154
Echard 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 Safe, 2013, 111: 232–240
Hasofer A M, Lind N C. An exact and invariant first-order reliability format. ASCE J Eng Mech, 1974, 100: 111–121
Cadini F, Santos F, Zio E. An improved adaptive Kriging-based importance technique for sampling multiple failure regions of low probability. Reliab Eng Syst Safet, 2014, 131: 109–117
Zhao H, Yue Z, Liu Y, et al. An efficient reliability method combining adaptive importance sampling and Kriging metamodel. Appl Math Model, 2015, 39: 1853–1866
Tong C, Sun Z, Zhao Q, et al. A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling. J Mech Sci Technol, 2015, 29: 3183–3193
Zhang L, Lu Z, Wang P. Efficient structural reliability analysis method based on advanced Kriging model. Appl Math Model, 2015, 39: 781–793
Fauriat W, Gayton N. AK-SYS: An adaptation of the AK-MCS method for system reliability. Reliab Eng Syst Safe, 2014, 123: 137–144
Sacks J, Welch W J, Mitchell T J, et al. Design and analysis of computer experiments. Statist Sci, 1989, 4: 409–423
Nie J, Ellingwood B R. Directional methods for structural reliability analysis. Struct Saf, 2000, 22: 233–249
Liu P L, Der Kiureghian A. Multivariate distribution models with prescribed marginals and covariances. Probabilist Eng Mech, 1986, 1: 105–112
Au S K, Beck J L. A new adaptive importance sampling scheme for reliability calculations. Struct Saf, 1999, 21: 135–158
Engelund S, Rackwitz R. A benchmark study on importance sampling techniques in structural reliability. Struct Saf, 1993, 12: 255–276
Mao H, Mahadevan S. Reliability analysis of creep-fatigue failure. Int J Fatigue, 2000, 22: 789–797
Borri A, Speranzini E. Structural reliability analysis using a standard deterministic finite element code. Struct Saf, 1997, 19: 361–382
Zhao G F. Reliability Theory and Its Applications for Engineering Structures (in Chinese). Dalian: Dalian University of Technology Press, 1996
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Xiong, B., Tan, H. A robust and efficient structural reliability method combining radial-based importance sampling and Kriging. Sci. China Technol. Sci. 61, 724–734 (2018). https://doi.org/10.1007/s11431-016-9068-1
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DOI: https://doi.org/10.1007/s11431-016-9068-1