Parametric modelling and scatter prediction of rainflow matrices

For service life prediction and stochastic reconstruction of load histories, rainflow matrices have been recently predominately used to describe the scatter of loading. Typically, only limited data are available due to the costs of measurements. As a consequence of this, discrete rainflow matrices have to be modelled and extrapolated. So far non-parametric methods have most frequently been used to transform discrete matrices into smooth functions. In this paper, two appropriate parametric models: a mixture of joint Weibull–normal distributions and a mixture of multi-variate normals, as well as two algorithms for parameter estimation: the EM algorithm and the algorithm developed by Nagode and Fajdiga are thoroughly discussed and compared. Finally, a method to describe the scatter of rainflow matrices is presented.