Time-dependent reliability analysis for deteriorating structures using imprecise probability theory

Abstract

Reliability analysis, which takes into account uncertainties, is considered to be the best tool for modern structural evaluation. In this assessment, the deterioration model is one of the most important factors, but it is complicated for modelling due to the inherent uncertainties in the deterioration process. Theoretically, the uncertainties of the deterioration process can be modelled using a probabilistic approach. However, there are practical difficulties in identifying the probabilistic model for the deterioration process as the actual deterioration data are rather limited. Also, the dependencies between different uncertainties are often ignored. Thus the present study proposes a probabilistic analysis framework, using dependent p-boxes in which copulas describe the dependence, for modelling the deterioration process with incomplete information. There are two main parts of the framework. Firstly, the theory of statistical inference is developed for the quantification of uncertainties and their dependence structure. Secondly, simulation techniques in the structural reliability analysis are also developed. Two simulation approaches are integrated to propagate the dependent p-boxes for reliability analysis, including interval MC simulation and importance sampling. The accuracy and efficiency of the uncertainty framework are also verified through numerical examples. When the accuracy and efficiency of the framework are verified, the framework is then applied to the proposed deterioration models. Due to the different properties involved in the process, deterioration models for steel structures and reinforced concrete structures are considered separately. The finding suggests that significant epistemic uncertainties exist in the current deterioration models due to the limited availability of reliable corrosion data. In addition, new dependence structure of Frank copula is discovered in the deterioration models of steel and RC structures. In summary, the proposed framework in the study is recommended as a useful tool to model the uncertain corrosion process, accounting for both the aleatory and epistemic uncertainties. The inaccuracy of error measurements and insufficient data have been taken into account for modelling of uncertainty and dependence structure.