An efficient method for reliability analysis under epistemic uncertainty based on evidence theory and support vector regression

With a great capability of dealing with epistemic uncertainty, evidence theory has been utilised to conduct reliability analysis for engineering systems recently. Unfortunately, the discontinuous nature of uncertainty quantification using evidence theory incurs a huge computational cost. This paper proposes an efficient method to improve the computational efficiency of evidence theory for reliability analysis. In this method, evidence variables are transformed into random variables. Support vector regression is used to construct the approximation model of the limit-state function. The most probable point (MPP) of the approximate reliability problem with only random variables is searched out. Based on the MPP, the most probable focal element (MPFE) of the original problem with evidence variables is identified. According to the MPFE and the monotonicity of the limit-state function, contributions of some focal elements to belief and plausibility in evidence theory can be judged directly. Hence, the number of focal elements involved in the calculation of extreme values of the limit-state function is reduced. Four numerical examples are utilised to test the performance of the proposed method. Results indicate that the proposed method can reduce the computational cost on reliability analysis under epistemic uncertainty while ensuring the high accuracy of reliability analysis results.