Keywords: time-variant reliability, reliability-based design optimization, timber structures.

The reliability-based design optimization (RBDO) allows us to reach effectively balanced cost-safety designs [1,2]. However, to design structures subjected to deterioration (e.g. damage, fatigue, etc.), the RBDO approach should use time-variant instead of time-invariant reliability analysis, where load and environmental fluctuations are modeled using stochastic processes [3]. The classical formulation of the time-variant reliability-based design optimization (TV-RBDO) consists in minimizing an objective function defined by initial and expected failure costs subject to reliability constraints. This formulation is not suitable for real engineering structures because of the very large time consumption and convergence difficulties.

In this paper, a new methodology for TV-RBDO is proposed, where the TV-RBDO problem is transformed to a sequence of equivalent deterministic design optimization sub-problems. This transformation is based on setting the optimal safety factors, which are calibrated to link the reliability constraints with the equivalent deterministic optimization. At the end of each optimization sub-problem, the reliability constraint is verified by performing a full time-variant reliability analysis based on the out-crossing procedures. The safety factors corresponding to the target reliability level at the design time (i.e. before degradation) are calibrated using the inverse probabilistic approach. Finally, these safety factors are provided to the next sub-problem to be solved in the deterministic space, and so on, until convergence.

The objective function is approximated by a first-order Taylor expansion on the basis of the time-variant reliability analysis performed in the previous sub-problem loop. The safety factors link reliability constraints to deterministic optimization, in order to avoid the reliability analysis inside the optimization loops. The evaluation of these safety factors may be performed in a probabilistic manner, in order to meet the reliability requirement. A probabilistic procedure is proposed to calibrate the safety factors on the basis of the target reliability index at the construction time (i.e. initial time).

The numerical application concerns timber structures, where the ultimate capacity decreases with aging due to load application with time. This application shows the efficiency and the good-standing of the proposed method, through comparisons with a classical TV-RBDO approach and a fully deterministic optimization.

1

D.M. Frangopol, F. Moses, "Reliability-based structural optimization", H. Adeli, editor, Advances in design optimization, Chapman Hall, London, 1994.

2

A. Chateauneuf, Y. Aoues, "Advances in solution methods for Reliability-Based Design Optimization", In Y. Tsompanakis, N.D. Lagaros, M. Papadrakakis, (editors), Structural Design Optimization Considering Uncertainties, Taylor & Francis, 2008.

3

N. Kuschel, R. Rackwitz, "Optimal design under time-variant reliability constraints", Structural Safety, 22(2):113-127, 2000. doi:10.1016/S0167-4730(99)00043-0

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £78 +P&P)