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 s catter of loading. Typically, only limited data are available due to the co sts of measurements. As a consequence of this, discrete rainflow matrices h ave to be modelled and extrapolated. So far non-parametric methods have mos t frequently been used to transform discrete matrices into smooth functions . In this paper, two appropriate parametric models: a mixture of joint Weib ull-normal distributions and a mixture of multi-variate normals. as well as two algorithms for parameter estimation: the EM algorithm and the algorith m developed by Nagode and Fajdiga are thoroughly discussed and compared. Fi nally, a method to describe the scatter of rainflow matrices is presented. (C) 2001 Elsevier Science Ltd. All rights reserved.