A commonly used tool for estimating the parameters of a mixture model is the Expectation–Maximization (EM) algorithm, which is an iterative procedure that can serve as a maximum-likelihood estimator. The EM algorithm has well-documented drawbacks, such as the need for good initial values and the possibility of being trapped in local optima. Nevertheless, because of its appealing properties, EM plays an important role in estimating the parameters of mixture models. To overcome these initialization problems with EM, in this paper, we propose the Rough-Enhanced-Bayes mixture estimation (REBMIX) algorithm as a more effective initialization algorithm. Three different strategies are derived for dealing with the unknown number of components in the mixture model. These strategies are thoroughly tested on artificial datasets, density–estimation datasets and image–segmentation problems and compared with state-of-the-art initialization methods for the EM. Our proposal shows promising results in terms of clustering and density-estimation performance as well as in terms of computational efficiency. All the improvements are implemented in the rebmix R package.

The influence of the working load on the dynamic loading of the bolt was investigated in our study for two cases of flange joints. The analytical calculation according to the Verein Deutscher Ingenieure (VDI) 2230 recommendation and the numerical analysis using the finite element method (FEM) were performed for a model of a four-bolt joint. To verify the FEM analysis, the forces in the bolts were measured during preloading and during the application of the working load on the test rig. Based on the analytical and numerical results, the influence of the working load application point on the bolt load and its fatigue life was analysed for different cases. Comparison of the results shows that the analytical method overestimates the additional bolt stresses at low working load, mainly due to the extremely large fraction of bending stress. As the working load increases, the differences between the two methods decrease, but only for the reason that the analytical method can only linearly scale the overestimated results at lower working load, and FEM analysis, on the other hand, shows a progressive increase of the additional stress in the bolt at higher working loads due to the spreading of the flange. It is also shown that a high washer significantly increases the fatigue life of the bolt for two reasons: (i) a high washer reduces the additional stress in the bolt, and (ii) the high washer shifts the critical fatigue point from the thread area to the transition of the bolt shank to the head.