Keywords: reliability-based optimization, advanced simulation techniques, decoupling, sequential approximate optimization, line search, weighted approximation.

This contribution proposes a framework for solving reliability-based optimization (RBO) problems efficiently. The proposed approach is based on a decoupling approach [1], where the reliability assessment step and the optimization step are separated. This is achieved by generating an approximation of the structural reliability as an explicit function of the design variables of the RBO problem. The explicit approximation is constructed in a local domain of the space of the design variables. Given that these approximations are valid only in a local domain, it is necessary to solve the RBO problem using a sequential optimization approach, i.e. the original RBO problem is broken into a series of RBO subproblems. Starting from an initial candidate optimal design, a RBO subproblem is solved. The solution of this RBO subproblem is used to construct a new RBO subproblem. By repeating this procedure a number of times, it is possible to generate a series of candidate optimal designs which can converge to the solution of the original RBO problem [2,3].

In order to improve the efficiency of the approach for solving RBO problems described above, this contribution introduces two new techniques: a line search strategy and weighted approximations. The line search strategy explores a reduced space of the design variables, involving a single dimension. This allows to construct an approximation of the failure probabilities with an improved quality, as a one-dimensional space is easier to explore than the full space of the design variables. Thus, the line search can produce an improved design solution at relatively low numerical costs. The weighted approximation strategy aims at improving the convergence properties of the sequential approximations. Specifically, this strategy is useful when the reliability estimates present a large variability. The strategy consists of generating an estimate of the structural reliability based on the weighted average of several local approximations of the reliability.

The application example presented in the paper addresses the weight minimization of a non-linear structure under dynamic loading, subject to a probabilistic constraint. The results obtained show that the proposed approach can be very efficient and effective.

1

M. Gasser, G.I. Schuëller, "Reliability-based optimization of structural systems", Mathematical Methods of Operations Research, 46(3):287-307, 1997. doi:10.1007/BF01194858

2

R.T. Haftka, Z. Gürdal, "Elements of Structural Optimization", Kluwer, 3rd edition, 1992.

3

H.A. Jensen, M.A. Valdebenito, G.I. Schuëller, "An efficient reliability-based optimization scheme for uncertain linear systems subject to general Gaussian excitation", Computer Methods in Applied Mechanics and Engineering, 2008, in press. doi:10.1016/j.cma.2008.01.003

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