On Change Detection in the Complexity of Time Series

This work is an exploratory and preliminary study on change detection in the structure of time series based on structural entropy processing, with direct application to fault detection in production processes. Starting with some theoretical elements related to entropy, various types of estimators are presented, and some are discussed, as the approximate entropy (ApEn), the sample entropy (SampEn), and the multiscale entropies (MSE). The case studies contain synthetized signals as white Gaussian noise, 1/f noise, and random signals with a probabilistic structure, ended with real vibration signals generated by faults in bearings. Finally, a change detection criterion is promoted based on the average of multiscale entropy and cumulative sum technique. The study is useful for a better understanding of the entropy-based methods for change detection in the structure of the time-series and it prepares the next level of the research, i.e. methods based on Renyi entropy with recursive estimators – when possible - and their extension to chaotic and stochastic systems, especially from the structure change detection point of view.