Keywords: probabilistic entropy, relative entropy, stochastic finite element method, structural analysis, reliability assessment.

This work aims an idea of application of various relative entropies models in reliability analysis of the most popular civil engineering steel structures. Reliability indices computed according to the Cornell theory, included in the Eurocode 0 approach, have been contrasted here with these coming from Kullback-Leibler, Bhattacharyya, Jensen-Shannon as well as Mahalanobis. It was necessary for this purpose to calculate the first two probabilistic moments of different structural responses like extreme stresses and/or deformations assuming Gaussian distributions of both design parameters and structural output. Numerical analysis of this moments has been completed with the use of triple Stochastic Finite Element Method. It was implemented according to (i) the iterative generalized stochastic perturbation technique, (ii) Monte-Carlo simulation as well as (iii) the semi-analytical integral approach. This variety of probabilistic methods allows us to recognize the applicability and accuracy of various stochastic algorithms in addition to the input uncertainty level, to a number of random trials in statistical approach, and to order of Taylor expansion in the stochastic perturbation approach. Finally, the resulting relative entropies have been all rescaled to the variability interval of the First Order Reliability Method.

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