A Detailed Assessment of Model Form Uncertainty in a Load-Carrying Truss Structure

Abstract

In structural engineering, different assumptions and simplifications during the mathematical modeling process may lead to a set of competing mathematical models with different complexity and functional relationships. The quantification of the resulting model form uncertainty for competing mathematical models may be used to select the model that predicts the experimental measurements of a system most adequately for given requirements, e.g. highest possible accuracy or low computational costs. In this paper, a review and application of four selected approaches to detect and quantify model form uncertainty using experimental measurements and simulation data are conducted: detection of model form uncertainty by (1) parameter estimation with optimal design of experiments as well as quantification of model form uncertainty by (2) the area validation metric for comparing the cumulative density function of a numerical simulation with measurements, (3) a non-parametric regression approach to describe the model error and (4) a Gaussian process based quantification of model form uncertainty. As an exemplary system, an experimental load-carrying truss structure is considered with its system output being the maximum axial tensions in selected truss members due to static and dynamic loads. In two competing mathematical models, the truss structure is either assembled with rigidly connected beams or pin jointed rods. The proposed approaches (1) to (4) detect and quantify model form uncertainty in the two competing models of the load-carrying truss structure, which are subsequently compared and evaluated in terms of their simulation accuracy. Depending on the model requirements, the adequate truss structure model with quantified model form uncertainty may then be selected for further investigations.KeywordsUncertainty quantificationModel form uncertaintyConfidence regionsOptimal design of experimentsParameter identification