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.
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Denis, A., Crémoux, F. Using the Entropy of Curves to Segment a Time or Spatial Series. Mathematical Geology 34, 899–914 (2002). https://doi.org/10.1023/A:1021302922108
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DOI: https://doi.org/10.1023/A:1021302922108