Keywords: Monte Carlo simulation, probability distribution, random number generation, multivariate sampling, correlation matrix, simulated annealing.

Probabilistic concepts are increasingly implemented in structural engineering applications, in order to incorporate the effect of randomness in material properties, geometric characteristics, loads, etc. Such uncertainties in structural analysis input give rise also to uncertainties in structural analysis output. This uncertainty propagation can be quantitatively assessed using the well-known Monte Carlo (MC) simulation procedure or other variability or reliability estimation methods. In order to perform a quantitative probabilistic assessment with such methods, the random parameters involved in the assessment need to be modelled as realistically and accurately as possible. Thus, we need to carefully specify the probability distributions of random variables, but also the interdependencies (correlations) between these variables.

The present work is concerned with probabilistic structural analysis using several random variables, which model uncertain material properties. Within this context, the overall uncertainty in a structural system is jointly described with a multivariate probability distribution. Each marginal of the multivariate distribution corresponds to the probability distribution of a random material property of the structural system. The correlation matrix of the multivariate distribution specifies the interdependencies among the random material properties.

Probabilistic analyses are conducted in this paper with the direct MC simulation method. This is a very effective and widely applicable simulation technique, but it typically requires the generation of large numbers of samples for the random parameters considered. A particular difficulty, with which we are confronted in the present work, is the task of sampling from a multivariate probability distribution with arbitrarily intercorrelated marginals. This is not a trivial task; in fact, this is still an active research topic. Therefore, a specialized two-step sampling approach is employed in the present paper: first a univariate random sample from each specified material property's distribution is independently generated; then a discrete simulated annealing (SA) optimizer rearranges the generated univariate samples, in order to obtain the desired correlations between them.

The MC simulation method combined with the aforementioned multivariate sampling procedure allows us to examine the effect of intercorrelations among random material properties on probabilistic structural analysis results. As an application example, an elastoplastic steel frame is considered with its members organized into a number of column-beam categories. Each category is characterized by a random variable corresponding to uncertain yield stress. Probabilistic limit elastoplastic analyses are performed for various correlation values specifying the interdependencies among the random yield stresses of the member categories. Based on the results obtained, a significant effect on probabilistic limit load results was observed for various correlation values of the random material properties.

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