An efficient epistemic uncertainty analysis method using evidence theory

Evidence theory is widely regarded as a promising mathematical tool for epistemic uncertainty analysis. However, the heavy computational burden has severely hindered its application in practical engineering problems, which is essentially caused by the discrete uncertainty quantification mechanism of evidence variables. In this paper, an efficient epistemic uncertainty analysis method using evidence theory is proposed, based on a probabilistic and continuous representation of the epistemic uncertainty presented in evidence variables. Firstly, each evidence variable is equivalently transformed to a Johnson p-box which is a family of Johnson distributions enveloped by the CDF bounds. Subsequently, the probability bound analysis is conducted for the input Johnson p-box and the response CDF based on monotonicity analysis. Finally, the CDF bounds of the response are directly calculated using the CDF bounds of the input Johnson p-boxes, by which a high computational efficiency is achieved for the proposed method. Two mathematical problems and two engineering applications are presented to demonstrate the effectiveness of the proposed method.