Observer-biased bearing condition monitoring: from fault detection to multi-fault classification

Bearings are simultaneously a fundamental component and one of the principal causes of failure in rotary machinery. The work focuses on the employment of fuzzy clustering for bearing condition monitoring, i.e., fault detection and classification. The output of a clustering algorithm is a data partition (a set of clusters) which is merely a hypothesis on the structure of the data. This hypothesis requires validation by domain experts. In general, clustering algorithms allow a limited usage of domain knowledge on the cluster formation process. In this study, a novel method allowing for interactive clustering in bearing fault diagnosis is proposed. The method resorts to shrinkage to generalize an otherwise unbiased clustering algorithm into a biased one. In this way, the method provides a natural and intuitive way to control the cluster formation process, allowing for the employment of domain knowledge to guiding it. The domain expert can select a desirable level of granularity ranging from fault detection to classification of a variable number of faults and can select a specific region of the feature space for detailed analysis. Moreover, experimental results under realistic conditions show that the adopted algorithm outperforms the corresponding unbiased algorithm (fuzzy c-means) which is being widely used in this type of problems. (C) 2016 Elsevier Ltd. All rights reserved.Grant number: 145602

Affine Registration of label maps in Label Space

Two key aspects of coupled multi-object shape\ud analysis and atlas generation are the choice of representation\ud and subsequent registration methods used to align the sample\ud set. For example, a typical brain image can be labeled into\ud three structures: grey matter, white matter and cerebrospinal\ud fluid. Many manipulations such as interpolation, transformation,\ud smoothing, or registration need to be performed on these images\ud before they can be used in further analysis. Current techniques\ud for such analysis tend to trade off performance between the two\ud tasks, performing well for one task but developing problems when\ud used for the other.\ud This article proposes to use a representation that is both\ud flexible and well suited for both tasks. We propose to map object\ud labels to vertices of a regular simplex, e.g. the unit interval for\ud two labels, a triangle for three labels, a tetrahedron for four\ud labels, etc. This representation, which is routinely used in fuzzy\ud classification, is ideally suited for representing and registering\ud multiple shapes. On closer examination, this representation\ud reveals several desirable properties: algebraic operations may\ud be done directly, label uncertainty is expressed as a weighted\ud mixture of labels (probabilistic interpretation), interpolation is\ud unbiased toward any label or the background, and registration\ud may be performed directly.\ud We demonstrate these properties by using label space in a gradient\ud descent based registration scheme to obtain a probabilistic\ud atlas. While straightforward, this iterative method is very slow,\ud could get stuck in local minima, and depends heavily on the initial\ud conditions. To address these issues, two fast methods are proposed\ud which serve as coarse registration schemes following which the\ud iterative descent method can be used to refine the results. Further,\ud we derive an analytical formulation for direct computation of the\ud "group mean" from the parameters of pairwise registration of all\ud the images in the sample set. We show results on richly labeled\ud 2D and 3D data sets

Functional estimation and hypothesis testing in nonparametric boundary models

Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a nonparametric maximum-likelihood approach, we construct an estimator which is UMVU over H\"older balls and achieves the (local) minimax rate of convergence. These results hold under weak assumptions on $\Phi$ which are satisfied for $\Phi(u)=|u|^p$, $p\ge 1$. As an application, we consider the problem of estimating the $L^p$-norm and derive the minimax separation rates in the corresponding nonparametric hypothesis testing problem. Structural differences to results for regular nonparametric models are discussed.Comment: 21 pages, 1 figur

