Florent Chatelain

Nonparametric Bayesian Extraction of Object Configurations in Massive Data

This study presents an unsupervised method for detection of configurations of objects based on a point process in a nonparametric Bayesian framework. This is of interest as the model presented here has a number of parameters that increases with the number of objects detected. The marked point process yields a natural sparse representation of the object configuration, even in massive data fields. However, Bayesian methods can lead to the evaluation of some densities that raise computational issues, due to the huge number of detected objects. We have developed an iterative update of these densities when changes in the object configurations are made, which allows the computational cost to be reduced. The performance of the proposed algorithm is illustrated on synthetic data and very challenging quasi-real hyperspectral data for young galaxy detection.

Bayesian Model for Multiple Change-Points Detection in Multivariate Time Series

This paper addresses the issue of detecting change-points in time series. The proposed model, called the Bernoulli Detector, is presented first in a univariate context. This approach differs from existing counterparts by making only assumptions on the nature of the change-points, and does not depend on hypothesis on the distribution of the data, contrary to the parametric methods. It relies on the combination of a local robust statistical test, based on the computation of ranks and acting on individual time segments, with a global Bayesian framework able to optimize the change-points configurations from multiple local statistics, provided as

Multi-branch hidden Markov models for remaining useful life estimation of systems under multiple deterioration modes

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Multi-branch Hidden semi-Markov modeling for RUL prognosis

-values. The control of the detection of a single change-point is proved even for small samples. The interest of such a generalizable nonparametric approach is shown on simulated data by the good performances attained for Gaussian noise as well as in presence of outliers, without adapting the model. The model is extended to the multivariate case by introducing the probabilities that the change-points affect simultaneously several time series. The method presents then the advantage to detect both unique and shared change-points for each signal. We finally illustrate our algorithm with real datasets from energy monitoring and genomic. Segmentations are compared to state-of-the-art approaches like the group lasso and the BARD algorithm.

Error control for the detection of rare and weak signatures in massive data

Remaining Useful Life (RUL) estimation plays an important role in implementing a condition-based maintenance (CBM) program, since it could provide sufficient time for maintenance crew to act before an actual system failure. This prognostic task becomes harder when several deterioration mechanisms co-exist within the same system due to the variability and dynamics of its operating environment, since the RUL obviously depends on the mode that the system is following. In this paper, we propose a multi-branch modeling framework to deal with such problems. The proposed model consists of several branches in which each one represents a deterioration mode and is considered as a hidden Markov model. The system’s conditions are modeled by several discrete meaningful states, such as “good”, “minor defect”, “maintenance required” and “failure”, which would be easy to interpret for maintenance personnel. Furthermore, these states are considered to be “hidden” and can only be revealed through observations. These observations are the condition monitoring information in the CBM context. The performance of the proposed model is evaluated through numerical studies. The results show that the multi-branch model can outperform the standard one-branch HMM model in RUL estimation, especially when the “distance” between the deterioration modes is considerable.

Isotropic Multiple Scattering Processes on Hyperspheres

Deterioration modeling and remaining useful life (RUL) estimation of equipment are key enabling tasks for the implementation of a predictive maintenance (PM) policy, which plays nowadays an important role for maintaining engineering systems. Hidden Markov Models (HMM) have been used as an efficient tool for modeling the deterioration mechanisms as well as for estimating the RUL of monitored equipment. However, due to some assumptions not always justified in practice, the applications of HMM on real-life problems are still very limited. To tackle this issue and to relax some of these unrealistic assumptions, this paper proposes a multi-branch Hidden semi-Markov modeling (MB-HSMM) framework. The proposed deterioration model comprises several different branches, each one being itself an HSMM. The proposed model offers thus the capacity to 1) explicitly model the sojourn time in the different states and 2) take into account multiple co-existing and competing deterioration modes, even within a single component. A diagnosis and RUL prognosis methodology based on the MB-HSMM model is also proposed. Thanks to its multiple branches property, the MB-HSMM model makes it possible not only to assess the current health status of the component but also to detect the actual deterioration mechanism. Based on the diagnostic results, the component RUL can then be calculated. The performance of the proposed model and prognosis method is evaluated through a numerical study. A Fatigue Crack Growth (FCG) model based on the Paris-Erdogan law is used to simulate deterioration data of a bearing under different operation conditions. The results show that the proposed MB-HSMM gives a very promising performance in deterioration mo de detection as well as in the RUL estimation, especially in the case where these deterioration modes exhibit very different dynamics.

An adaptive robust regression method: Application to galaxy spectrum baseline estimation

In this paper, we address the general issue of detecting rare and weak signatures in very noisy data. Multiple hypothe ses testing approaches can be used to extract a list of com ponents of the data that are likely to be contaminated by a source while controlling a global error criterion. However most of efficients methods available in the literature are de rived for independent tests. Based on the work of Benjamini and Yekutieli [1], we show that under some classical positivity assumptions, the Benjamini-Hochberg procedure for False Discovery Rate (FDR) control can be directly applied to the result produced by a very common tool in signal and image processing: the matched filter. This shows that despite the de pendency structure between the components of the matched filter output, the Benjamini-Hochberg procedure still guaran tee the FDR control. This is illustrated on both synthetic and real data.

SPECT/CT registration with the DCC and MC simulations for SPECT imaging

This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres Sp-1. It allows one to derive the Fourier expansions on Sp-1 of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions on Sp-1 is also introduced. Such processes are then studied in the case where the scattering distribution is von Mises-Fisher (vMF). Asymptotic distributions for the multiconvolution of vMFs on Sp-1 are obtained. Both Fourier expansion and asymptotic approximation allow us to compute estimation bounds for the parameters of compound cox processes on Sp-1.

Global error control procedure for spatially structured targets

In this paper, a new robust regression method based on the Least Trimmed Squares (LTS) is proposed. The novelty of this approach consists in a simple adaptive estimation of the number of outliers. This method can be applied to baseline estimation, for example to improve the detection of gas spectral signature in astronomical hyperspectral data such as those produced by the new Multi Unit Spectroscopic Explorer (MUSE) instrument. To do so a method following the general idea of the LOWESS algorithm, a classical robust smoothing method, is developed. It consists in a windowed local linear regression, the local regression being done here by the new adaptive LTS approach. The developed method is compared with state-of-the art baseline estimated algorithms on simulated data closed to the real data produced by the MUSE instrument.

Density Estimation for Compound Cox Processes on Hyperspheres

We want to perform the attenuation correction in the case of 3D attenuated ray transform with a parallel geometry. We suppose that the attenuation function is available but not registered with the data. We use the sum on each slice of the 2D data consistency conditions of the attenuated Radon transform to register the attenuation function with the data. We then correct for the attenuation using the Novikov formula. We show numerical experiments indicating the feasibility of the approach and propose a scheme including the diffusion correction for the registration of CT to SPECT for SPECT imaging improvement.