Keywords: fatigue cracks, maintenance scheduling, non-destructive inspection, advanced simulation techniques, reliability-based optimization, reliability sensitivity.

This contribution presents an approach for the optimal scheduling of maintenance activities of metallic structures prone to develop fatigue cracks. The design variables associated with the scheduling of maintenance are the time at which inspection and repair take place and the quality of the inspection activities. By selecting appropriate values of these two design variables, the objective is to minimize the cost of operation of the structure (i.e. cost associated with inspection, repair and eventual failure). Due to the inherent uncertainties in crack propagation phenomena and in the inspection activities, probabilistic tools are used to quantify the effects of uncertainty. Thus, the problem of scheduling maintenance activities is addressed within the framework of reliability-based optimization (RBO); in this way, it is possible to minimize the cost of inspection, repair and eventual failure while explicitly accounting for the effects of uncertainties.

RBO problems are known to be numerically demanding. Therefore, in this contribution, a novel approach for solving RBO problems (recently introduced in [1]) is applied. Key features of this method are the identification of descent-feasible directions and the implementation of a line search strategy. In particular, the identification of descent directions requires the computation of the sensitivity of the structural reliability w.r.t. the design variables; this is accomplished by applying a novel algorithm recently developed by the authors in [2].

Numerical results presented in this contribution highlight the importance of optimization tools in context with the design of an optimal maintenance schedule. That is, the best maintenance strategy is not necessarily the one that minimizes the cost associated with a failure but, actually, is a tradeoff between the cost associated with inspection, repair and failure. Moreover, the time at which an inspection is performed plays a key role in the overall effectiveness of the maintenance strategies, i.e. in case inspection takes place either too early or too late, the effectiveness of maintenance activity is completely lost.

Finally, the results presented in this contribution also indicate that the proposed approach for solving RBO problems is very efficient, as most of the improvement of the objective function is attained within only a few iterations; thus, the number of probability estimations required, which is a critical issue from the point of view of efficiency in any RBO problem, can be considerably reduced.

1

H.A. Jensen, M.A. Valdebenito, G.I. Schuëller, D.S. Kusanovic, "Efficient reliability-based optimization of stochastic systems using line search", Computer Methods in Applied Mechanics and Engineering, 2009, submitted.

2

M.A. Valdebenito, G.I. Schuëller. "Efficient strategies for reliability-based optimization involving non linear, dynamical structures", Computers & Structures, 2009, submitted.

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