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The Application of Methods of Nonlinear Time Series Analysis in Engineering

Study program:
Mining Engineering (I semester -PhD)
Name of subject: The Application of Methods of Nonlinear Time Series Analysis in Engineering
Instructors:
Prof. Nebojša Vasović
Status: Optional
ECTS: 10
Prerequisites: -
Course Objectives:
Introduction to the basic concepts of nonlinear, discrete and continuous time series analysis.
Learning Outcomes:
Techniques of nonlinear time series analysis will be applied to the observation data series from engineering practice: the dynamics of landslide movement, oscillations of soil during mining and mining-induced earthquakes, machine vibrations, etc.
Content:

Theory teaching
1. Introduction to nonlinear time series analysis. 2. Phase plane. 3. Fourier’s power spectrum. 4. Surrogate data analysis. 5. Linearity testing. 6. A delay embedding theorem in a certain time interval. 7. Computation procedure for mutual information. 8. Nearest neighbor methods. 9. Deterministicity testing. 10. Stationarity testing. 11. Calculation of maximal Lyapunov exponent - Wulf’s and Rosenstein’s methods. 12. Correlation dimension.

Practical teaching
The application of numerical analysis to a given time series.

Suggested Reading List:
  1. Kantz, H., Schreiber, T. 2004. Nonlinear time series analysis, Cambridge University Press.
  2. Small, M. 2005. Applied nonlinear time series analysis - applications in physics, physiology and finance, World Scientific series on Nonlinear Science, Series A, Vol.52.
  3. Perc, M. 2006. Introducing nonlinear time series analysis in undergraduate courses, Fizika A, Zagreb.
  4. Kugiumtzis, D., Tsimpiris, A. 2010. Measure of analysis of time series (MATS): A MATLAB toolkit for computation of multiple measures on time series data bases. Journal of statistical software, Vol.33, Issue 5.
  5. Abarbanel, H. 1996. Analysis of observed chaotic data, Springer.
Conduct of the Course:
Presentations, consultations
Fund hours:
Lectures Exercises Other forms of teaching Study research
4 0 0 0
Assessment:
Final Exam ECTS
Oral Exam60

Classwork Assessment ECTS
Seminars40
Additional Assessment Criteria: -


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