A new probabilistic transformation technique for evidence-theory-based structural reliability analysis

Reliability analysis signifies an indispensable approach for ensuring the safety and functionality of engineering structures. Evidence-theory-based reliability analysis (ETRA) has been developed attributable to its superior ability to deal with various epistemic uncertainties presented in practice. However, ETRA could inevitably result in a high computational burden due to its repeated call for costly performance functions. To tackle such a computational efficiency problem, an effective reliability analysis method is proposed here to deal with epistemic uncertainty. First, a new probabilistic transformation technique is developed based on cubic spline interpolation (CSI). Second, with the help of CSI, the most probable focal element is located using an improved HL-RF algorithm accurately. Third, the actual performance function is replaced by a response surface model which is constructed by the central composite design around the most probable focal element. Finally, the belief measure and plausibility measure of the reliability problem are performed. The effectiveness of the proposed reliability analysis method is verified by three benchmarking numerical examples and an engineering case study on kinematic trajectory precision of an industrial robot. The results indicate that the proposed method has high efficiency with satisfactory computational accuracy.