Time-dependent reliability
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Structural reliability is assessed by means of a time-dependent fuzzy failure probability. All fuzzy-random functions are discretized and described with the aid of the fuzzy joint probability density function. In order to integrate the fuzzy joint probability density function over the fuzzy failure region the fuzzy Monte-Carlo simulation (FMCS) was developed. The numerical efficiency of the simulation (variance minimization) is improved by an extension of importance sampling under consideration of fuzzy randomness. This finally leads to fuzzy adaptive importance sampling (FAIS).
The computation of the fuzzy failure probability to several time points results in a time dependent fuzzy function (fig. 1).
Figure 1. Time-dependent fuzzy failure probability
The
time-dependent fuzzy failure probability enables the detection of time
points, where permissible values of fuzzy failure probability are
exceeded. The non-permissible fuzzy
failure probability can be mutated into a permissible probability
by
rehabilitation or strengthening of structures. For
strengthening
of reinforced concrete structures,e.g., a new technology is developed
based
on textile-reinforced concrete layers. This technology and the
accompanying numerical methods are developed in the project - Safety assessment of textile strengthened structures, that is part of the Collaborative Research Center
Textile Reinforcement for Structural Strengthening and Retrofitting(SFB 528) granted by the
German Research Foundation(DFG).
References
- Möller, B, Graf, W, Sickert, J, and Beer, M (2006) Time-dependent reliability of textile strengthened RC structures under consideration of fuzzy randomness, Computers and Structures 8-9(84):585–603.
- Sickert, J, Graf, W, and Reuter, U (2005) Application of fuzzy randomness to time-dependent reliability, In: Safety and Reliability of Engineering Systems and Structures Proceedings of the 9th Int. Conference on Structural Safety and Reliability, edited by Augusti, G.; Schueller, G.I. and Ciampoli, M.. Millpress, Rotterdam, pages 1709–1716.
