Reliability analysis based on the principle of maximum entropy and Dempster–Shafer evidence theory

Abstract

The Probability density functions (PDFs) of some uncertain parameters are difficult to determine precisely due to insufficient information. Only the varying intervals of such parameters can be obtained. A method of reliability analysis based on the principle of maximum entropy and evidence theory was proposed to address the reliability problems of random and interval parameters. First, the PDFs and cumulative distribution functions of interval parameters were obtained on the basis of the principle of maximum entropy and Dempster–Shafer evidence theory. Second, the normalized means and standard deviations of interval parameters were obtained using the equivalent normalization method. Third, two explicit iteration algorithms of reliability analysis were proposed on the basis of the advanced firstorder and second-moment method to avoid solving the limit state function and obtain the reliability index. Finally, the accuracy and efficiency of the proposed methods were verified through a numerical example and an engineering case.