Methods and Models for Information Data Analysis

  • Vitalii P. BabakEmail author
  • Serhii V. Babak
  • Mykhailo V. Myslovych
  • Artur O. Zaporozhets
  • Valeriy M. Zvaritch
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 281)


The article presents the definition of linear random processes of many of their stochastic characteristics such as moments, correlation functions, characteristic functions. Linear AR and ARMA processes are also considered. Kernels and characteristic functions of the random processes are represented for the processes. Not only stationary linear random processes are considered. Linear random processes with periodic structures are also discussed. The properties of kernels and the characteristic functions of such processes are shown. Cases of both non-stationary random processes with continuous time and random processes with discrete time are considered. Random processes with discrete time and periodic structures are linear AR and ARMA processes with periodic kernels and periodic generating processes. The properties of the kernels of linear AR and ARMA which are important for the practical use of such models are also presented. Method of forecasting the time of failure using statistical spline-function is considered. The estimation of random signals stationarity with practical examples of the estimation stationarity of vibration signals of rolling bearings is also discussed. A procedure of decision-making rule development for the vibration signals is represented.


Linear random process Linear AR and ARMA processes Kernel of linear random process Characteristic function Linear random process with periodic structures Statistical—spline function Forecasting Decision-making rule Vibration of rolling bearing 


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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vitalii P. Babak
    • 1
    Email author
  • Serhii V. Babak
    • 2
  • Mykhailo V. Myslovych
    • 3
  • Artur O. Zaporozhets
    • 4
  • Valeriy M. Zvaritch
    • 5
  1. 1.Institute of Engineering Thermophysics of NAS of UkraineKyivUkraine
  2. 2.Committee on Education, Science and Innovation of Verkhovna Rada of UkraineKyivUkraine
  3. 3.Department of Theoretical Electrical EngineeringInstitute of Electrodynamics of NAS of UkraineKyivUkraine
  4. 4.Department of Monitoring and Optimization of Thermophysical ProcessesInstitute of Engineering Thermophysics of NAS of UkraineKyivUkraine
  5. 5.Department of Theoretical Electrical EngineeringInstitute of Electrodynamics of NAS of UkraineKyivUkraine

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