A reliability analysis method including confidence level and probability reliability under epistemic and aleatory uncertainty

Reliability analysis is a synthesis problem affected by both epistemic and aleatory uncertainties, due to the difficulties such as lack of statistical data and insufficient subjective information, which implies that the reliability analysis method has been seriously restricted in engineering applications. The reliability analysis results are expressed as evidence layer and probability layer here, and an analysis method based on hybrid evidence and probability is presented. First, the evidence layer of epistemic uncertainties has been constructed based on evidence theory. In the independence case of evidence variables, the joint basic probability assignment of the focal element is expressed as the product of all the evidence variables’ basic probability assignments involved; in the dependence case of evidence variables, the joint basic probability assignment of the focal element is derived through ellipsoid equation. Then, according to the limit state function characteristics, an analytic or numerical method is employed for the failure probability calculation, and the probability layer of aleatory uncertainty has been constructed. Finally, the probability calculation result with maximum credibility is chosen, and the corresponding focal element including the evidence variables is regarded as the design scheme. Numerical and engineering examples show the feasibility and effectiveness of the proposed method.