An improvement to the methods for estimating the statistical dependencies of the parameters of random load states

One of the biggest problems in the fatigue-life analysis of structures is predicting the parameters of the structure loading spectra under real operating conditions. If the loading spectrum is obtained from a load time series using a two-parametric rainflow counting method, then it is possible to present the distribution of the corresponding load cycles in the two-dimensional space of the loading-spectrum parameters: the amplitude and the mean of the load cycles. It is beneficial for the prediction of the load cycles if the distribution of load cycles is described by a continuous probability density function. We found in our previous studies that the different shapes of the multi-component probability density functions of load cycles can be modelled by a mixture of Gaussian functions if the parameters of the mixture are estimated using a maximum-likelihood method. One of the main problems connected with such an approach is the estimation of the number of components of the load-cycle distribution. This is usually done by a researcher, so the estimation is to a large extent subjective. In this paper, we will describe two methods for estimating the parameters of the mixture of Gaussian functions that almost eliminate the subjective influence of a researcher. The applicability of the two methods will be presented using examples of real load cases.