D-S quantification of aleatory uncertainty based on error assessment of intervals' endpoints

Because of coexistence of aleatory uncertainty and epistemic uncertainty in engineering design, we represented a method of unifying aleatory uncertainty and epistemic uncertainty, and that is to quantifying probability uncertainty for structures of evidence theory (D-S theory), thereafter this method will provide theory foundation for uncertainty quantification of complex machinery. Probability density function (PDF) is a token for aleatory uncertainty usually, and it expresses normal distribution. According to evidence theory, the equal interval is adopted to disperse the PDFs. Based on the analyzing the error of dispersed function and divided intervals, the endpoints' error of a single interval between the PDF and interval are set up for the principles, and we represent three principles. Lastly, the PDFs are quantified as D-S structure by using these methods, and the quantification results show principle I reflects the distribution better during similarly acceptable error, and quantification results will express the real distribution of PDFs much better while the acceptable error is smaller.