Global reliability sensitivity analysis index and its efficient numerical simulation solution in presence of both random and interval hybrid uncertainty

In the presence of both random and interval hybrid uncertainty (RI-HU), investigating global reliability sensitivity (GRS) can identify the effect of random input on the structural safety globally. To this end, this work establishes the GRS index model and its corresponding efficient solution, and the innovation includes three aspects. Firstly, the GRS of the random input is defined by the average absolute difference between the failure probability upper bound (FP-UB) and the conditional FP-UB on the fixed random input under the RI-HU, and it can reflect the effect of the fixed random input on the structural safety. Secondly, the conditional FP-UB on fixing the random input at the realization is approximated by the conditional FP-UB on fixing the random input in a differential interval. Then the conditional probability theorem can be employed to convert estimating the GRS into the state recognition of the samples, which is the by-product of estimating the FP-UB by the numerical simulation. Finally, by the strategy of surrogating the performance function twice, the meta-importance sampling method is developed to efficiently estimate the GRS in presence of the RI-HU. The rationality of the proposed GRS index model and the efficiency of the developed estimation method are fully verified by the numerical and engineering examples.

[1]  Pan Wang,et al.  Two Efficient AK-Based Global Reliability Sensitivity Methods by Elaborative Combination of Bayes’ Theorem and the Law of Total Expectation in the Successive Intervals Without Overlapping , 2020, IEEE Transactions on Reliability.

[2]  Li Luyi,et al.  Moment-independent importance measure of basic variable and its state dependent parameter solution , 2012 .

[3]  Liang Gao,et al.  A novel projection outline based active learning method and its combination with Kriging metamodel for hybrid reliability analysis with random and interval variables , 2018, Computer Methods in Applied Mechanics and Engineering.

[4]  Siu-Kui Au,et al.  Probabilistic Failure Analysis by Importance Sampling Markov Chain Simulation , 2004 .

[5]  B. Sudret,et al.  Metamodel-based importance sampling for structural reliability analysis , 2011, 1105.0562.

[6]  Yi Gao,et al.  An active learning kriging model for hybrid reliability analysis with both random and interval variables , 2015 .

[7]  Zhen-zhou Lü,et al.  Moment-independent importance measure of basic random variable and its probability density evolution solution , 2010 .

[8]  Enrico Zio,et al.  An Improvement of a Metamodel-Based Importance Sampling Algorithm for Estimating Small Failure Probabilities , 2014 .

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

[10]  J.-M. Bourinet,et al.  Rare-event probability estimation with adaptive support vector regression surrogates , 2016, Reliab. Eng. Syst. Saf..

[11]  Zhenzhou Lu,et al.  A novel extended crossing rate method for time-dependent hybrid reliability analysis under random and interval inputs , 2020 .

[12]  Yanping Wang,et al.  A new efficient simulation method based on Bayes' theorem and importance sampling Markov chain simulation to estimate the failure-probability-based global sensitivity measure , 2018 .

[13]  C. Jiang,et al.  A new reliability analysis method for uncertain structures with random and interval variables , 2012 .

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

[15]  Nicolas Gayton,et al.  AK-SYS: An adaptation of the AK-MCS method for system reliability , 2014, Reliab. Eng. Syst. Saf..

[16]  Xiaoping Du,et al.  Reliability sensitivity analysis with random and interval variables , 2009 .

[17]  Zheng Zhang,et al.  Reliability analysis of motion mechanism under three types of hybrid uncertainties , 2018 .

[18]  Gang Li,et al.  An active weight learning method for efficient reliability assessment with small failure probability , 2020 .

[19]  Weiqing Liu,et al.  Microstructural modification and strength enhancement by SiC nanoparticles in AZ31 magnesium alloy during hot rolling , 2018 .

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

[21]  Zeng Meng,et al.  A novel experimental data-driven exponential convex model for reliability assessment with uncertain-but-bounded parameters , 2020 .

[22]  C. Jiang,et al.  Response-surface-based structural reliability analysis with random and interval mixed uncertainties , 2014 .

[23]  Zhonglai Wang,et al.  Unified uncertainty analysis by the mean value first order saddlepoint approximation , 2012 .

[24]  Zeng Meng,et al.  Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization , 2019, Computer Methods in Applied Mechanics and Engineering.

[25]  Jorge E. Hurtado,et al.  An efficient method for the estimation of structural reliability intervals with random sets, dependence modeling and uncertain inputs , 2014 .

[26]  Yu Zhang,et al.  An efficient global reliability sensitivity analysis algorithm based on classification of model output and subset simulation , 2018, Structural Safety.

[27]  Zhenzhou Lu,et al.  Aircraft Icing Severity Analysis Considering Three Uncertainty Types , 2019, AIAA Journal.

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

[29]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .

[30]  Maurice Lemaire,et al.  Assessing small failure probabilities by combined subset simulation and Support Vector Machines , 2011 .

[31]  Xiaoping Du.  Interval Reliability Analysis , 2007, DAC 2007.

[32]  Zhenzhou Lu,et al.  An efficient method for moment-independent global sensitivity analysis by dimensional reduction technique and principle of maximum entropy , 2019, Reliab. Eng. Syst. Saf..

[33]  Mathieu Balesdent,et al.  Reliability Analysis in the Presence of Aleatory and Epistemic Uncertainties, Application to the Prediction of a Launch Vehicle Fallout Zone , 2016 .

[34]  N. Strömberg,et al.  Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias , 2017 .

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

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

[37]  Wen-Bin Shangguan,et al.  A new hybrid uncertainty analysis method and its application to squeal analysis with random and interval variables , 2018 .

[38]  Xiaoping Du.  Unified Uncertainty Analysis by the First Order Reliability Method , 2008 .

[39]  Jorge E. Hurtado,et al.  Interval reliability analysis under the specification of statistical information on the input variables , 2017 .