The problem of change detection in signals using linear regression models is addressed. It is assumed that the signal can be accurately described by a linear regression model with piece-wise constant parameters. Due to the limitations of some classical approaches, based upon the innovation of one autoregressive (AR) model, the most algorithms for change detection presented make use of two AR models: the first one is a reference model, and the second one is a current model updated via a sliding block. Changes are detected when a suitable distance between these two models is high. Three distance measures are considered in the paper: cepstral distance, log-likelihood ratio (justified by GLR) and a distance involving the cross-entropy of the two conditional probabilities laws (divergence test). Finally, on original change detection algorithm using three models and the evolution of Akaike Information Criterion is presented. All the presented algorithms constituted the object of evaluation by multiple simulation and have been used to change detection in seismic signals.
The proposed problem formulation assumes off-line or batch-wise data processing, although the solution is sequential in data and an on-line data processing can be used. The segmentation model is the simplest possible extension of linear regression models to signals with abruptly changing properties, or piece-wise linearizations of non-linear models.
The paper is organized as follows. Section 2 contains the problem formulation and a review of the change detection algorithms. A change detection algorithm using one AR model and a cumulative sum detector is found in Section 3. The change detection schemes using two AR models and different distance measures between spectral densities: cepstral distance, log-likelihood ratio and a distance involving the cross-entropy of the two conditional probabilities laws are presented in Section 4. A change detection algorithm using three AR models and the evaluation of Akaike Information Criterion is proposed in Section 5. Some implementation aspects of the change detection schemes previously discussed make the object of Section 6. Finally, the discussed change detection strategies are evaluated in an application for seismic signal segmentation.
Application. The discussed methods have been used in segmentation of the transversal (N-S) and longitudinal (E-W) components of a strong seismic motion during the August 30-31, 1996, Romanian earthquake. The results are presented in the extended version of the paper. samplig period of the signals was 0.02 seconds.