Fault detection and classification is an important part of assessing the structural and system health status. The classification and detection of faults and faulty units is mostly done with ...statistical methods. After the data are measured and collected, the use of statistical software is necessary. Currently, many statistical software packages are being developed for the R programming language, as a result of R implementation being open source and free to use. This paper focuses on the rebmixR package, which concentrates on mixture model estimation. Mixture models, in particular Gaussian mixture models, are the main driver for many practical applications, such as clustering and classification. Hence, in this paper, we have expanded the rebmix for the estimation of the Gaussian mixtures. The results acquired on three different fault classification datasets were promising. Additionally, the process of obtaining those results is shown in detail, giving the researchers in the fault classification field useful resources for their research.
•REBMIX algorithm is derived for Gaussian mixture model estimation.•Main methods and classes of the corresponding R package rebmix are described.•Three different datasets for fault detection and classification are processed.•The R package rebmix has achieved better results than other popular R packages.
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.
A maximum-likelihood estimation of a multivariate mixture model’s parameters is a difficult problem. One approach is to combine the REBMIX and EM algorithms. However, the REBMIX algorithm requires ...the use of histogram estimation, which is the most rudimentary approach to an empirical density estimation and has many drawbacks. Nevertheless, because of its simplicity, it is still one of the most commonly used techniques. The main problem is to estimate the optimum histogram-bin width, which is usually set by the number of non-overlapping, regularly spaced bins. For univariate problems it is usually denoted by an integer value; i.e., the number of bins. However, for multivariate problems, in order to obtain a histogram estimation, a regular grid must be formed. Thus, to obtain the optimum histogram estimation, an integer-optimization problem must be solved. The aim is therefore the estimation of optimum histogram binning, alone and in application to the mixture model parameter estimation with the REBMIX&EM strategy. As an estimator, the Knuth rule was used. For the optimization algorithm, a derivative based on the coordinate-descent optimization was composed. These proposals yielded promising results. The optimization algorithm was efficient and the results were accurate. When applied to the multivariate, Gaussian-mixture-model parameter estimation, the results were competitive. All the improvements were implemented in the rebmix R package.
•An improved mixture parameter estimation algorithm is proposed.•The joint mixture distribution model of wind speed and direction is established.•The wind direction observations are represented by ...von Mises mixed distributions.•The proposed algorithm exhibits a better performance with less computing time.
A statistical analysis of the wind speed and wind direction serves as a solid foundation for the wind-induced vibration analysis. The probabilistic modeling of wind speed and direction can effectively characterize the stochastic properties of wind field. The joint distribution model of wind speed and direction involves a circular distribution and has a multimodal characteristic. In this paper, the finite mixture distribution model is introduced and used to represent the joint distribution model that is comprised of the mixture Weibull distributions and von Mises distributions. An extended parameters estimation algorithm for multivariate and multimodal circular distributions is proposed to construct the joint distribution model. The proposed algorithm estimates the component parameters, mixture weight of each component and the number of components successively by an iterative process. The major improvement is accomplished by adding a circular distribution model. The effectiveness of the proposed algorithm is verified with numerical simulations and one-year field monitoring data and compared with the expectation maximization algorithm-based angular-linear approach in terms of the Akaike’s information criterion and computing time. The results indicate that the finite mixture model represents the joint distribution model of wind speed and direction well and that the proposed algorithm has a good and time-saving performance in parameter estimation for multivariate and multimodal models.
The shape of a rainflow matrix is complex and cannot be approximated by a simple distribution function. In this paper, the Weibull–normal mixture distribution is used, for which the number of ...components and unknown parameters are required to be estimated. The scope of the paper is to estimate the number of components and unknown parameters using the FlexMix and REBMIX algorithms, and compare their results. The results are then used in Goodman and Walker mean stress correction methods. This correction is not made as a point-to-point transformation, where the information about the distribution function of the rainflow matrix is lost. Instead, the used distribution function of the rainflow matrix with estimated parameters is transformed in accordance with Goodman and Walker mean stress correction methods. With this procedure, the probability density of the equivalent stress amplitude is immediately obtained, and the information about the distribution function of the rainflow matrix is not lost.
•Rainflow matrix is modelled with Weibull–normal mixture distribution.•FlexMix and REBMIX algorithms are used for mixture parameter estimation.•Goodman and Walker mean stress corrections are studied.•PDF of the equivalent stress amplitude is derived by statistical transformation.•Flexmix and rebmix R packages are compared by analyzing two cases.
Ispitivanja pokazuju da se pojave nehomogenosti ne bi trebale zanemariti kod procjene loma zbog zamora lijevanih dijelova. Objašnjavanje njihovog postojanja predstavlja problem zbog slučajnosti ...njihovih lokacija, raspodjele i dimenzija. Poznavanje statističkih karakteristika nehomogenosti od osnovnog je značenja za opis hjihovog učinka na lom zbog zamora. U ovom se radu daje statistička analiza oksidnih umetaka koji su doveli do loma AlSi9Cu3 uzoraka. Geometrijske karakteristike su opisane pomoću geometrijskih parametara i L. Upotrebljena su tri različita miješana PDFa za modeliranje distribucije izabranih geometrijskih parametara, a Gaussian funkcija s više varijanti je odabrana kao najpogodnija. Za procjenu nepoznatih parametara mješavine upotrebljeni su i uspoređeni modificirani EM algoritam i REBMIX. Prikladnijim se, prema rezultatima, pokazao modificirani EM algoritam. Provedena je bootstrap analiza za PDF i algoritam odabranog spoja kako bi se odredila veličina promjene procijenjenih PDF parametara.
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