Using the Entropy of Curves to Segment a Time or Spatial Series

Abstract

The concept of the thermodynamics of curves is used to analyze change in the variability of time or spatial series. More specifically, the entropy of a curve makes it possible to divide a nonstationary random field, because of a change in variance, into subdomains where data are said to be stationary. It is demonstrated that for time and spatial series the entropy of a curve is the slope of the cumulative sum of absolute differences. Numerical simulations show the efficiency of this tool. It can be shown that the presence of a linear or quadratic trend is without effect on the localization of the stationary subdomains. A practical case is studied with data collected from a tunnel boring machine where several parameters are recorded. This analysis can bring more information on the mechanical behavior of the different geological formations and explain or justify unplanned delays.