This paper deals with the probabilistic description of the random response of linear uncertain structural system when the uncertainties are modeled as random variables with assigned probability density function (pdf). In particular, a novel approach is presented that allows the direct evaluation of the response pdf starting from the joint pdf characterizing the structural uncertainties. It consists in matching adequately two methods, recently proposed by the authors, which are the Approximated Principal Deformation Modes method and the Probability Transformation Method. The proposed approach, obtained by this coupling, reveals to have good levels of accuracy, even for relatively high uncertainties, and of computational efficiency, as the reported numerical applications show. KEYWORDS probabilistic approaches, probability density function, uncertain systems Int J Numer Methods Eng. 2019;118:395-410.wileyonlinelibrary.com/journal/nme

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Using theoretical arguments, we present two novel spectrum models of the streamwise velocity component with robust correlation structures, which account for and decouple the fractal dimension and Hurst effect. The formulations that use isotropic concepts are adapted from the modern probability theory using the so-called generalized Cauchy and Dagum models, which belong to wide-sense-stationary random fields. A complementary inspection of these two models with field data from a met-tower-mounted sonic anemometer located within the atmospheric surface layer reveals good agreement and better performance than other conventionally used isotropic-based models of streamwise velocity spectra. The fractal dimension, D, of both models is consistent with the well-known Kolmogorov −5/3 power law in the inertial sub-range. For completeness, the study includes a derivation of the explicit forms of the energy spectral densities of the Cauchy and Dagum covariances.

Purpose This paper aims to present an approach for the probabilistic characterization of the response of linear structural systems subjected to random time-dependent non-Gaussian actions. Design/methodology/approach Its fundamental property is working directly on the probability density functions of the actions and responses. This avoids passing through the evaluation of the response statistical moments or cumulants, reducing the computational effort in a consistent measure. Findings It is an efficient method, for both its computational effort and its accuracy, above all when the input and output processes are strongly non-Gaussian. Originality/value This approach can be considered as a dynamic generalization of the probability transformation method recently used for static applications.

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