Estimation of Moment-Independent Importance Measure on Failure Probability and Its Application in Reliability Analysis
Publication: Journal of Structural Engineering
Volume 141, Issue 8
Abstract
Similar to the definition of the moment-independent importance measure on model failure probability, the authors define the moment-independent importance measure concerning the importance sampling method. After combining the importance sampling procedure, the sampling efficiency is improved and the cost of computation is cheaper. After the moment-independent importance measures of all inputs are obtained, a new method called conditional importance sampling is proposed to calculate the failure probability and those inputs with high importance measures are chosen to be conditional variables. And state-dependent parameter method is employed in the new method. A numerical example and two structural engineering examples are used to demonstrate that the failure probability estimated by the proposed conditional importance sampling method is accurate and converges faster than those estimated by the traditional importance sampling method.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China (NSFC 51175425) and the Aviation Science Foundation of China (2011ZA53015).
References
Arne, B. H., Morten, N., and Ingeborg, D. V. (2004). “System reliability evaluation using conditional Monte Carlo methods.”, 0806–3842.
Au, S. K., and Beck, J. L. (2003). “Importance sampling in high dimensions.” Struct. Saf., 25(2), 139–163.
Borgonovo, E. (2007). “A new uncertainty importance measure.” Reliab. Eng. Syst. Saf., 92(6), 771–784.
Cui, L. J., Lu, Z. Z., and Zhao, X. P. (2010). “Moment-independent importance measure of basic random variable and its probability density evolution solution.” Sci. China Technol. Sci., 53(4), 1138–1145.
Harbitz, A. (1986). “An efficient sampling method for probability of failure calculation.” Struct. Saf., 3(2), 109–115.
Hasfer, A. M., and Lind, N. C. (1974). “Exact and invariant second moment code format.” J. Eng. Mech. Div., 100(1), 111–121.
Helton, J. C., and Davis, F. J. (2003). “Latin hypercube sampling and the propagation of uncertainty in analysis of complex systems.” Reliab. Eng. Syst. Saf., 81(1), 23–69.
Kalman, R. (1960). “A new approach to linear filtering and prediction problems.” ASME Trans. J. Basic Eng., 82(1), 35–45.
Lance, G. H., and Williams, W. T. (1966). “A generalized sorting strategy for computer classifications.” Nature, 212, 218.
Li, L. Y., Lu, Z. Z., Feng, J., and Wang, B. T. (2012). “Moment-independent importance measure of basic variable and its state dependent parameter solution.” Struct. Saf., 38, 40–47.
McKay, M. D., Beckman, R. J., and Conover, W. J. (2000). “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code.” Technometrics, 42(1), 55–61.
McRae, G. J., Tilden, J. W., and Seinfeld, J. H. (1982). “Global sensitivity analysis: A computational implementation of the Fourier amplitude sensitivity test (FAST).” Comput. Chem. Eng., 6(1), 15–25.
Ratto, M., Pagano, A., and Young, P. C. (2007). “State dependent parameter meta-modeling and sensitivity analysis.” Comput. Phys. Commun., 177(11), 863–876.
Ratto, M., Pagano, A., and Young, P. C. (2009). “Non-parametric estimation of conditional moments for sensitivity analysis.” Reliab. Eng. Syst. Saf., 94(2), 237–243.
Ratto, M., Tarantola, S., Saltelli, A., and Young, P. C. (2004). “Accelerated estimation of sensitivity indices using state dependent parameter models.” Proc., 4th Int. Conf. on sensitivity analysis of model output (SAMO 2004), K. M. Hanson and F. M. Hemez, eds., Santa Fe, New Mexico, 61–70.
Ruan, W. B., Lu, Z. Z., and Tian, L. F. (2013). “A modified variance-based importance measure and its solution by state dependent parameter.” Proc. Inst. Mech. Eng. Part O: J. Risk Reliab., 227(1), 3–15.
Saltelli, A. (2002). “Sensitivity analysis for importance assessment.” Risk Anal., 22(3), 579–590.
Young, P. C. (1993). “Time variable and state dependent modeling of non-stationary and nonlinear time series.” Developments in time series analysis, Chapman and Hall, London, 374–413.
Young, P. C. (2000). “Stochastic dynamic modeling and signal processing: Time variable and state dependent parameter estimation.” Nonlinear and non-stationary signal processing, Cambridge University Press, Cambridge, U.K., 74–114.
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© 2014 American Society of Civil Engineers.
History
Received: May 3, 2013
Accepted: Aug 16, 2014
Published online: Sep 15, 2014
Discussion open until: Feb 15, 2015
Published in print: Aug 1, 2015
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