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