Description of statistical dependencies of parameters of random load states (dependency of random load parameters)

In order to predict fatigue life of structures under random loading, the probability distribution of parameters of random load states of structures should be determined, given that the material endurance is known and a proper damage rule is chosen. In this article a statistical dependency of two parameters of random load states (the amplitude and the mean of load cycles) is estimated by means of the multivariate p.d.f. of rainflow load cycles that are represented as vectors S=(Sa,Sm). The multivariate p.d.f of load cycles is modelled with a mixture of multivariate normal functions. A comparison of different methods for an estimation of the unknown parameters of the normal mixture is carried out. Agreement of numerically modelled and experimentally obtained data is checked by comparison of corresponding marginal probability distributions of load cycle amplitudes and means. The maximum likelihood method was recognised to be the most appropriate for the determination of the multivariate p.d.f. of load cycles.