Emulator Model–Based Analytical Solution for Reliability Sensitivity Analysis
Publication: Journal of Engineering Mechanics
Volume 141, Issue 8
Abstract
Sensitivity analysis is frequently considered an essential component in engineering design. In the design process of engineered structures, the output is implicitly related with the input variables. The Kriging model, one of the most commonly used emulator models, is sometimes used for structure analysis. In order to efficiently estimate the sensitivities of failure probability or statistical moments of performance function with respect to distribution parameters of input variables, the analytical solutions are derived based on the Kriging model. Generally, the Kriging model can be expressed as a tensor product basis function, thus the multivariate integrals can be decomposed into the sum of univariate integrals, which makes it possible to solve the sensitivity of statistical moments with respect to distribution parameters of normal input variables by the properties of kernel functions. Next, the fourth-moment reliability sensitivity method is applied to compute the sensitivity of failure probability analytically. Numerical and engineering examples are introduced to demonstrate the accuracy and efficiency of the derived analytical solution of sensitivity of failure probability.
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Acknowledgments
This work was supported by the Natural Science Foundation of China (Grant 51175425) and the Research Found for the Doctoral Program of Higher Education of China (Grant 20116102110003).
References
Chen, W., Ruichen, J., and Agus, S. (2005). “Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty.” J. Mech. Des., 127(5), 875–886.
Currin, C., Mitchell, T., Morris, M. D., and Ylvisaker, D. (1991). “Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments.” J. Am. Stat. Assoc., 86(416), 953–963.
Guan, X. L., and Melchers, R. E. (2001). “Effect of response surface parameter variation on structural reliability estimates.” Struct. Saf., 23(4), 429–444.
Karamchandani, A., and Cornell, C. A. (1991). “Sensitivity estimation within first and second order reliability methods.” Struct. Saf., 11(2), 95–107.
Kaymaz, I. (2005). “Application of Kriging method to structural reliability problems.” Struct. Saf., 27(2), 133–151.
Kaymaz, I., and McMahon, C. A. (2005). “A response surface method based on weighted regression for structural reliability analysis.” Probab. Eng. Mech., 20(1), 11–17.
Lataillade, A. D, et al. (2002). “Monte carlo method and sensitivity estimations.” J. Quant. Spectrosc. Radiat., 75(5), 529–538.
Lu, Z. Z., and Song, J. (2010). “Reliability sensitivity by method of moments.” Appl. Math. Modell., 34(10), 2860–2871.
Lucifredi, A., Mazzieri, C., and Rossi, M. (2000). “Application of multi-regressive linear models, dynamic Kriging models and neural network models to predictive maintenance of hydroelectric power systems.” Mech. Syst. Signal Process., 14(3), 471–494.
Melchers, R. E. (1989). “Importance sampling in structural system.” Struct. Saf., 6(1), 3–10.
Melchers, R. E., and Ahammed, M. (2004). “A fast approximate method for parameter sensitivity estimation in Monte Carlo structural reliability.” Comput. Struct., 82(1), 55–61.
Millwater, H. (2009). “Universal properties of kernel functions for probabilistic sensitivity analysis.” Probab. Eng. Mech., 24(1), 89–99.
Roger, M., Jan, C. M., and Noortwijk, V. (1999). “Local probabilistic sensitivity measures for comparing FORM and Monte Carlo calculations illustrated with dike ring reliability calculations.” Comput. Phys. Commun., 117(1-2), 86–98.
Rosenblueth, E. (1975). “Point estimation for probability moments.” Proc. Nat. Acad. Sci., 72(10), 3812–3814.
Rosenblueth, E. (1981). “Two-point estimates in probability.” Appl. Math. Modell., 5(5), 329–335.
Sacks, J., Schiller, S. B., and Welch, W. J. (1989). “Design for computer experiment.” Technometrics, 31(1), 41–47.
Sakata, S., Ashida, F., and Zako, M. (2003). “Structural optimization using kriging approximation.” Comput. Methods Appl. Mech. Eng., 192(7-8), 923–939.
Wang, P., Lu, Z. Z., and Tang, Z. C. (2013). “An application of the Kriging method in global sensitivity analysis with parameter uncertainty.” Appl. Math. Modell., 37(9), 6543–6555.
Zhang, L. G., Lu, Z. Z., Cheng, L., and Fan, C. Q. (2014). “A new method for evaluating Borgonovo moment-independent importance measure with its application in an aircraft structure.” Reliab. Eng. Syst. Saf., 132(2), 163–175.
Zhang, L. G., Lu, Z. Z, and Wang, P. (2015). “Efficient structural reliability analysis method based on advanced Kriging model.” Appl. Math. Modell., 39(2), 781–793.
Zhao, Y. G., and Ang, A. H. (2003). “System reliability assessment by method of moments.” J. Struct. Eng., 1341–1349.
Zhao, Y. G., and Ono, T. (2001). “Moment methods for structural reliability.” Struct. Saf., 23(1), 47–75.
Zhao, Y. G., and Ono, T. (2000). “New point estimates for probability moments.” J. Eng. Mech., 433–436.
Zhao, Y. G., and Ono, T. (2004). “On the problems of the fourth moment method.” Struct. Saf., 26(3), 343–347.
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© 2015 American Society of Civil Engineers.
History
Received: Apr 24, 2014
Accepted: Oct 24, 2014
Published online: Apr 23, 2015
Published in print: Aug 1, 2015
Discussion open until: Sep 23, 2015
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