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.
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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
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DOI: https://doi.org/10.1007/BF00045337