Keywords: reliability analysis, latin hypercube method, hyperspace division method, biased sampling, genetic algorithms, competition, population dynamics.

A method for the reliability analysis for complex structures is proposed. The aim is to reduce the computational effort through domain decomposition (partitioning) of the probabilistic space and subsequent biased sampling in the areas of interest. A reduction of the size of the probabilistic space results into an increase of the sapling density that improves the accuracy of the outcome in less computing time. The probabilistic space is divided in 2NRV hypercubes of equal size. The critical elements of the structure are identified based on their failure probability estimates obtained using First Order Reliability Methods (FORM). Incomplete failure modes are derived with the appropriate synthesis of the critical elements. The resulting series system of these modes is used to produce a measure of importance for the hypercubes and the Random Variables of the problem. Random Variables (RV) of marginal importance are curled to reduce the dimensionality of the problem under investigation and the probabilistic space is re-partitioned with regard to the active set of RVs. Hypercubes of importance up to a certain percentile, as compared to the most "critical" hypercube are excluded from sampling. For the hypercubes selected, the point of the intersection of the principal diagonal and the safe/fail boundary is found to confine the sampling space in the volume of interest close to the fail/safe boundary. The overall failure probability and the probabilities of failure of its elements are obtained from sampling in these zones. The results from the reliability analysis are compared to those obtained from Monte Carlo simulation, and other methods and the performance of the proposed algorithm is examined. Two non-linear limit states, a combination of disjoint linear limit states and two indeterminate truss structures are used as benchmarks. The algorithm's robustness is verified in all cases. The method managed to produce these results in only a fraction of the computing time needed for the crude MC method. In addition its computational efficiency increases as the target failure probability decreases making this method particularly suitable for structures with high reliability indices. Moreover, an optimization scheme combining genetic algorithms and competition is coupled with the reliability analysis algorithm for the cost minimization of indeterminate truss structures subject to reliability constraints. Competition is introduced among the populations of a number of Genetic Algorithms (GAs) in solving the optimization problem. The evolution of the different populations, having different sets of parameters, is controlled at the level of metapopulation, i.e. the union of populations, on the basis of statistics and trends of the evolution of every population. The fuzzy outcome of the conflict among the populations guides the evolution of the different GAs towards better solutions in the statistical sense. The optimization scheme utilizes the reliability analysis algorithm and the results from the analysis of a planar 10-bar truss and a 25-bar space truss are presented. From the optimization process it is seen that an increase of the average of the active loads results to optimal designs with decreasing reliability indices for constant ratios of the cost of construction to the cost of potential failure.

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