A single-loop Kriging surrogate model method by considering the first failure instant for time-dependent reliability analysis and safety lifetime analysis

Abstract The safety lifetime analysis under the constraint of a required time-dependent failure probability is of great significance to ensure the structural safety, and the vital point in safety lifetime analysis is efficiently estimating the time-dependent failure probability in any subinterval of the time interval of interest. For addressing this issue, a new single-loop Kriging method is proposed by considering the first failure instant, and a new learning function is constructed for selecting the most contributing candidate point to accurately recognize the first failure instant. Then the Kriging model can converge to accurately recognize the first failure instant. By this convergent Kriging model, the time-dependent failure probability in any subinterval of the time interval of interest can be estimated accurately, and then the safety lifetime can be obtained by dichotomy search directly. According to the strategy of identifying the first failure instant of each input sample, the proposed method is more efficient than the existing method named the single-loop adaptive sampling Kriging surrogate model. Three examples are used to validate the accuracy and efficiency of the proposed method.

[1]  Z. Hou,et al.  A model updating method based on response surface models of reserved singular values , 2018, Mechanical Systems and Signal Processing.

[2]  Zhen Zhou Lu,et al.  Improved Line Sampling Reliability Analysis Method and its Application , 2007 .

[3]  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 .

[4]  Cem Celal Tutum,et al.  Reliability Estimation of the Pultrusion Process Using the First-Order Reliability Method (FORM) , 2013, Applied Composite Materials.

[5]  Kaichao Zhang,et al.  Reliability analysis for structures with multiple temporal and spatial parameters based on the effective first-crossing point , 2017 .

[6]  Jianbing Chen,et al.  The equivalent extreme-value event and evaluation of the structural system reliability , 2007 .

[7]  Zhenzhou Lu,et al.  Time-dependent reliability analysis model under fuzzy state and its safety lifetime model , 2019, Structural and Multidisciplinary Optimization.

[8]  Pingfeng Wang,et al.  A double-loop adaptive sampling approach for sensitivity-free dynamic reliability analysis , 2015, Reliab. Eng. Syst. Saf..

[9]  Bruno Sudret,et al.  The PHI2 method: a way to compute time-variant reliability , 2004, Reliab. Eng. Syst. Saf..

[10]  Sankaran Mahadevan,et al.  Time-Dependent System Reliability Analysis Using Random Field Discretization , 2015 .

[11]  Bruce R. Ellingwood,et al.  Orthogonal Series Expansions of Random Fields in Reliability Analysis , 1994 .

[12]  Zhen Hu,et al.  Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis , 2015 .

[13]  Sankaran Mahadevan,et al.  A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis , 2016 .

[14]  M. Stein.  Large sample properties of simulations using latin hypercube sampling , 1987 .

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

[16]  Zhen Hu,et al.  A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis , 2013 .

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

[18]  Søren Nymand Lophaven,et al.  Aspects of the Matlab toolbox DACE , 2002 .

[19]  Mohammad Reza Moarefzadeh.  Time-Dependent Reliability Analysis of Mechanical Structures using an Analytical Approach , 2017 .

[20]  Paul Bratley,et al.  Algorithm 659: Implementing Sobol's quasirandom sequence generator , 1988, TOMS.

[21]  Xiaoping Du.  Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation , 2014 .

[22]  Franck Schoefs,et al.  Principal component analysis and polynomial chaos expansion for time-variant reliability problems , 2017, Reliab. Eng. Syst. Saf..

[23]  Kok-Kwang Phoon,et al.  Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes , 2001 .

[24]  Sankaran Mahadevan,et al.  Uncertainty Quantification of Time-Dependent Reliability Analysis in the Presence of Parametric Uncertainty , 2016 .

[25]  Zhenzhou Lu,et al.  Temporal and spatial multi-parameter dynamic reliability and global reliability sensitivity analysis based on the extreme value moments , 2017 .

[26]  Hong-shuang Li,et al.  A sampling-based method for high-dimensional time-variant reliability analysis , 2019, Mechanical Systems and Signal Processing.

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

[28]  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.

[29]  Bruno Sudret,et al.  Analytical derivation of the outcrossing rate in time-variant reliability problems , 2008 .

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

[31]  Yan Shi,et al.  A reliability analysis method based on analytical expressions of the first four moments of the surrogate model of the performance function , 2018, Mechanical Systems and Signal Processing.

[32]  Zhenzhou Lu,et al.  Maximum probable life time analysis under the required time-dependent failure probability constraint and its meta-model estimation , 2017 .

[33]  Zhenzhou Lu,et al.  An innovative estimation of failure probability function based on conditional probability of parameter interval and augmented failure probability , 2019 .

[34]  Pingfeng Wang,et al.  A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design , 2013, DAC 2013.

[35]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[36]  A. Kiureghian,et al.  OPTIMAL DISCRETIZATION OF RANDOM FIELDS , 1993 .

[37]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[38]  Yan Shi,et al.  Safety life analysis under the required failure possibility constraint for structure involving fuzzy uncertainty , 2018 .

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

[40]  Jack P. C. Kleijnen,et al.  Kriging Metamodeling in Simulation: A Review , 2007, Eur. J. Oper. Res..

[41]  Zhenzhou Lu,et al.  Time-variant reliability analysis based on high dimensional model representation , 2019, Reliab. Eng. Syst. Saf..

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