Automated second moment analysis of systems with probabilistic constitutive components

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Abstract
Second-moment analysis is receiving increasing attention from various disciplines, including structural engineering, geomechanics, hydrology, hydraulics, and transport engineering. While much work has been done in the area of solution techniques, little attention has been given to automated model building and the computation of second moments for large complex systems. In this paper, we show how existing deterministic software systems can be augmented with the ability to efficiently build second-moment models of large structures with probabilistic constitutive components. This follows recently published work involving random excitations. We use the Kronecker Product operator to simplify procedures for handling the multiplicative uncertainty that results from random constitutive components. It is clearly shown that the only additional information required to be specified by the user is the variances and covariances of probabilistic component parameters. We also propose a “p-part n-terminal postulate” to maintain the concept of characterization of component behaviour as a task that proceeds independently of other components and system topology. A new approximate solution approach to the second moments, that follows naturally from the model-building procedure, is presented and applied to a simple pipe network problem.