A distributionally robust data-driven framework to reliability analysis

This paper proposes a reliability analysis framework that accounts for the error caused by characterizing a data set as a probabilistic model. To this end we model the uncertain parameters as a probability box (p-box) of Sliced-Normal (SN) distributions. This class of distributions enables the analyst to characterize complex parameter dependencies with minimal modeling effort. The p-box, which spans the maximum likelihood and the moment-bounded maximum entropy estimates, yields a range of failure probability values. This range shrinks as the amount of data available increases. In addition, we leverage the semi-algebraic nature of the SNs to identify the most likely points of failure (MLPs). Such points allow the efficient estimation of failure probabilities using importance sampling. When the limit state functions are also semi-algebraic, semidefinite programming is used to guarantee that the computed MLPs are correct and complete, therefore ensuring that the resulting reliability analysis is accurate. This framework is applied to the reliability analysis of a truss structure subject to deflection and weight requirements.