A Comparative Study of Uncertainty Propagation Methods in Structural Problems

Abstract

Several uncertainty propagation algorithms are available in literature: (i) MonteCarlo simulations based on response surfaces, (ii) approximate uncertainty propagation algorithms, and (iii) non probabilistic algorithms. All of these approaches are based on some a priori assumptions about the nature of design variables uncertainty and on the models and systems behavior. Some of these assumptions could misrepresent the original problem and, consequently, could yield to erroneous design solutions, in particular where the prior information is poor or inexistent (complete ignorance). Therefore, when selecting a method to solve an uncertainty based design problem, several aspects should be considered: prior assumptions, non-linearity of the performance function, number of input random variables and required accuracy. It could be useful to develop some guidelines to choose an appropriate method for a specific situation. In the present work some classical structural problems will be studied in order to investigate which probabilistic approach, in terms of accuracy and computational cost, better propagates the uncertainty from input to output data. The methods under analysis will be: Univariate Dimension Reduction methods, Polynomial Chaos Expansion, First-Order Second Moment method, and algorithms based on the Evidence Theory for epistemic uncertainty. The performances of these methods will be compared in terms of moment estimations and probability density function construction corresponding to several scenarios of reliability based design and robust design. The structural problems presented will be: (1) the static, dynamic and buckling behavior of a composite plate, (2) the reconstruction of the deformed shape of a structure from measured surface strains.