Fuzzy Supernova Templates II: Parameter Estimation

Wide field surveys will soon be discovering Type Ia supernovae (SNe) at rates of several thousand per year. Spectroscopic follow-up can only scratch the surface for such enormous samples, so these extensive data sets will only be useful to the extent that they can be characterized by the survey photometry alone. In a companion paper (Rodney and Tonry, 2009) we introduced the SOFT method for analyzing SNe using direct comparison to template light curves, and demonstrated its application for photometric SN classification. In this work we extend the SOFT method to derive estimates of redshift and luminosity distance for Type Ia SNe, using light curves from the SDSS and SNLS surveys as a validation set. Redshifts determined by SOFT using light curves alone are consistent with spectroscopic redshifts, showing a root-mean-square scatter in the residuals of RMS_z=0.051. SOFT can also derive simultaneous redshift and distance estimates, yielding results that are consistent with the currently favored Lambda-CDM cosmological model. When SOFT is given spectroscopic information for SN classification and redshift priors, the RMS scatter in Hubble diagram residuals is 0.18 mags for the SDSS data and 0.28 mags for the SNLS objects. Without access to any spectroscopic information, and even without any redshift priors from host galaxy photometry, SOFT can still measure reliable redshifts and distances, with an increase in the Hubble residuals to 0.37 mags for the combined SDSS and SNLS data set. Using Monte Carlo simulations we predict that SOFT will be able to improve constraints on time-variable dark energy models by a factor of 2-3 with each new generation of large-scale SN surveys.Comment: 20 pages, 7 figures, accepted to ApJ; paper 1 is arXiv:0910.370

Analysis of a Gibbs sampler method for model based clustering of gene expression data

Over the last decade, a large variety of clustering algorithms have been developed to detect coregulatory relationships among genes from microarray gene expression data. Model based clustering approaches have emerged as statistically well grounded methods, but the properties of these algorithms when applied to large-scale data sets are not always well understood. An in-depth analysis can reveal important insights about the performance of the algorithm, the expected quality of the output clusters, and the possibilities for extracting more relevant information out of a particular data set. We have extended an existing algorithm for model based clustering of genes to simultaneously cluster genes and conditions, and used three large compendia of gene expression data for S. cerevisiae to analyze its properties. The algorithm uses a Bayesian approach and a Gibbs sampling procedure to iteratively update the cluster assignment of each gene and condition. For large-scale data sets, the posterior distribution is strongly peaked on a limited number of equiprobable clusterings. A GO annotation analysis shows that these local maxima are all biologically equally significant, and that simultaneously clustering genes and conditions performs better than only clustering genes and assuming independent conditions. A collection of distinct equivalent clusterings can be summarized as a weighted graph on the set of genes, from which we extract fuzzy, overlapping clusters using a graph spectral method. The cores of these fuzzy clusters contain tight sets of strongly coexpressed genes, while the overlaps exhibit relations between genes showing only partial coexpression.Comment: 8 pages, 7 figure

Democracy and Economic Development: a Fuzzy Classification Approach

The aim of this work is to (1) analyse whether countries differ on political indicators (democracy, rule of law, government effectiveness and corruption) and (2) study whether countries with different political profiles are associated with different levels of economic, human development and gender-related development indicators. Using a fuzzy classification approach (fuzzy k-means algorithm), we propose a typology of 124 countries based on 10 political variables. Six segments are identified; these political groups implicate the access to different levels of economic and human development. In this study evidence of a positive but not perfect relationship between democracy and economic and human development is observed, thus presenting new insights for the understanding of the heterogeneity of behaviors relatively to political indicators.Democracy, Economic Development, Fuzzy k-means

On transient dynamics, off-equilibrium behaviour and identification in blended multiple model structures

The use of multiple-model techniques has been reported in a variety of control and signal processing applications. However, several theoretical analyses have recently appeared which outline fundamental limitations of these techniques in certain domains of application. In particular, the identifiability and interpretability of local linear model parameters in transient operating regimes is shown to be limited. Some modifications to the basic paradigm are suggested which overcome a number of problems. As an alternative to parametric identification of blended multiple model structures, nonparametric Gaussian process priors are suggested as a means of providing local models, and the results compared to a multiple-model approach in a Monte Carlo simulation on some simulated vehicle dynamics data