The paper considers a new prospect of the arbitrary continuous function approximation from a limited set of input data with the REBMIX algorithm, developed for the finite mixture density estimation. Since the REBMIX estimates the unknown parameters with the unique semi-parametric method, it is assumed that it could be used also for the estimation of the unknown parameters in the fields that are not directly connected to density function estimation.For the approximation of the arbitrary continuous function with the REBMIX algorithm, the required procedure is developed in the paper. The results gained by the proposed procedure and by the radial basis function network for three different datasets are compared by calculating the RMSE values between estimated and test output values. The adequacy of the proposed procedure is estimated by using both univariate and bivariate datasets. It can be concluded that with the developed procedure, the REBMIX algorithm can be applied successfully for the continuous function approximation.

In the field of predicting structural safety and reliability the operating conditions play an essential role. Since the time and cost limitations are a significant factors in engineering it is important to predict the future operating conditions as close to the actual state as possible from small amount of available data. Because of the randomness of the environment the shape of measured load spectra can vary considerably and therefore simple distribution functions are frequently not sufficient for their modelling. Thus mixed distribution functions have to be used. In general their major weakness is the complicated calculation of unknown parameters. The scope of the paper is to investigate the load spectra growth for actual operating conditions and to investigate the modelling and extrapolation of load spectra with algorithm for mixed distribution estimation, REBMIX The data obtained from the measurements of wheel forces and the braking moment on proving ground is used to generate load spectra.