Importance Sampling Technique for Simulating Time Histories for Efficient Rainflow Fatigue Analysis
Publication: Journal of Engineering Mechanics
Volume 142, Issue 4
Abstract
Frequency domain analysis of a dynamical system yields the response spectral density. There are many spectral fatigue methods for evaluating the mean fatigue damage from a stress spectrum, but they are only approximate. The only accurate method is to simulate the time history from the spectrum, succeeded by rainflow counting. However, this procedure is time-consuming because of the need for numerous realizations to achieve statistical convergence, making it incompatible with the high efficiency of frequency domain analysis. To overcome the slow convergence rate of conventional Monte Carlo simulation (MCS), this paper proposes an efficient simulation approach, which to date, appears to be the first of its kind for such an application. The proposed approach reduces the variance of the fatigue damage samples by invoking the technique of importance sampling, and entails only the coefficient of variation (CoV) of the damage to construct the importance sampling density. The CoV can be estimated initially using an analytical approach, and subsequently updated adaptively. The proposed approach is implemented on a diversity of spectral shapes, and is found to provide a substantial computational advantage over MCS.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abdi, H. (2010). “Coefficient of variation.” Encyclopedia of research design, N. J. Salkind, ed., Sage, Thousand Oaks, CA.
Au, S. K., and Beck, J. L. (2001). “Estimation of small failure probabilities in high dimensions by subset simulation.” Prob. Eng. Mech., 16(4), 263–277.
Benasciutti, D., and Tovo, R. (2006). “Comparison of spectral methods for fatigue analysis of broad-band Gaussian random processes.” Prob. Eng. Mech., 21(4), 287–299.
Cuong, H. T., Troesch, A. W., and Birdsall, T. G. (1982). “The generation of digital random time histories.” Ocean Eng., 9(6), 581–588.
Der Kiureghian, A. (2000). “The geometry of random vibrations and solutions by FORM and SORM.” Prob. Eng. Mech., 15(1), 81–90.
Dirlik, T. (1985). “Application of computers in fatigue analysis.” Ph.D. thesis, Univ. of Warwick, Coventry, U.K.
Elgar, S., Guza, T. T., and Seymour, R. J. (1985). “Wave group statistics from numerical simulations of a random sea.” Appl. Ocean Res., 7(2), 93–96.
Goodman, L. A. (1962). “The variance of the product of K random variables.” J. Am. Stat. Assoc., 57(297), 54–60.
Grigoriu, M. (1993). “On the spectral representation method in simulation.” Prob. Eng. Mech., 8(2), 75–90.
Hartung, J., Knapp, G., and Sinha, B. K. (2008). Statistical meta-analysis with applications, Wiley, New York.
Jensen, J. J. (2011). “Extreme value predictions using Monte Carlo simulations with artificially increased load spectrum.” Prob. Eng. Mech., 26(2), 399–404.
Larsen, C. E., and Lutes, L. D. (1991). “Predicting the fatigue life of offshore structures by the single-moment spectral method.” Prob. Eng. Mech., 6(2), 96–108.
Low, Y. M. (2012). “Variance of the fatigue damage due to a Gaussian narrowband process.” Struct. Saf., 34(1), 381–389.
Low, Y. M. (2014). “A simple surrogate model for the rainflow fatigue damage arising from processes with bimodal spectra.” Marine Struct., 38, 72–88.
Macke, M., and Bucher, C. (2003). “Importance sampling for randomly excited dynamical systems.” J. Sound Vib., 268(2), 269–290.
Miles, J. W. (1954). “On structural fatigue under random loading.” J. Aeronaut. Sci., 21(11), 753–762.
Mouri, H. (2013). “Log-normal distribution from a process that is not multiplicative but is additive.” Phys. Rev. E, 88(4), 042124.
Naess, A., and Gaidai, O. (2008). “Monte Carlo methods for estimating the extreme response of dynamical systems.” J. Eng. Mech., 628–636.
Papadimitriou, C., Beck, J. L., and Katafygiotis, L. S. (1997). “Asymptotic expansions for reliability and moments of uncertain systems.” J. Eng. Mech., 1219–1229.
Penrose, R. (1956). “On best approximate solution of linear matrix equations.” Math. Proc. Cambridge Phil. Soc., 52(1), 17–19.
Rubinstein, R. Y., and Kroese, D. P. (2008). Simulation and the Monte Carlo method, Wiley, New York.
Tucker, M. J., Challenor, P. G., and Carter, D. J. T. (1984). “Numerical simulation of a random sea: A common error and its effect upon wave group statistics.” Appl. Ocean Res., 6(2), 118–122.
Vanmarcke, E. H. (1972). “Properties of spectral moments with application to random vibrations.” J. Eng. Mech. Div., 98(2), 425–446.
Wirsching, P. H., and Chen, Y. N. (1988). “Considerations of probability-based fatigue design for marine structures.” Marine Strut., 1(1), 23–45.
Wirsching, P. H., and Light, C. L. (1980). “Fatigue under wide band random stresses.” J. Struct. Div., 106(7), 1593–1607.
Zhao, Y. G., and Ono, T. (2001). “Moment methods for structural reliability.” Struct. Saf., 23(1), 47–75.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 142 • Issue 4 • April 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Aug 24, 2015
Accepted: Nov 3, 2015
Published online: Jan 8, 2016
Published in print: Apr 1, 2016
Discussion open until: Jun 8, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.