First-passage reliability of high-dimensional nonlinear systems under additive excitation by the ensemble-evolving-based generalized density evolution equation
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[1] M. Wehner. Numerical Evaluation of Path Integral Solutions to Fokker-Planck Equations with Application to Void Formation. , 1983 .
[2] Yu-Kweng Michael Lin. Probabilistic Theory of Structural Dynamics , 1976 .
[3] Jianbing Chen,et al. The equivalent extreme-value event and evaluation of the structural system reliability , 2007 .
[4] Jianbing Chen,et al. Advances of the probability density evolution method for nonlinear stochastic systems , 2012 .
[5] Peihui Lin,et al. Dimension-reduction of FPK equation via equivalent drift coefficient , 2014 .
[6] Zhen Hu,et al. A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis , 2013 .
[7] Masanobu Shinozuka,et al. On the First-Excursion Probability in Stationary Narrow-Band Random Vibration, II , 1971 .
[8] C. W. Gardiner,et al. Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.
[9] Jianbing Chen,et al. The principle of preservation of probability and the generalized density evolution equation , 2008 .
[10] Jianbing Chen,et al. Error estimate of point selection in uncertainty quantification of nonlinear structures involving multiple nonuniformly distributed parameters , 2019, International Journal for Numerical Methods in Engineering.
[11] Antonina Pirrotta,et al. A novel method based on augmented Markov vector process for the time-variant extreme value distribution of stochastic dynamical systems enforced by Poisson white noise , 2020, Commun. Nonlinear Sci. Numer. Simul..
[12] Helmut J. Pradlwarter,et al. Evolution of probability densities in the phase space for reliability analysis of non-linear structures , 2009 .
[13] Bernt J. Leira,et al. Stochastic nonlinear ship rolling in random beam seas by the path integration method , 2016 .
[14] P. Spanos,et al. An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems , 2015 .
[15] R. Roy. Asymptotic analysis of first-passage problems , 1997 .
[16] Response statistics of van der Pol oscillators excited by white noise , 1994 .
[17] Jun Xu,et al. A novel fractional moments-based maximum entropy method for high-dimensional reliability analysis , 2019, Applied Mathematical Modelling.
[18] R. Santoro,et al. Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution , 2008 .
[19] Zhao-Hui Lu,et al. Time-variant reliability analysis considering parameter uncertainties , 2014 .
[20] Erik H. Vanmarcke,et al. Random Fields: Analysis and Synthesis. , 1985 .
[21] Dixiong Yang,et al. Reliability analysis of structures with complex limit state functions using probability density evolution method , 2014 .
[22] W. Cleveland. Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .
[23] Xiaole Yue,et al. First-passage time statistics in a bistable system subject to Poisson white noise by the generalized cell mapping method , 2015, Commun. Nonlinear Sci. Numer. Simul..
[24] Oleg Gaidai,et al. Monte Carlo Methods for Estimating the Extreme Response of Dynamical Systems , 2008 .
[25] Armen Der Kiureghian,et al. TAIL EQUIVALENT LINEARIZATION METHOD FOR NONLINEAR RANDOM VIBRATION , 2007 .
[26] S. Redner. A guide to first-passage processes , 2001 .
[27] Jianbing Chen,et al. Stochastic Dynamics of Structures , 2009 .
[28] Zhongming Jiang,et al. A data-based CR-FPK method for nonlinear structural dynamic systems , 2018, Theoretical and Applied Mechanics Letters.
[29] Antonina Pirrotta,et al. Poisson white noise parametric input and response by using complex fractional moments , 2014 .
[30] A. Siegert. On the First Passage Time Probability Problem , 1951 .
[31] A. Harbitz. An Accurate Probability-of-Failure Calculation Method , 1983, IEEE Transactions on Reliability.
[32] Jianbing Chen,et al. Stochastic seismic response analysis of structures exhibiting high nonlinearity , 2010 .
[33] Jianbing Chen,et al. Dynamic response and reliability analysis of structures with uncertain parameters , 2005 .
[34] Jianbing Chen,et al. Dimension-reduced FPK equation for additive white-noise excited nonlinear structures , 2018, Probabilistic Engineering Mechanics.
[35] Jun Xu,et al. An adaptive trivariate dimension-reduction method for statistical moments assessment and reliability analysis , 2020, Applied Mathematical Modelling.
[36] Shurong Yuan,et al. Dimension Reduction of the FPK Equation via an Equivalence of Probability Flux for Additively Excited Systems , 2014 .
[37] G. Er. Methodology for the solutions of some reduced Fokker‐Planck equations in high dimensions , 2011 .
[38] Meng-Ze Lyu,et al. Closed-Form Solutions for the Probability Distribution of Time-Variant Maximal Value Processes for Some Classes of Markov Processes , 2021, Commun. Nonlinear Sci. Numer. Simul..
[39] P. Spanos,et al. Random vibration and statistical linearization , 1990 .
[40] H. Risken. The Fokker-Planck equation : methods of solution and applications , 1985 .
[41] Jian-Bing Chen,et al. A new approach for time-variant probability density function of the maximal value of stochastic dynamical systems , 2020, J. Comput. Phys..
[42] P. Spanos,et al. An analytical Wiener path integral technique for non-stationary response determination of nonlinear oscillators , 2012 .
[43] S. Rice. Mathematical analysis of random noise , 1944 .
[44] Y. Wen. Method for Random Vibration of Hysteretic Systems , 1976 .
[45] Pol D. Spanos,et al. Nonstationary Stochastic Response Determination of Nonlinear Systems: A Wiener Path Integral Formalism , 2014 .
[46] Weiqiu Zhu,et al. Nonlinear Stochastic Dynamics and Control in Hamiltonian Formulation , 2006 .
[47] Jianbing Chen,et al. A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters , 2016 .
[48] J. J. Coleman. Reliability of Aircraft Structures in Resisting Chance Failure , 1959 .
[49] W. Zhu,et al. Stochastic averaging of quasi-linear systems driven by Poisson white noise , 2010 .
[50] J. Beck,et al. Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .
[51] Honeycutt,et al. Stochastic Runge-Kutta algorithms. I. White noise. , 1992, Physical review. A, Atomic, molecular, and optical physics.
[52] Xiaole Yue,et al. The Estimates of the Mean First Exit Time of a Bistable System Excited by Poisson White Noise , 2017 .
[53] H. Zhang,et al. Parameter Analysis of the Differential Model of Hysteresis , 2004 .