Uncertainty quantification using evidence theory in concrete fatigue damage prognosis

Abstract

Fatigue failure is the main failure mode of mechanical components in the research of engineering structures. As fatigue life may be a basis for the fatigue reliability design, it is very important to predict it for the normal usage of the structure. Uncertainties rooted in physical variability, data uncertainty and modeling errors of the fatigue life prediction analysis. Furthermore, the predicted life of concrete structures in civil engineering field will be more obviously uncertain than other engineering structures. Due to lack of knowledge or incomplete, inaccurate, unclear information in the modeling, there are limitations in using only one framework (probability theory) to quantify the uncertainty in the concrete fatigue life prediction problem because of the impreciseness of data or knowledge. Therefore the study of uncertainty theory in the prediction of fatigue life is very necessary. This study explores the use of evidence theory for concrete fatigue life prediction analysis in the presence of epistemic uncertainty. The empirical formula S-N curve and the Paris law based on the fracture mechanics are selected as the fatigue life prediction models. The evidence theory is used to quantify the uncertainty present in the models' parameters. The parameters in fatigue damage prognosis model are obtained by fitting the available sparse experimental data and then the uncertainty in these parameters is taken into account. In order to alleviate the computational difficulties in the evidence theory based uncertainty quantification (UQ) analysis, a differential evolution (DE) based interval optimization method is used for finding the propagated belief structure. The object of the current study is to investigate uncertainty of concrete fatigue damage prognosis using sparse experimental data in order to explore the feasibility of the approach. The proposed approach is demonstrated using the experimental results of the plain concrete beams and the steel fibred reinforced concrete beams.