A reliability analysis method based on analytical expressions of the first four moments of the surrogate model of the performance function

Abstract For efficiently and accurately analyzing the reliability of structure, the analytical expressions of the first four moments of output are deduced by the Bayesian Monte Carlo method, on which the analytical failure probability can be directly obtained by employing the existing high-order moment standardization technique and the Edgeworth expansion. By use of the proposed procedure, the failure probability of structure can be estimated by an analytical expression without introducing additional errors. Also, only the training points are needed to gain the analytical expressions of the first four moments. Several examples involving numerical test and engineering application are introduced to illustrate the accuracy and the efficiency of the proposed method for reliability analysis of structure.

[1]  Zhenzhou Lu,et al.  Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression , 2018 .

[2]  Yan-Gang Zhao,et al.  Applicable Range of the Fourth-Moment Method for Structural Reliability , 2007 .

[3]  Zhenzhou Lu,et al.  Saddlepoint approximation based structural reliability analysis with non-normal random variables , 2010 .

[4]  Francesco Cadini,et al.  A Bayesian Monte Carlo-based algorithm for the estimation of small failure probabilities of systems affected by uncertainties , 2016, Reliab. Eng. Syst. Saf..

[5]  Yan-Gang Zhao,et al.  New Point Estimates for Probability Moments , 2000 .

[6]  Chong Wang,et al.  Frequency response function-based model updating using Kriging model , 2017 .

[7]  Xiaoping Du,et al.  Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations , 2005, DAC 2005.

[8]  Cheng-Wei Fei,et al.  A stochastic model updating strategy-based improved response surface model and advanced Monte Carlo simulation , 2017 .

[9]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[10]  Zhenzhou Lu,et al.  Global sensitivity analysis for fuzzy inputs based on the decomposition of fuzzy output entropy , 2017 .

[11]  Enrico Zio,et al.  An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability , 2014, Reliab. Eng. Syst. Saf..

[12]  Zhenzhou Lu,et al.  An efficient sampling approach for variance-based sensitivity analysis based on the law of total variance in the successive intervals without overlapping , 2018, Mechanical Systems and Signal Processing.

[13]  Claudio M. Rocco Sanseverino,et al.  Uncertainty propagation and sensitivity analysis in system reliability assessment via unscented transformation , 2014, Reliab. Eng. Syst. Saf..

[14]  Zhenzhou Lu,et al.  Sparse polynomial chaos expansion based on D-MORPH regression , 2018, Appl. Math. Comput..

[15]  Diego A. Alvarez,et al.  Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory , 2018 .

[16]  Jun He,et al.  A Sparse Grid Stochastic Collocation Method for Structural Reliability Analysis , 2014, 8th International Symposium on Reliability Engineering and Risk Management.

[17]  Yan Shi,et al.  Cross-covariance based global dynamic sensitivity analysis , 2018 .

[18]  Nicolas Gayton,et al.  AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation , 2011 .

[19]  Pan Wang,et al.  Multivariate global sensitivity analysis for dynamic models based on wavelet analysis , 2018, Reliab. Eng. Syst. Saf..

[20]  Qing Liu,et al.  A note on Gauss—Hermite quadrature , 1994 .

[21]  Sondipon Adhikari,et al.  A second-moment approach for direct probabilistic model updating in structural dynamics , 2012 .

[22]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[23]  Carl E. Rasmussen,et al.  Bayesian Monte Carlo , 2002, NIPS.

[24]  Antoine Dumas,et al.  AK-ILS: An Active learning method based on Kriging for the Inspection of Large Surfaces , 2013 .

[25]  Zhenzhou Lu,et al.  Structural reliability sensitivity analysis based on classification of model output , 2017 .

[26]  Shay Assaf,et al.  Approximate analysis of non-linear stochastic systems , 1976 .

[27]  Yan-Gang Zhao,et al.  A general procedure for first/second-order reliabilitymethod (FORM/SORM) , 1999 .

[28]  J. Beck,et al.  A new adaptive importance sampling scheme for reliability calculations , 1999 .