Evidence theory and differential evolution based uncertainty quantification for buckling load of semi-rigid jointed frames

The paper describes a procedure for the uncertainty quantification (UQ) using evidence theory in buckling analysis of semi-rigid jointed frame structures under mixed epistemic-aleatory uncertainty. The design uncertainties (geometrical, material, strength, and manufacturing) are often prevalent in engineering applications. Due to lack of knowledge or incomplete, inaccurate, unclear information in the modeling, simulation, measurement, and design, there are limitations in using only one framework (probability theory) to quantify uncertainty in a system because of the impreciseness of data or knowledge. Evidence theory provides an alternative to probability theory for the representation of epistemic uncertainty that derives from a lack of knowledge with respect to the appropriate values to use for various inputs to the model. Unfortunately, propagation of an evidence theory representation for uncertainty through a model is more computationally demanding than propagation of a probabilistic representation for uncertainty. In order to alleviate the computational difficulties in the evidence theory based UQ analysis, a differential evolution-based computational strategy for propagation of epistemic uncertainty in a system with evidence theory is presented here. A UQ analysis for the buckling load of steel-plane frames with semi-rigid connections is given herein to demonstrate accuracy and efficiency of the proposed method.