Keywords: optimisation, reliability based design optimisation, safety factors, first order reliability method, global optimisation, particle swarm optimisation.

Optimisation techniques have been applied in several engineering fields, for instance, in structural engineering, they have been employed in order to obtain minimum weight structures. In deterministic optimisation, however, the uncertainties of the system (i.e. dimension, model, material, loads, etc.) are not taken into account. Doing so, the resulting optimum solution may lead to a lower level of reliability and, as a consequence, a higher risk of failure. Thus, it is the objective of reliability based design optimisation (RBDO) to optimize structures while guaranteeing a minimum reliability level defined a priori.

As the reliability analysis is an optimisation procedure itself, the RBDO, in its classical version, is a double-loop strategy. The inner loop is the reliability analysis, which is pursued in the normalized space, and the outer loop, the structural optimisation, is pursued in the so called physical space. Thus, the two optimisations are coupled. Such coupling leads to a high computational cost, the reliability analysis being the most time consuming task in RBDO.

To reduce the computational burden of the RBDO, several papers decoupled the structural optimisation and the reliability analysis. This procedure may be divided into two groups: (i) the serial single loop methods and, (ii) the unilevel methods.

The basic idea of the serial single loop methods is to decouple the structural optimisation (outer loop) and the reliability analysis (inner loop). Each method of this group utilizes a specific strategy to decouple such loops and then, perform them sequentially until some convergence criterion is achieved. Among these methods, the following may be cited: traditional approximation method, single loop single variable (SLSV), sequential optimisation and reliability assessment (SORA) and the safety factor approach (SFA).

The central idea of the unilevel methods (also called monolevel) is concurrent convergence of the design optimisation and reliability calculation, in other words, they are sought simultaneously and independently.

Despite all advances in the RBDO, just a few papers have dealt with global optimisation mainly resulting from its high computational cost. One way to take into account uncertainties would be the use of safety factors and then, pursue the deterministic optimisation of the structure. However, such factors are usually based on engineering experience and/or experimental work and may lead to either high cost or low reliability levels. It would be interesting to develop safety factors that achieve both minimum reliability level and an optimized structure. The main advantage of such a procedure is that it requires a little additional computational effort if compared to the standard deterministic optimisation and at the same time it guarantees the minimum reliability level of the structure. Thus, this paper presents a RBDO methodology based on safety factors, which are derived from the Karush-Kuhn-Tucker optimality conditions of the first order reliability method (FORM). Numerical results are then analyzed to validate the method. Furthermore, the advantages and disadvantages of the method are pointed out and finally, it is coupled with an evolutionary algorithm (the particle swarm optimisation (PSO) method) as an attempt to pursue global RBDO. The proposed methodology and its coupling with the evolutionary optimisation strategy are the main features of this paper.

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