Abstract
Nonlinear dynamics problems can generally be solved only in a numerical way. This prevents from a direct application of standard reliability methods. A technique which makes use of iterated response-surface analytical approximations of the system performance function was therefore proposed in view of reliability assessment. The limitation of this technique was of working in a standard normalized space, so that appropriate space transformations are preliminarly required.
This paper shows how this response-surface iterative scheme can also be used in the original space of the random variables, provided a maximum log-likelihood constrained optimization problem is solved. Moreover, asymptotic theory also provides a better estimate of the probability of failure of the dynamical system against any assigned limit state.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Faravelli, L., ‘Structural reliability via response surface’. in Nonlinear Stochastic Mechanics, Bellomo, N. and Casciati, F., eds., Springer Verlag, 1992, 213–224.
Faravelli, L., ‘Stochastic finite elements and reliability analysis, Proceedings of ASCE Probabilistic Mechanics and Structural Reliability Conference, Denver, CO. 1992, 45–53.
Hohenbichler, M. and Rackwitz, R., ‘Non-normal dependent vectors in structural safety’, Journal of Engineering Mechanics Division, ASCE 107, 1981, 1227–1241.
Faravelli, L., A response surface approach for reliability analysis, Journal of Engineering Mechanics, ASCE 115, 1989, 2763–2781.
Faravelli, L., ‘Finite-element analysis of stochastic nonlinear continua, in Computer Mechanics of Probability and Reliability Analysis, Liu, W. K. et al., eds., Elmepress, Lausanne, 1989, 263–280.
Caseiati, F. and Faravelli, L., Fragility Analysis of Complex Structural System, Research Studies Press, Taunton, UK, 1991.
Breitung, K., ‘Asymptotic approximations for multinormal integrals’, Journal of Engineering Mechanics Division, ASCE 110, 1984, 357–366.
Breitung, K., ‘Probability approximations by log likelihood maximization’, Journal of Engineering Mechanics, ASCE 117, 1991, 457–477.
Breitung, K., ‘Parameter sensitivity of failure probabilities’, in Reliability and Optimization of Structures '90, Der Kiureghian, A., and Thoft-Cristensen, P., eds., Proceedings of 3rd IFIP WG7.5 Conference, Berkeley, Lecture Notes in Engineering 61, Springer, Berlin, 1990, 43–51.
Breitung, K., ‘Asymptotic crossing rates for stationary Gaussian vector processes, Stochastic Processes and Their Applications 29, 1988, 195–207.
Breitung, K., ‘Asymptotic approximations for the extreme value distribution of non-stationary differentiable normal processes’, in Transactions of the 10th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes 1986, Academia, Prague, 1988, 207–215.
Breitung, K., ‘The extreme value distribution of non-stationary vector processes’, in Proceedings of ICOSSAR '89, A. H. S. Ang et al., eds., 5th International Conference on Structural Safety and Reliability, ASCE, New York, 1990, 1327–1332.
Schittkowski, K., ‘NLPQL: A Fortran subroutine solving constrained nonlinear programming problems’. Annales of Operation Research 5, 1985, 485–500.
Johnson, N. L. and Kotz, S., ‘Distributions in statistics’, Vol. 4, Continuous Multivariate Distributions, John Wiley and Sons, NY, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Breitung, K., Faravelli, L. Log-likelihood maximization and response surface in reliability assessment. Nonlinear Dyn 5, 273–285 (1994). https://doi.org/10.1007/BF00045337
Issue Date:
DOI: https://doi.org/10.1007/BF00045337