Détection et caractérisation de signaux transitoires : application à la surveillance de courbes de charge

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Detection and characterization of transient signals : methodology and application for surveillance and diagnosis

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Modèle polynomial par morceaux muni de transitions régulières - Application à la modélisation de signaux transitoires électriques

National audienceA smooth transition model is introduced and studied. Such a model extend piecewise regression ones by introducing smooth transition functions achieving transition from a segment to another in the neighborhood of each rupture. The joint estimation of the parameters and of the number of segment is an ill-posed problem. A regularization is performed through a hierarchical Bayesian framework. As standard Bayesian estimates can not be computed analytically, a reversible-jump MCMC algorithm is derived to sample the parameters according to their posterior distribution. This method is applied to the modeling of real-world electrical transient

A reversible jump MCMC algorithm for Bayesian curve fitting by using smooth transition regression models

International audienceThis paper proposes a Bayesian algorithm to estimate the parameters of a smooth transition regression model. Within this modelling, time series are divided into segments and a linear regression analysis is performed on each segment. Unlike piecewise regression model, smooth transition functions are introduced to model smooth transitions between the sub-models. Appropriate prior distributions are associated with each parameter to penalize a data-driven criterion, leading to a fully Bayesian model. Then, a reversible jump Markov Chain Monte Carlo algorithm is derived to sample the parameter posterior distributions. It allows one to compute standard Bayesian estimators, providing a sparse representation of the data. Results are obtained for real-world electrical transients with a view to non-intrusive load monitoring applications

Hierarchical Bayesian learning for electrical transient classification

International audienceThis paper addresses the problem of the supervised signal classification, by using a hierarchical Bayesian method. Each signal is characterized by a set of parameters, the features, which are estimated from a set of learning signals. Moreover, these parameters are distributed according to a class-specific posterior distribution which allows one to capture the variability of the features within the same class. Within the hierarchical Bayesian framework, the feature extraction step and the learning step can be performed jointly. Unfortunately, the estimation of the class-specific distribution parameters requires the computation of intractable multi-dimensional integrals. Then a Markov-chain Monte Carlo (MCMC) algorithm is used to sample the posterior distributions of the features over all the training signals of each class. An application to electrical transient classification for non-intrusive load monitoring is introduced. Simulations over real-world electrical transients signals are driven and show the capacity of the proposed methodology to discriminate two classes of transient

A Smooth Transition Model for Multiple-Regime Time Series

Curve fitting , MCMC methods , hierarchical Bayesian models , nonintrusive appliance load monitoring , smooth transition regression modelsInternational audienceThis study deals with the problem of fitting a time series modeled by a smooth transition regression function. This model extends the standard linear piecewise model. Within the piecewise model, the regression function parameters change abruptly at the changepoints. In the smooth transition model, parametric transition functions are introduced that allow for gradual changes of the regression function around the changepoints. This model can very accurately reproduce both nonregular and smooth random processes. Moreover it allows the extraction of information about the changes in the regression function through the transition function parameters. The estimation of the model is performed through a fully Bayesian framework. Prior distributions are set for each parameter and the full joint posterior distribution is expressed. The computation of standard Bayesian estimates involves intractable multi-dimensional integrals. Therefore, a reversible-jump Markov chain Monte-Carlo algorithm is derived to sample the joint posterior distributions. A comparative simulation study shows that the smooth transition approach achieves competitive performances and provides more sparse representations of standard test functions. Finally, the smooth transition framework is applied to estimate real world electrical transients, which allows the extraction of the relevant features for signal classification

Bayesian curve fitting for transient signals by using smooth transition regression models

International audienceThis communication addresses the problem of fitting time series with smooth transition regression models. These models are of interest to characterize transient signals in the context of system monitoring and diagnosis. Within this modelling, time series are segmented by sequences of piecewise constant polynomial regression models. Moreover, smooth transitions between each segment are obtained by introducing some smooth, monotically increasing parametric transition functions. It allows one to give a synthetic representation of signals composed by smooth transitions between different regimes. However, the estimation of the parameters of these models appears to be an ill-posed problem. Direct optimization algorithms are not robust enough with regard to the initial parameters guess. Therefore, to achieve parameter estimation, we introduce a Bayesian framework. Appropriate priors for the unknown model parameters are introduced to penalize a data-driven criterion built from the likelihood of the observations. As the resulting posterior probability distributions does not admit closed-form analytical expressions, Markov Chain Monte Carlo (MCMC) sampling methods are derived to obtain the standard Bayesian estimators of the model parameters. Results are shown for synthetic and real appliance load monitoring data

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