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S. Au, J. Beck (2001)
First excursion probabilities for linear systems by very efficient importance samplingProbabilistic Engineering Mechanics, 16
M. Barbato, J. Conte (2011)
Structural Reliability Applications of Nonstationary Spectral CharacteristicsJournal of Engineering Mechanics-asce, 137
J. Ding, Xinzhong Chen (2014)
Assessment of methods for extreme value analysis of non-Gaussian wind effects with short-term time history samplesEngineering Structures, 80
(2012)
New analytical solution of the first passage reliability problem for linear oscillator
S. Winterstein, C. MacKenzie (2013)
Extremes of Nonlinear Vibration: Comparing Models Based on Moments, L-Moments, and Maximum EntropyJournal of Offshore Mechanics and Arctic Engineering-transactions of The Asme, 135
A. Naess (1987)
The response statistics of non-linear, second-order transformations to Gaussian loadsJournal of Sound and Vibration, 115
E. Vanmarcke (1975)
On the Distribution of the First-Passage Time for Normal Stationary Random ProcessesJournal of Applied Mechanics, 42
(2010)
Prediction of extreme response statistic of narrow-band vibrations
S. Winterstein (1988)
Nonlinear Vibration Models for Extremes and FatigueJournal of Engineering Mechanics-asce, 114
B. Puig, J. Akian (2004)
Non-Gaussian simulation using Hermite polynomials expansion and maximum entropy principleProbabilistic Engineering Mechanics, 19
J. Coleman (1959)
Reliability of Aircraft Structures in Resisting Chance FailureOperations Research, 7
A. Naess, O. Gaidai, O. Batsevych (2010)
Prediction of Extreme Response Statistics of Narrow-Band Random VibrationsJournal of Engineering Mechanics-asce, 136
(1945)
Mathematical analysis of random noise. part III: statistical properties of random noise currents
S. Winterstein, Tina Kashef (1999)
Moment-based load and response models with wind engineering applicationsJournal of Solar Energy Engineering-transactions of The Asme, 122
(1975)
On the distribution of the first passage time for normal stationary process
O. Ditlevsen (1986)
Duration of visit to critical set by Gaussian processProbabilistic Engineering Mechanics, 1
Aglaia Dimofte, B. Ioniță (2010)
What Is Random Vibration?
H. Cramér (1966)
On the intersections between the trajectories of a normal stationary stochastic process and a high levelArkiv för Matematik, 6
Y. Low (2013)
A new distribution for fitting four moments and its applications to reliability analysisStructural Safety, 42
A. Naess, O. Gaidai (2009)
Estimation of extreme values from sampled time seriesStructural Safety, 31
Jun He, Yan-Gang Zhao (2007)
First passage times of stationary non-Gaussian structural responsesComputers & Structures, 85
M. Ochi (1986)
Non-Gaussian random processes in ocean engineeringProbabilistic Engineering Mechanics, 1
Cao Wang, Quanwang Li, B. Ellingwood (2016)
Time-dependent reliability of ageing structures: an approximate approachStructure and Infrastructure Engineering, 12
Yan-Gang Zhao, Zhao-Hui Lu (2008)
Cubic normal distribution and its significance in structural reliabilityStructural Engineering and Mechanics, 28
S. Crandall (1970)
First-crossing probabilities of the linear oscillatorJournal of Sound and Vibration, 12
Y. Lin (1970)
First-excursion failure of randomly excited structuresAIAA Journal, 8
V. Bayer, C. Bucher (1999)
Importance sampling for first passage problems of nonlinear structuresProbabilistic Engineering Mechanics, 14
Allen Fleishman (1978)
A method for simulating non-normal distributionsPsychometrika, 43
S. Au, J. Beck (2001)
Estimation of Small Failure Probabilities in High Dimensions by Subset SimulationProbabilistic Engineering Mechanics, 16
Xuan-Yi Zhang, Yan-Gang Zhao, Zhao-Hui Lu (2018)
The inverse transformation of the explicit fourth-moment standardization for structural reliabilityAdvances in Structural Engineering, 21
S. Rice (1944)
Mathematical analysis of random noiseBell System Technical Journal, 23
S. Ghazizadeh, M. Barbato, E. Tubaldi (2012)
New Analytical Solution of the First-Passage Reliability Problem for Linear OscillatorsJournal of Engineering Mechanics-asce, 138
M. Choi, B. Sweetman (2010)
The Hermite Moment Model for Highly Skewed Response With Application to Tension Leg PlatformsJournal of Offshore Mechanics and Arctic Engineering-transactions of The Asme, 132
A. Naess (1990)
Approximate first-passage and extremes of narrow-band Gaussian and non-Gaussian random vibrationsJournal of Sound and Vibration, 138
Jun He (2015)
Approximate Method for Estimating Extreme Value Responses of Nonlinear Stochastic Dynamic SystemsJournal of Engineering Mechanics-asce, 141
M. Grigoriu (1984)
Crossings of non-gaussian translation processesJournal of Engineering Mechanics-asce, 110
Jun He (2009)
Numerical calculation for first excursion probabilities of linear systemsProbabilistic Engineering Mechanics, 24
R. Langley (1988)
A first passage approximation for normal stationary random processesJournal of Sound and Vibration, 122
J. Jensen (1994)
Dynamic amplification of offshore steel platform responses due to non-Gaussian wave loadsMarine Structures, 7
J. Ding, Chen Xinzhong (2016)
Moment-Based Translation Model for Hardening Non-Gaussian Response ProcessesJournal of Engineering Mechanics-asce, 142
D. Kwon, A. Kareem (2011)
Peak Factors for Non-Gaussian Load Effects RevisitedJournal of Structural Engineering-asce, 137
M. Hohenbichler, R. Rackwitz (1981)
Non-Normal Dependent Vectors in Structural SafetyJournal of Engineering Mechanics-asce, 107
Cao Wang, Hao Zhang (2018)
Roles of load temporal correlation and deterioration-load dependency in structural time-dependent reliabilityComputers & Structures, 194
Yan-Gang Zhao, Zhao-Hui Lu (2007)
Fourth-Moment Standardization for Structural Reliability AssessmentJournal of Structural Engineering-asce, 133
Jun He (2010)
An efficient numerical method for estimating reliabilities of linear structures under fully nonstationary earthquakeStructural Safety, 32
In this article, an analytical moment-based procedure is developed for estimating the first passage probability of stationary non-Gaussian structural responses for practical applications. In the procedure, an improved explicit third-order polynomial transformation (fourth-moment Gaussian transformation) is proposed, and the coefficients of the third-order polynomial transformation are first determined by the first four moments (i.e. mean, standard deviation, skewness, and kurtosis) of the structural response. The inverse transformation (the equivalent Gaussian fractile) of the third-order polynomial transformation is then used to map the marginal distributions of a non-Gaussian response into the standard Gaussian distributions. Finally, the first passage probabilities can be calculated with the consideration of the effects of clumping crossings and initial conditions. The accuracy and efficiency of the proposed transformation are demonstrated through several numerical examples for both the “softening” responses (with wider tails than Gaussian distribution; for example, kurtosis > 3) and “hardening” responses (with narrower tails; for example, kurtosis < 3). It is found that the proposed method has better accuracy for estimating the first passage probabilities than the existing methods, which provides an efficient and rational tool for the first passage probability assessment of stationary non-Gaussian process.
Advances in Structural Engineering – SAGE
Published: Jan 1, 2019
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