The importance sampling method is an extensively used numerical simulation method in reliability analysis. In this paper, a modification to the importance sampling method (ISM) is proposed, and the modified ISM divides the sample set of input variables into different subsets based on the contributive weight of the importance sample defined in this paper and the maximum super-sphere denoted by β-sphere in the safe domain defined by the truncated ISM. By this proposed modification, only samples with large contributive weight and locating outside of the β-sphere need to call the limit state function. This amelioration remarkably reduces the number of limit state function evaluations required in the simulation procedure, and it doesn’t sacrifice the precision of the results by controlling the level of relative error. Based on this modified ISM and the space-partition idea in variance-based sensitivity analysis, the global reliability sensitivity indices can be estimated as byproducts, which is especially useful for reliability-based design optimization. This process of estimating the global reliability sensitivity indices only needs the sample points used in reliability analysis and is independent of the dimensionality of input variables. A roof truss structure and a composite cantilever beam structure are analyzed by the modified ISM. The results demonstrate the efficiency, accuracy, and robustness of the proposed method.
This is a preview of subscription content, log in to check access.
This work was supported by the Natural Science Foundation of China (Grant 51475370, 51775439) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant CX201708).
Bourinet JM, Deheeger F, Lemaire M (2011) Assessing small failure probabilities by combined subset simulation and support vector machines. Struct Saf 33(6):343–353CrossRefGoogle Scholar
Cui LJ, Lu ZZ, Zhao XP (2010) Moment-independent importance measure of basic random variable and its probability density evolution solution. SCIENCE CHINA Technol Sci 53(4):1138–1145CrossRefzbMATHGoogle Scholar
De Der Kiureghian A (1991) stefano M. Efficient algorithm for second-order reliability analysis. J Eng Mech ASCE 117(2):2904–2923CrossRefGoogle Scholar
Echard B, Gayton N, Lemaire M (2011) AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation. Struct Saf 33:145–154CrossRefGoogle Scholar
Grooteman F (2008) Adaptive radial-based importance sampling method for structural reliability. Struct Saf 30:533–542CrossRefGoogle Scholar
Harbitz A (1986) An efficient sampling method for probability of failure calculation. Struct Saf 3:109–115CrossRefGoogle Scholar
Hasofer AM, Lind NC (1974) An exact and invariant first order reliability format. J Eng Mech ASCE 100(1):111–121Google Scholar
Hu Z, Mahadevan S (2016) Global sensitivity analysis-enhanced surrogate (GSAS) modeling for reliability analysis. Struct Multidiscip Optim 53:501–521MathSciNetCrossRefGoogle Scholar
Kim SH, Na SW (1997) Response surface method using vector projected sampling points. Struct Saf 19(1):3–19CrossRefGoogle Scholar
Li CZ, Mahadevan S (2016) An efficient modularized sample-based method to estimate the first-order Sobol' index. Reliab Eng Syst Saf 153:110–121CrossRefGoogle Scholar
Li LY, Lu ZZ, Feng J, Wang BT (2012) Moment-independent importance measure of basic variable and its state dependent parameter solution. Struct Saf 38:40–47CrossRefGoogle Scholar
Lu ZZ, Feng YS (1995) An importance sampling function for computing failure probability for a limit state equation with multiple design point. Acta Aeronautica et Astronautica Sinica 16(4):484–487 (in Chinese)Google Scholar
Song H, Choi KK, Lee CI, Zhao L, Lamb D (2013) Adaptive virtual support vector machine for reliability analysis of high-dimensional problems. Struct Multidiscip Optim 47:479–491MathSciNetCrossRefzbMATHGoogle Scholar
Wei PF, Lu ZZ, Song JW (2014) Extended Monte Carlo simulation for parametric global sensitivity analysis and optimization. AIAA J 52(4):867–878CrossRefGoogle Scholar
Xu L, Cheng GD (2003) Discussion on: moment methods for structural reliability. Struct Saf 25:193–199CrossRefGoogle Scholar
Zhai QQ, Yang J, Zhao Y (2014) Space-partition method for the variance-based sensitivity analysis: Optimal partition scheme and comparative study. Reliab Eng Syst Saf 131:66–82CrossRefGoogle Scholar
Zhang XF, Pandey MD (2013) Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method. Struct Saf 43:28–40CrossRefGoogle Scholar
Zhang XF, Pandey MD, Zhang YM (2014) Computationally efficient reliability analysis of mechanisms based on a multiplicative dimensional reduction method. J Mech Des ASME 136(6):061006CrossRefGoogle Scholar
Zhao YG, Ono T (1999a) A general procedure for first/second-order reliability method (FORM/SORM). Struct Saf 21(2):95–112CrossRefGoogle Scholar
Zhao YG, Ono T (1999b) New approximations for SORM: part 1. J Eng Mech ASCE 125(1):79–85CrossRefGoogle Scholar