Probability density function of the equivalent stress amplitude using statistical transformation

The shape of a rainflow matrix is complex and cannot be approximated by a simple distribution function. In this paper, the Weibull-normal mixture distribution is used, for which the number of components and unknown parameters are required to be estimated. The scope of the paper is to estimate the number of components and unknown parameters using the FlexMix and REBMIX algorithms, and compare their results. The results are then used in Goodman and Walker mean stress correction methods. This correction is not made as a point-to-point transformation, where the information about the distribution function of the rainflow matrix is lost. Instead, the used distribution function of the rainflow matrix with estimated parameters is transformed in accordance with Goodman and Walker mean stress correction methods. With this procedure, the probability density of the equivalent stress amplitude is immediately obtained, and the information about the distribution function of the rainflow matrix is not lost.