A unified evidence variable transformation framework for structural reliability analysis with aleatory and epistemic uncertainties

In structural engineering, reliability is a critical metric for safety assessment, yet it is invariably challenged by the existence of aleatory and epistemic uncertainties. The evidence theory has been introduced into reliability analysis for its ability to well quantify epistemic uncertainty using expert information or limited data. Thus, this paper proposes a framework for both the time-independent and time-dependent reliability analysis under hybrid uncertainties involving random and evidence variables. First, a new probabilistic transformation method named the uniformity-constrained equal area approach is proposed to transform the evidence variables into random variables, enabling the most probable focal element to be identified with the help of the first-order reliability method. Then, the initial training points for the radial basis function surrogate model are located via the central composite design and numerical integration. On this basis, the shape parameter of the radial basis function is calculated through the evolutionary algorithm to obtain the initial surrogate model. Subsequently, the prediction variance is obtained by using the leave-one-out cross-validation, and the selection of the best training sample points is carried out based on the active learning function, thereby constructing the final refined surrogate model to approximate the true limit-state function to obtain the interval failure probability under hybrid uncertainties. Note that incorporating the time parameter as an evidence input variable naturally unifies time-independent and time-dependent reliability analyses. Finally, two time-independent reliability problems and four time-dependent reliability problems are analyzed and compared with the previous methods to demonstrate the effectiveness of the proposed method.