Temporal and spatial multi-parameter dynamic reliability and global reliability sensitivity analysis based on the extreme value moments

Aiming at efficiently estimating the dynamic failure probability with multiple temporal and spatial parameters and analyzing the global reliability sensitivity of the dynamic problem, a method is presented on the moment estimation of the extreme value of the dynamic limit state function. Firstly, two strategies are proposed to estimate the dynamic failure probability. One strategy is combining sparse grid technique for the extreme value moments with the fourth-moment method for the dynamic failure probability. Another is combining dimensional reduction method for fractional extreme value moments and the maximum entropy for dynamic failure probability. In the proposed two strategies, the key step is how to determine the temporal and spatial parameters where the dynamic limit state function takes their minimum value. This issue is efficiently addressed by solving the differential equations satisfying the extreme value condition. Secondly, three-point estimation is used to evaluate the global dynamic reliability sensitivity by combining with the dynamic failure probability method. The significance and the effectiveness of the proposed methods for estimating the temporal and spatial multi-parameter dynamic reliability and global sensitivity indices are demonstrated with several examples.

[1]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

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

[3]  H. Rabitz,et al.  General foundations of high‐dimensional model representations , 1999 .

[4]  G. Schuëller,et al.  Chair of Engineering Mechanics Ifm-publication 2-374 a Critical Appraisal of Reliability Estimation Procedures for High Dimensions , 2022 .

[5]  Z. Kang,et al.  Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models , 2009 .

[6]  Shahram Sarkani,et al.  Random Vibrations: Analysis of Structural and Mechanical Systems , 2003 .

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

[8]  Zhenzhou Lu,et al.  A new method for evaluating Borgonovo moment-independent importance measure with its application in an aircraft structure , 2014, Reliab. Eng. Syst. Saf..

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

[10]  Yaduvir Singh,et al.  Genetic Algorithms: Concepts, Design for Optimization of Process Controllers , 2011, Comput. Inf. Sci..

[11]  Kurt Binder,et al.  Applications of Monte Carlo methods to statistical physics , 1997 .

[12]  Wenrui Hao,et al.  Efficient sampling methods for global reliability sensitivity analysis , 2012, Comput. Phys. Commun..

[13]  Mahesh D. Pandey,et al.  Computationally Efficient Reliability Analysis of Mechanisms Based on a Multiplicative Dimensional Reduction Method , 2014 .

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

[15]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[16]  P. L. Novi Inverardi,et al.  Maximum Entropy Density Estimation from Fractional Moments , 2003 .

[17]  Z. Kang,et al.  Reliability-based structural optimization with probability and convex set hybrid models , 2010 .

[18]  Claude J. P. Bélisle.  Convergence theorems for a class of simulated annealing algorithms on ℝd , 1992 .

[19]  Zissimos P. Mourelatos,et al.  Design for Lifecycle Cost Using Time-Dependent Reliability Analysis , 2008 .

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

[21]  Zissimos P. Mourelatos,et al.  Time-Dependent Reliability Analysis Using the Total Probability Theorem , 2014, DAC 2014.

[22]  Dequan Zhang,et al.  A time-variant reliability analysis method based on stochastic process discretization , 2014 .

[23]  Mei Li,et al.  The deformation behavior of isothermally compressed Ti-17 titanium alloy in α + β field , 2012 .

[24]  Emanuele Borgonovo,et al.  A new uncertainty importance measure , 2007, Reliab. Eng. Syst. Saf..

[25]  J. Beck,et al.  Important sampling in high dimensions , 2003 .

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

[27]  Herschel Rabitz,et al.  High‐dimensional model representations generated from low order terms—lp‐RS‐HDMR , 2003, J. Comput. Chem..

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

[29]  Zissimos P. Mourelatos,et al.  Time-Dependent Reliability Estimation for Dynamic Problems Using a Niching Genetic Algorithm , 2009 .

[30]  Zhenzhou Lu,et al.  Global sensitivity analysis for model with random inputs characterized by probability-box , 2015 .

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

[32]  P. Brandimarte.  Finite Difference Methods for Partial Differential Equations , 2006 .

[33]  Xiaoping Du,et al.  Time-dependent reliability analysis with joint upcrossing rates , 2013 .

[34]  S. Rice.  Mathematical analysis of random noise , 1944 .

[35]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

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

[37]  C. Jiang,et al.  A time-variant reliability analysis method for structural systems based on stochastic process discretization , 2017 .

[38]  M. Pandey,et al.  Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method , 2013 .